SECTION: General Questions about SCIP
    QUESTION: What is SCIP?
    LABEL:whatisscip
    ANSWER:
    <p>
      SCIP is a solver for Mixed Integer Linear and Nonlinear Problems that allows for an easy integration of arbitrary constraints.
      It can be used as a framework for <b>branch-cut-and-price</b>
      and contains all necessary plugins to serve as a <b>standalone solver</b> for MIP and MINLP.
    </p>
    <ul>
      <li>You can use the <a href="https://scipopt.org/#download">precompiled binaries</a>
          to solve MIPs and MINLPs. Learn more about the <a href="PATHTODOC/group__FILEREADERS.LINKEXT">file formats supported by SCIP</a>,
          and get <a href="PATHTODOC/WHATPROBLEMS.LINKEXT">an overview</a>
          of the supported problem classes and additional recommendations for solving them.
      </li>
      <li>You can use SCIP as a subroutine for solving MINLPs and more general constraint integer programs from your own source code.</li>
      <li>You can use SCIP as a framework in which you implement your own plugins.</li>
      <li>You can use SCIP in any combination of the three purposes above.</li>
    </ul>
    <p>
      This FAQ contains separate sections covering each of these usages of SCIP. It further considers specific questions for some features.
    </p>

    QUESTION: When should I use SCIP?
    LABEL:whenusescip
    ANSWER:
    <p>
      If you are either looking for a fast non-commercial MIP/MINLP-solver or for a
      branch-cut-and-price-framework into which you can directly implement your own methods.
      SCIP allows full control of the solving process through parametrization and user callbacks.
    </p>

    QUESTION: I heard something about licenses. Do I have to pay for using SCIP?
    LABEL:licensefaq
    ANSWER:
    <p>
      Since November 4, 2022, and SCIP version 8.0.3, SCIP is distributed under a permissive open source license, see the <a href="https://scipopt.org/index.php#license">SCIP homepage</a>.
    </p>

    QUESTION: How do I get started?
    LABEL:howtogetstarted
    ANSWER:
    <p>
      An easy way is to use the SCIP-binaries and call SCIP from a shell, see <a href="PATHTODOC/SHELL.LINKEXT">here</a> for a tutorial.
      For that, you just have to use one of the installers from the
      <a href="https://scipopt.org/#download">download section</a>, or the zipped source code and compile it
      with your favorite settings.
      Note that the coding examples are only contained in the source code bundle, but not in the precompiled packages.
      The compilation from source is described in detail in the <code><a href="PATHTODOC/INSTALL.LINKEXT">INSTALL</a></code> file in the SCIP main directory.
    </p>
    <p>
      Another way is to use SCIP as a solver integrated into your own program source code.
      See the directories &quot;examples/MIPsolver/&quot; and &quot;examples/Queens/&quot;
      for simple examples and <a href="#howtocreateproblem">this point</a>.
    </p>
    <p>
      A third way is to implement your own plugins into SCIP.
      This is explained in the HowTos for all plugin types, which you can find in the
      <a href="PATHTODOC/HOWTOADD.LINKEXT">"How to add" section</a>.
      See also <a href="PATHTODOC/START.LINKEXT">How to start a new project</a>.
    </p>

    QUESTION: Do I need any extra software?
    LABEL:extrasoftware
    ANSWER:
    <p>Unless you want to use SCIP as a pure CP-Solver (see <a href="#scipascpsolver">here</a>),
      you need an underlying LP-Solver installed and linked to the libraries
      (see the <code><a href="PATHTODOC/INSTALL.LINKEXT">INSTALL</a></code> file in the SCIP root directory).
      LP-solvers currently supported by SCIP are:
    </p>
    <ul>
      <li><a href="https://soplex.zib.de/">SoPlex</a></li>
      <li><a href="http://www-01.ibm.com/software/integration/optimization/cplex-optimizer/">IBM ILOG CPLEX</a></li>
      <li><a href="http://www.fico.com/en/Products/DMTools/Pages/FICO-Xpress-Optimization-Suite.aspx">FICO XPress</a></li>
      <li><a href="http://www.gurobi.com/">Gurobi</a> (version at least 7.0.2 required)</li>
      <li><a href="https://projects.coin-or.org/Clp/">CLP</a> (interface currently sometimes produces wrong results)</li>
      <li><a href="https://github.com/google/or-tools">Glop, Google OR tools</a> (experimental, LPI contained in OR tools)</li>
      <li><a href="http://www.mosek.com/">Mosek</a></li>
      <li><a href="http://www2.isye.gatech.edu/~wcook/qsopt/">QSopt</a> (experimental)</li>
    </ul>
    <p>
      If you want to use SCIP for mixed integer nonlinear programming, you might want to use an underlying NLP solver (e.g.,
      <a href="https://projects.coin-or.org/Ipopt">Ipopt</a>). SCIP already comes with the CppAD expression interpreter (e.g., <a href="http://www.coin-or.org/CppAD/">CppAD</a>) as part of the source code.
    </p>
    <p>
      Besides that, you might need a modeling language like <a href="https://zimpl.zib.de/">ZIMPL</a> to generate *.mps
      or *.lp files. ZIMPL files (.zpl extension) can also be read directly into SCIP.
      Downloading the SCIP Optimization Suite includes SCIP, SoPlex and ZIMPL, as well as GCG and UG. Find installers for different platforms
      and the source code bundle of all versions <a href="https://scipopt.org/#download">here</a>.
    </p>

    QUESTION: How can I build/compile SCIP?
    LABEL:howtousemakefiles
    ANSWER:
    <p>
        SCIP can be compiled using either <a href="PATHTODOC/MAKE.LINKEXT">Makefiles</a>
        or <a href="PATHTODOC/CMAKE.LINKEXT">CMake</a>. It's strongly recommended to use the new CMake build system both for new
        and long-time users of SCIP. Consult the CMake documentation for further information about the changes introduced
        in the new system (like Linux-conform naming conventions for libraries). We still support the traditional Makefile
        system for backwards compatibility but it might be discontinued at some point.
    </p>

    QUESTION: What are the main differences between the CMake and the Makefile system?
    LABEL: differencescmakevsmake
    ANSWER:
    <p>
        SCIP and the SCIP Optimization Suite provide two ways of compilation, one by using the Cross-Platform configuration system CMake, and the
        alternative of using the manually maintained Makefile-system.
        Find instructions how to use each of them in the <a href="PATHTODOC/INSTALL.LINKEXT">INSTALL</a> file in the SCIP root directory.
        The most notable difference is that the CMake system creates a single (complete) library "libscip" to link against, whereas the Makefile system only generates
        a partial library "libscip" and requires linking of further libraries for a successful compilation of a SCIP project.
    </p>
    <p>
        The following list highlights some of the advantages of the CMake system, which we recommend for new users.
    </p>
    <ul>
        <li>Configuration step detects the required system libraries such as readline. Missing libraries turn off the corresponding options</li>
        <li>Use of our <a href="PATHTODOC/INTERFACES.LINKEXT">Python and Java Interfaces</a> depends on a library "libscip" built with CMake</li>
        <li>Generation of Visual Studio project files under Windows</li>
        <li>Support of build systems other than <code>make</code>, such as <code>ninja</code></li>
    </ul>
    <p>
        The following list highlights some of the advantages of the Makefile system.
    </p>
    <ul>
        <li>Backwards compatibility when switching to older SCIP versions (CMake support introduced with SCIP version 4.0.1) </li>
        <li>Situations (old operating systems) where CMake is unavailable</li>
        <li>Compilation of the UG framework is not (yet) supported by CMake, only possible using make</li>
    </ul>

    QUESTION: I have installation problems. What can I do?
    LABEL:installationproblems
    ANSWER:
    <p>
      Read the <code><a href="PATHTODOC/INSTALL.LINKEXT">INSTALL</a></code> file in the SCIP root directory. It contains hints of how to get around problems. You can also try
      the precompiled binaries by choosing one of the available installers from the <a href="https://scipopt.org#download">SCIP page</a> for your operating system.<br>
    </p>
    <p>
      If you encounter compilation problems dealing with the <code>explicit</code> keyword you should try a newer compiler.
    </p>

    QUESTION: I changed to a new version of SCIP and now compiling breaks with some error messages which I don't understand.
      Do you have a general hint on that?
    LABEL:versionchange
    ANSWER:
    <p>
        Maybe the parameters of a function in SCIP changed. Please have a look at the <a href="PATHTODOC/CHG.LINKEXT">Changelog</a>
    </p>

    QUESTION: How can I debug in SCIP?
    LABEL:howtodebug
    ANSWER:
    <p>
      Compile SCIP in debug mode (<code>"cmake -DCMAKE_BUILD_TYPE=Debug"</code> in CMake or <code>make OPT=dbg</code> using the Makefile system). Put the binary into a debugger, e.g., <a href="http://www.gnu.org/s/gdb/">gdb</a>
      and let it run again. If you get an impression which component is causing the trouble, set <code>#define SCIP_DEBUG</code> as the first
      line of the corresponding *.c file, recompile and let it run again. This will print debug messages from that piece of code.
      Find a short debugging tutorial <a href="PATHTODOC/DEBUG.LINKEXT">here</a>.
    </p>

    QUESTION: SCIP prints error messages, aborts, produces segmentation faults, or just behaves strangely. What should I do?
    LABEL:errorhandling
    ANSWER:
    <p>
       <a href="#howtodebug">See above.</a> Often, the asserts that show up in debug mode already help to clarify misunderstandings
       and suggest fixes, if you were calling SCIP functions in an unexpected manner. For sending bug reports,
       please see our <a href="scipopt.org/#contact">Contact information</a> from which you can directly access an online form for reporting bugs.
    </p>

    QUESTION: I would like to check whether some functionality is implemented in SCIP.
      How does the naming of the methods work? Where do I find the most common methods?
    LABEL:searchdocumentation
    ANSWER:
    <p>
      For an explanation of the naming see the
      <a href="PATHTODOC/CODE.LINKEXT">coding style guidelines</a>. <br>
      The <a href="PATHTODOC/modules.LINKEXT">Public C-API</a> of SCIP is separated
      into a Core API provided by the header scip.h and a default plugin API provided
      by scipdefplugins.h. The large API is structured into topics for a better overview.
    </p>

    QUESTION: Can I use SCIP as a pure CP/SAT Solver?
    LABEL:scipascpsolver
    ANSWER:
    <p>
        Yes. SCIP can be used as a pure CP/SAT Solver by typing
        <code>set emphasis cpsolver</code> in the shell or by using the function <code>SCIPsetEmphasis()</code>.
        Furthermore, you can compile SCIP without any LP-Solver by <code>cmake -DLPS=none</code> (<code>make LPS=none</code> in the Makefile system).
        See <a href="#howtochangebehaviour">here</a> for more on changing the behavior of SCIP.
    </p>

    QUESTION: Can I use SCIP as a pure LP-Solver?
    LABEL:scipaslpsolver
    ANSWER:
    <p>
        Since LPs are only special types of MIPs and CIPs, the principal answer is yes. If you feed a pure LP to SCIP, it
        will first apply presolving and then hand this presolved problem to the underlying LP solver. If the LP is solved to
        optimality, you can query the optimal solution values as always. You can also access the values of an optimal dual
        solution by using <code>display dualsolution</code>.
    </p>
    <p>
        However, there are certain limitations to this: Reduced costs are not accessible. If the LP
        turns out to be infeasible, you cannot currently obtain a Farkas proof. And recall that this approach is only
        meaningful if the problem is an LP (no integer variables, only linear constraints).
    </p>
    <p>
        Hence, if you need more, "LP specific", information than the primal solution, you are better off using an LP-Solver
        directly. If you are using the SCIP Optimization Suite, you could, e.g., use the included LP solver
        <a href=https://soplex.zib.de>SoPlex</a>.  If you want to solve an LP not from the command line, but within your
        C/C++ program, you could also use SCIP's LP-Interface, see also <a href="#howtosolvelps">here</a>.
    </p>

    QUESTION: Which kind of MINLPs are supported by SCIP?
    LABEL:minlptypes
    ANSWER:
    <p>
        SCIP supports nonlinear constraints of the form lhs &le; f(x) &le; rhs, where the function f(x) is an algebraic
        expression that can be represented as expression tree. Such an expression tree has constants and variables as terminal
        nodes and operands as non-terminal nodes.
        Expression operands supported by SCIP include addition, subtraction, multiplication, division, exponentiation and
        logarithm. Trigonometric functions are not yet supported by SCIP.
    </p>
    <p>
        Nonlinear objective functions are not supported by SCIP and must be modeled as constraint function.
        <em>Note</em>, that the support for non-quadratic nonlinear constraints is not yet as
        robust as the rest of SCIP.
        Missing bounds on nonlinear variables and tiny or huge coefficients can easily lead to numerical problems,
        which can be avoided by careful modeling.
    </p>

    QUESTION: What is this business with .a and .so libraries in the directory <code>lib/</code>?
    LABEL:staticvsshared
    ANSWER:
    <p>
        When SCIP builds the binary, it needs to link with the corresponding libraries, i.e., its own libraries and
        those of an LP-solver. There are usually two ways to distribute a library (on UNIX systems). In the first
        (with suffix ".a"), the library is linked <em>statically</em> to SCIP; this means that all information is packed
        into the binary. In the second way (with suffix ".so"), the library is a <em>shared</em> library. In this case,
        the code of the library is not inserted into the binary itself, but is loaded at runtime. This has the advantage
        that the binaries are smaller, but it comes at the cost that you have to make sure that the library is found at
        runtime. (SCIP adds <code>rpath</code> information containing the path to the shared libraries to the binary;
        this usually allows to find these libraries at runtime. If this does not work, for most systems it suffices to
        put the path of the library into the <code>LD_LIBRARY_PATH</code> environment variable).<br/><br/>
        There are compiler-dependent preferences which version should be included if both a static and a shared version
        of the same library are available. In order to avoid confusion, SCIP separates shared from static libraries into
        the directories "lib/static" and "lib/shared" when using the Makefile system. Note that some LP-solvers are only
        shipped with a shared version.
    </p>

    QUESTION: Can I compile SCIP as a shared library?
    LABEL:sharedlib
    ANSWER:
    <p>
        You can use the <code>SHARED=true</code> option
        when making SCIP. This will generate the libraries of SCIP in shared format. The binary then
        also uses this form. Note that the path to the <code>lib/shared</code> directory of SCIP is used to
        locate the libraries. If you want to move the libraries, you might need to set the
        <code>LD_LIBRARY_PATH</code> environment variable to include the new path.

        <!--
            If you have a different system or compiler (which supports shared libraries) you might try to
            copy the file <code>make/make.linux.x86.gnu.opt-shared</code> and modify it according to your
            needs (see also <code><a href="PATHTODOC/MAKE.LINKEXT">Makefiles</a></code>).
        -->
       If you are using your own build system: The "magic" changes are the <code>-fPIC</code>
       compiler/linker option and the <code>-Wl,-rpath</code> option.
    </p>

    QUESTION: The methods SCIPgetVarSol() and SCIPvarGetSol() seem to have the same
      functionality. Which one should I use?
    LABEL:scipgetvarsol
    ANSWER:
    <p>
        In fact, there is a slight difference: <code>SCIPvarGetSol()</code> is also able to return pseudo solution values.
        If you do not have an idea what pseudo solutions are, <code>SCIPgetVarSol()</code> should be just fine. This
        should be the only case of 'duplicate methods'. If you find, however, another one, please contact us.
    </p>

    QUESTION: Is there a way to visualize the branch and bound tree?
    LABEL:visualizebranchandbound
    ANSWER:
    <p>
        Here is a list of external tools that can be used to create interactive and noninteractive visualizations in
        various formats.
    </p>
    <ul>
        <li>
            <a href="https://hydraw.zib.de/">HyDraw</a>
            can display a live visualization of the tree using JavaView.
        </li>
        <li>
            <a href="http://www.informatik.uni-koeln.de/ls_juenger/vbctool">vbctool</a>
             comes with a viewer that has an option to uncover the nodes one-by-one (each time you
            hit the space key). Additional node information such as its lower bound, depth, and number are accessed through a
            context menu.
        </li>
        <li>
            <a href="https://www.uni-due.de/~si203go/#vbc">Vbc2dot</a> is a script that generates a visualization of SCIP's branch-and-bound tree
            in ps and pdf format. It is written in Ruby and requires dot (graphviz).
        </li>
        <li>
            <a href="https://www.uni-due.de/~si203go/vbctool/zimplTblConverter.rb">zimplTblConverter</a> is a small Ruby-script that converts a scip solution file to a file where all names are replaced according to a zimpl tbl-file output.
        </li>
        <li>
            <a href="https://github.com/coin-or/GrUMPy">GrUMPy</a>
            is a Python tool that allows to create noninteractive visualizations of the tree in various formats.
        </li>
    </ul>
    <p>
        For using one of these tools, SCIP lets you define file names <code>set visual vbcfilename somefilename.vbc</code>
        and <code>set visual bakfilename somefilename.dat</code>. GrUMPy uses BAK files while the other tools parse
        vbc output.
    </p>
    <p>
        For those who want to use the step-by-step functionality of vbctool,
        it is necessary to use a time-step counter for the visualization instead of the real time. The corresponding parameter
        is changed via <code>set visual realtime FALSE</code>.
     </p>
        For users of the callable library, the corresponding parameters are called "visual/bakfilename", "visual/vbcfilename", and
        "visual/realtime".
    </p>


    QUESTION: SCIP has found decent primal and dual bounds but still reports the gap as "Infinity". Why?
    LABEL:gapdefinition
    ANSWER:
    <p>
        By default, the SCIP output contains the display column "gap", which is computed as follows:
        If primal and dual bound have opposite signs, the gap is "Infinity".
        If primal and dual bound have the same sign, the gap is
        <code>|primalbound - dualbound|/min(|primalbound|,|dualbound|)| </code> (see SCIPgetGap()).
        This definition has the advantage, that the gap decreases monotonously during the solving process.
    </p>
    <p>
        An alternative definition of the gap is
        <code>(dual bound - primal bound) / abs(primal bound)</code>.
        As in the previous gap definition, if primal and dual bound have opposite signs, the gap is "Infinity".
        In SCIP, this definition can be included in the output by enabling the display column "primalgap":
        <code>display/primalgap/active = 2</code>.
    </p>

    QUESTION: SCIP crashes during symmetry detection with bliss. What can I do?
    LABEL:scipblisscrash
    ANSWER:
    <p>
        The bliss library can be compiled with or without GMP support. If bliss is compiled with GMP the macro defininiton
        <code>BLISS_USE_GMP</code> must be added, otherwise the headers do not match the library which produces the crash.
        If bliss is compiled as shared library, the CMake system should be able to detect this automatically.
        In case you do not need symmetry handling, the easiest way to resolve the problem is to just disable
        symmetry handling during compilation (see <a href="PATHTODOC/MAKE.LINKEXT">Makefiles</a> or <a href="PATHTODOC/CMAKE.LINKEXT">CMake</a>)
        or with the SCIP parameter <code>misc/usesymmetry = 0</code>.
        Otherwise it can be resolved by either adding the macro definition with the compile flag <code>-DBLISS_USE_GMP</code>
        or by compiling bliss differently, i.e. without GMP support.
    </p>

    QUESTION: How can I run SCIP in parallel?
    LABEL:howtorunscipinparallel
    ANSWER:
    <p>
       SCIP itself is mostly a sequential solver and does not feature internal parallelism, e.g., to process branch-and-bound nodes in parallel.
       However, there are two ways to make use of parallel hardware:
        <ul>
            <li>First, using the command <code>concurrentopt</code> in the
            interactive shell or the method <code>SCIPsolveConcurrent()</code>
            one can spawn multiple solves in parallel, which exchange bound
            changes and primal solutions and will terminate as soon as the
            fastest solver terminates. For this to work, SCIP must be built with
            the TPI option.</li>
            <li>Second, one can use the external UG framework for shared-memory
            and distributed-memory parallelization of the tree search.  See the
            <a href="https://ug.zib.de"></a> UG web page</a> for further
            details.</li>
        </ul>
    </p>

SECTION: Using SCIP as a standalone solver

    QUESTION: The output is too wide for my terminal window. What can I do?
    LABEL:outputtoolarge
    ANSWER:
    <p>
        In the interactive shell you can set the width of the output with the following command
        <code>set display width</code> followed by an appropriate number.
        See also the <a href="#displaycolumns">next question</a>.
    </p>

    QUESTION: What do the cryptic abbreviations for the columns mean which are displayed
      during the solving process of SCIP?
    LABEL:displaycolumns
    ANSWER:
    <p>
        Type <code>display display</code> in the interactive shell to get an explanation of them.<br>
        By the way: If a letter appears in front of a display row, it indicates,
        which heuristic found the new primal bound, a star representing an integral LP-relaxation.<br>
        Typing <code>display statistics</code> after finishing or interrupting the solving process gives
        you plenty of extra information about the solving process.<br>
        (Typing <code>display heuristics</code> gives you a list of the heuristics including their letters.)
    </p>

    QUESTION: Why does SCIP claim that it could not find the user parameters "scip.set"? Where can I get such a file?
    LABEL:whereareuserparameters
    ANSWER:
    <p>
    SCIP comes with default settings that are automatically active when you start the interactive shell.
    However, you have the possibility to save customized settings via the <code>set save</code> and <code>set diffsave</code> commands.
    Both commands will prompt you to enter a file name and save either all or customized parameters only to the specified file.

    A user parameter file that you save as "scip.set" has a special meaning; Whenever you invoke SCIP from a directory containing a file named "scip.set",
    the settings therein overwrite the default settings. For more information about customized settings, see the <a href="PATHTODOC/SHELL.LINKEXT">
    Tutorial on the interactive shell</a>.

    Settings files can become incompatible with later releases if we decide to rename/delete a parameter.
    Information about this can be found in the CHANGELOG for every release, see also <a href="#versionchange">this related question</a>.

    </p>

    QUESTION: How do I change the behavior of SCIP?
    LABEL:howtochangebehaviour
    ANSWER:
    <p>
        You can switch the settings for all presolving, heuristics, and separation plugins to three different modes
        via the <code>set {presolving, heuristics, separation} emphasis</code> parameters in the interactive shell.
        <code>off</code> turns off the respective type of plugins, <code>fast</code> chooses settings that lead to less time spent
        in this type of plugins, decreasing their impact, and <code>aggressive</code> increases the impact
        of this type of plugins.
        You can combine these general settings for cuts, presolving, and heuristics arbitrarily.<br>
        <code>display parameters</code> shows you which settings currently differ from their default,
        <code>set default</code> resets them all.
        Furthermore, there are complete settings that can be set by <code>set emphasis</code>, i.e. settings for pure
        feasibility problems, solution counting, and CP like search.
    </p>

    QUESTION: How can I learn more about/from the presolve reasoning SCIP applies to my combinatorial optimization problem?
    LABEL:displaystatistics
    ANSWER:
    <p>
        You can look at the statistics (type <code>display statistics</code> in the
        interactive shell or call SCIPprintStatistics() when using SCIP as a library).
        This way you can see, which of the presolvers, propagators or constraint
        handlers performed the reductions.
        Then, add a <code>#define SCIP_DEBUG</code> as first line of the corresponding *.c file
        in src/scip (e.g. cons_linear.c or prop_probing.c)
        Recompile and run again. You will get heaps of information now.
        Looking into the code and documentation of the corresponding plugin and ressources from the literature
        helps with the investigation.
    </p>

    QUESTION: I recognized that one special plugin works very poorly / very well for my problem and
      I want to disable it / weaken its influence / intensify its influence. How do I do this?
    LABEL:toggleplugin
    ANSWER:
    <ul>
        <li>
            For using a <b class="grey">non-default branching rule or node selection strategy</b> as
            standard, you just have to give it the highest priority, using
            <ul>
                <li><code> SCIP&gt; set branching &lt;name of a branching rule&gt; priority 9999999</code></li>
                <li><code> SCIP&gt; set nodeselectors &lt;name of a node selector&gt; priority 9999999</code></li>
            </ul>
            With the commands
            <ul>
                <li><code> SCIP&gt; display branching</code></li>
                <li><code> SCIP&gt; display nodeselectors</code></li>
            </ul>
            you get a list of all branching rules and node selectors, respectively.
            These lists give information about the different priorities.
        </li>
        <li>
            If you want to completely <b class="grey">disable a heuristic or a separator</b> you have
            to set its frequency to -1 and the sepafreq to -1 for separation by constraint handlers,
            respectively. The commands looks like this:
            <ul>
                <li><code> SCIP&gt; set heuristics &lt;name of a heuristic&gt; freq -1</code></li>
                <li><code> SCIP&gt; set separators &lt;name of a separator&gt; freq -1</code></li>
                <li><code> SCIP&gt; set constraints &lt;name of a constraint handler&gt; sepafreq -1</code></li>
            </ul>
        </li>
        <li>
            For <b class="grey">disabling a presolver</b>, you have to set its maxrounds parameter to 0.
            <ul>
                <li><code> SCIP&gt; set presolvers &lt;name of a presolver&gt; maxrounds 0</code></li>
            </ul>
        </li>
        <li>
            If you want to <b class="grey">intensify</b> the usage of a <b class="grey">heuristic</b>,
            you can reduce its frequency to some smaller, positive value, and/or raise the quotient and
            offset values (maxlpiterquot for diving heuristics, nodes for LNS heuristics).
            <ul>
                <li><code> SCIP&gt; set heuristics &lt;name of a heuristic&gt; freq &lt;some value&gt;</code></li>
                <li><code> SCIP&gt; set heuristic &lt;name of a diving heuristic&gt; maxlpiterquot &lt;some value&gt;</code></li>
                <li><code> SCIP&gt; set heuristic &lt;name of a LNS heuristic&gt; nodesquot &lt;some value&gt;</code></li>
            </ul>
        </li>
        <li>
            For <b class="grey">intensifying</b> the usage of a <b class="grey">separator</b>,
            you can raise its maxroundsroot and maxsepacutsroot values.
            <ul>
                <li><code> SCIP&gt; set separators &lt;name of a separator&gt; maxroundsroot &lt;some value&gt;</code></li>
                <li><code> SCIP&gt; set separators &lt;name of a separator&gt; maxrounds &lt;some value&gt;</code></li>
            </ul>
            If you also want to use this separator locally, you have to set its frequency to a positive value
            and possibly raise maxrounds and maxsepacuts.
            <ul>
                <li><code> SCIP&gt; set separators &lt;name of a separator&gt; freq &lt;some value&gt;</code></li>
                <li><code> SCIP&gt; set separators &lt;name of a separator&gt; maxsepacuts &lt;some value&gt;</code></li>
            </ul>
            Compare the parameters of the heuristic/separator in the appropriate <a href="#howtochangebehaviour">aggressive setting</a>
         </li>
        <li>
            For <b class="grey">weakening</b>, you should just do the opposite operation, i.e.,
            reducing the values  you would raise for intensification and vice versa.
        </li>
    </ul>

    QUESTION: How can I use my own functions in the interactive shell/extend the set of available interactive shell commands?
    LABEL:howtoeextendshell
    ANSWER:
    <p>
        If you want to keep the interactive shell functionality, you could add a
        dialog handler, that introduces a new SCIP shell command that
    </p>
    <ol type="a">
        <li> solves the problem and calls your function afterwards or </li>
        <li>checks whether the stage is SOLVED and only calls your function.</li>
    </ol>
    <p>
        Search <code>SCIPdialogExecOptimize</code> in src/scip/dialog_default.c to see how
        the functionality of the "optimize" command is invoked.
        Also, in src/scip/cons_countsols.c, you can see an example of a dialog handler
        being added to SCIP.
        If this is the way you go, please check the <a href="PATHTODOC/DIALOG.LINKEXT">How to add dialogs section</a>
        of the doxygen documentation.
    </p>

    QUESTION: How can I input a MINLP into SCIP?
    LABEL:howtoinputminlp
    ANSWER:
    <p>
        Please consult <a href="PATHTODOC/WHATPROBLEMS.LINKEXT">this overview</a> on the problem classes
        supported by SCIP and the recommendations and links for MINLPs therein.
    </p>

    QUESTION: Does SCIP handle symmetries inherent to my problem?
    LABEL:symmetryhandlinggeneral
    ANSWER:
    <p>
        SCIP provides two different mechanisms to handle symmetries on binary variables in mixed-integer programs.
        The first approach is based on symmetry handling inequalities as well as the propagation of these constraints,
        whereas the second approach is purely propagation based, so-called orbital fixing. To select which symmetry
        handling approach is used, you can use
        <ul>
            <li><code> SCIP&gt; set misc usesymmetry 1</code> to use symmetry handling inequalities,</li>
            <li><code> SCIP&gt; set misc usesymmetry 2</code> to use orbital fixing,</li>
            <li><code> SCIP&gt; set misc usesymmetry 0</code> to deactivate symmetry handling.</li>
        </ul>
        A detailed description of both symmetry handling approaches can be found in the
        <a href="https://opus4.kobv.de/opus4-zib/frontdoor/index/index/docId/6629"> release report of the SCIP
        Optimization Suite 5.0</a>.
    </p>
    <p>
        Symmetries of general integer or continuous variables in mixed-integer programs or symmetries in non-linear
        programs, however, are currently not handled in SCIP.
    </p>

    QUESTION: Which symmetry handling method should I use?
    LABEL:whichsymmetryhandling
    ANSWER:
    <p>
        There is no clear answer to this question. The advantage of orbital fixing is that all symmetry handling
        reductions are based on propagation decisions. Thus, symmetry handling does not increase the size of your
        LP relaxations. Depending on the problem, however, additional symmetry handling inequalities might interact
        with other cutting plane separators such that stronger cuts can be found. So, if you are dealing with a
        class of optimization problems, you should test which of both methods performs better.
    </p>

    QUESTION: SCIP's incumbent solution is infeasible in the original space. What can I do?
    LABEL:useemphasisnumericssetting
    ANSWER:
    <p>
        SCIP uses a relative feasibility tolerance to check if a solution satisfies a constraint.
        Thus, the acceptable violation of a constraint (in absolute terms) is higher for large left/right hand sides.
        Certain computations that change the lhs/rhs of constraints can lead to an increased tolerance in the
        transformed space while solving. In such cases,
        SCIP may find solutions that are infeasible in the original problem space, since the feasibility tolerance in
        the original space is smaller. Most of the time, this is due to (multi-)aggregations of variables,
        because SCIP cannot centrally guarantee that a (multi-)aggregation requested by one constraint handler does not lead to numerical
        instability of other constraints.
    </p>
    <p>
       The emphasis/numerics setting disables and enables different settings in SCIP to prevent violations in the original problem space.
       This numerical stability comes at the sacrifice of performance.
       You can enable it in one of the following ways:
       <ul>
            <li>In the interactive shell: <code> SCIP&gt; set emphasis numerics</code>,</li>
            <li>Through the C API: <code> SCIP_CALL( SCIPsetEmphasis(scip, SCIP_PARAMEMPHASIS_NUMERICS, quiet) );</code></li>
        </ul>
       If even this emphasis setting does not help, consider disabling (multi-)aggregations completely and decreasing the feasibility tolerance.
    </p>

    QUESTION: What is displayed in the column "compl." of the SCIP output?
    LABEL:searchcompletioncolumn
    ANSWER:
    <p>
        This display column displays an approximate percentage of search completion. Ideally, the displayed percentage is a close approximation
        of the fraction of completed search nodes (with respect to the end of the search).
        The column makes use of different search tree statistics to compute this approximation.
        The concrete method that is used can be changed via the <code>estimation/completiontype</code> user parameter.
        Several methods can be trained to perform well on instances of interest, see also <a href="PATHTODOC/TRAINESTIMATION.LINKEXT">this tutorial</a>.
    </p>

    QUESTION: What is the difference between SCIP's search tree and the "Estimation Tree" in the SCIP statistics?
    LABEL:estimationtree
    ANSWER:
    <p>
        The size of the search tree is reported in the SCIP statistics as "nodes" at termination does not necessarily include
        all nodes that have been created by branching. This statistic only reports the number of nodes that were processed during
        the search.
        In particular open nodes that are pruned from the search tree when a new and better incumbent solution becomes available,
        are unaccounted for.
        Several of the estimation methods rely on counting also these pruned nodes, such that the estimation tree is in fact
        a binary tree at all steps. Every pruned node is counted as a solved node by the estimation tree.
        Because of this discrepancy how nodes are counted, the estimation tree may contain more nodes than the actual search tree.
        Note that the estimation tree is not stored explicitly in memory, but only represented by a constant number of
        node counters and its tree weight.
    </p>


SECTION: Using SCIP included in another source code

    QUESTION: How do I construct a problem instance in SCIP?
    LABEL:howtocreateproblem
    ANSWER:
    <p>
        For starters, SCIP comes with complete examples in source code that illustrate the problem creation process.
        Please refer to the examples of the Callable Library section in the <a href="PATHTODOC/EXAMPLES.LINKEXT">
        Example Documentation</a> of SCIP.
    </p>
    <p>
        First you have to create a SCIP object via <code>SCIPcreate()</code>, then you start to build the problem via
        <code>SCIPcreateProb()</code>.  Then you create variables via <code>SCIPcreateVar()</code> and add them to the
        problem via <code>SCIPaddVar()</code>.
    </p>
    <p>
        The same has to be done for the constraints. For example, if you want to fill in the rows of a general MIP, you
        have to call <code>SCIPcreateConsLinear()</code>, <code>SCIPaddConsLinear()</code> and additionally
        <code>SCIPreleaseCons()</code> after finishing.  If all variables and constraints are present, you can initiate
        the solution process via <code>SCIPsolve()</code>.
    </p>
    <p>
        Make sure to also call <code>SCIPreleaseVar()</code> if you do not need the variable pointer anymore.  For an
        explanation of creating and releasing objects, please see the <a
        href="PATHTODOC/OBJ.LINKEXT">notes on releasing objects</a>.
    </p>

    QUESTION: I already know a solution in advance, which I want to pass to SCIP.
      How do I do this?
    LABEL:howtopasssolution
    ANSWER:
    <p>
        First you have to build your problem (at least all variables have to
        exist), then there are several different ways:
    </p>
    <p>
        <ul>
            <li>
                You have the solution in file which fits the solution format of
                SCIP, then you can use <code>SCIPreadSol()</code> to pass that
                solution to SCIP.
            </li>
            <li>
                You create a new SCIP primal solution candidate by
                calling <code>SCIPcreateSol()</code> and set all nonzero values by
                calling <code>SCIPsetSolVal()</code>. After that, you add this
                solution by calling <code>SCIPaddSol()</code> (the variable
                <code>stored</code> should be true afterwards, if your solution was
                added to solution candidate store) and then release it by calling
                <code>SCIPsolFree()</code>. Instead of adding and releasing
                sequentially, you can use <code>SCIPaddSolFree()</code> which
                tries to add the solution to the candidate store and
                free the solution afterwards.
            </li>
            <li>
                Since SCIP 4.0.0, there is the possibility to create partial solutions
                via <code>SCIPcreatePartialSol()</code>. A solution is partial if
                not all solution values are known before the solve.
                After creation, all solution values are unknown unless explicitly
                given via <code>SCIPsetSolVal()</code>.
                In contrast, solutions created via <code>SCIPcreateSol()</code> implicitly
                assume a solution value of zero.
                A typical example for problem involving integer and continuous variables
                is a tentative assignment for all integer variables so that values for the continuous
                variables should be determined through the solver.
                After starting the solving process, SCIP will try to heuristically complete
                all partial solutions that were added during problem creation.
            </li>
        </ul>
    </p>

    QUESTION: What operational stages of SCIP are there and are they important for me?
    LABEL:scipstages
    ANSWER:
    <p>
        There are fourteen different stages during a run of SCIP.
        <!--,
            a flow chart can be seen here: ????????. -->
        There are some methods which cannot be called in all stages, consider for example <code>SCIPtrySol()</code>
        (see <a href="#howtopasssolution">previous question</a>).
    </p>

    QUESTION: What is the difference between the original and the transformed problem?
    LABEL:originalvstransformed
    ANSWER:
    <p>
        Before the solving process starts, the original problem is copied.
        This copy is called &quot;transformed problem&quot;, and all modifications during the presolving
        and solving process are only applied to the transformed problem.<br>
        This has two main advantages: first, the user can also modify the problem after partially solving it.
        All modifications done by SCIP (presolving, cuts, variable fixings) during the partial solving process will
        be deleted together with the transformed problem, the user can modify the original problem and restart solving.
        Second, the feasibility of solutions is always tested on the original problem!
    </p>

    QUESTION: Why do the names, e.g., in debug messages often differ from the ones I
      defined?
    LABEL:namingissues
    ANSWER:
    <p>
        This can have several reasons. Especially names of binary variables can get different prefixes and suffixes.  Each
        transformed variable and constraint (see <a href="#originalvstransformed">here</a>) gets a &quot;t_&quot; as prefix.  Apart from
        that, the meaning of original and transformed variables and constraints is identical.
    </p>
    <p>
        General integers with bounds that differ just by 1 will be aggregated to binary variables which get the same name
        with the suffix &quot;_bin&quot; .  E.g. an integer variable <code>t_x</code> with lower bound 4 and upper bound 5
        will be aggregated to a binary variable <code>t_x_bin = t_x - 4</code>.
    </p>
    <p>
        Variables can have negated counterparts, e.g. for a binary <code>t_x</code> its (also binary) negated would be
        <code>t_x_neg = 1 - t_x</code>.
    </p>
    <p>
        The knapsack constraint handler is able to disaggregate its constraints to cliques, which are set packing
        constraints, and create names that consist of the knapsack's name and a suffix
        &quot;<code>_clq_&lt;int&gt;</code>&quot;.  E.g., a knapsack constraint
        <code>knap:&nbsp;x_1&nbsp;+&nbsp;x2&nbsp;+2 x_3&nbsp;&le;&nbsp;2</code> could be disaggregated to the set packing
        constraints <code>knap_clq_1:&nbsp;x_1&nbsp;+&nbsp;x_3&nbsp;&le;&nbsp;1</code> and
        <code>knap_clq_2:&nbsp;x_2&nbsp;+&nbsp;x_3&nbsp;&le;&nbsp;1</code>.
    </p>

    QUESTION: What is SCIP_CALL()? Do I need this?
    LABEL:scipcall
    ANSWER:
    <p>
        Yes, you do. SCIP_CALL() is a global define, which handles the return codes of all methods
        which return a SCIP_RETCODE and should therefore parenthesize each such method.
        SCIP_OKAY is the code which is returned if everything worked well;
        there are 17 different error codes, see <a href="PATHTODOC/type__retcode_8h.LINKEXT">type_retcode.h</a>.
        Each method that calls methods which return a SCIP_RETCODE should itself return a SCIP_RETCODE.
        If this is not possible, use SCIP_CALL_ABORT() to catch the return codes of the methods.
        If you do not want to use this either, you have to do the exception handling
        (i.e. the case that the return code is not SCIP_OKAY) on your own.
    </p>

    QUESTION: I want to stop the solving process after a certain time. How can I do this?
    LABEL:howtointerrupt
    ANSWER:
    <p>
        Limits are given by parameters in SCIP, for example <code>limits/time</code> for a time limit or
        <code>limits/nodes</code> for a node limit.
        If you want to set a limit, you have to change these parameters.
        For example, for setting the time limit to one hour, you have to call
        <code>SCIP_CALL( SCIPsetRealParam(scip, "limits/time", 3600) )</code>.
        In the interactive shell, you just enter <code>set limits time 3600</code>.
        For more examples, please have a look into heur_rens.c.
    </p>

    QUESTION: Is it possible to avoid that the SCIP library overrides my signal handler for interruptions?
    LABEL: interrupthandler
    ANSWER:
    <p>
        By default, the SCIP library has an internal handler for the handling of the SIGINT signal,
        which is usually emitted when a user presses CTRL-C during the solution process.
        In cases where this overrides the signal handling of a surrounding application,
        this may be undesirable.
        As a remedy, the parameter misc/catchctrlc can be set to FALSE or the SCIP library can be
        compiled with the special C compiler flag "-DNO_SIGACTION", both disabling SCIP's internal
        signal handling.
    </p>

SECTION: Using SCIP as a Branch-Cut-And-Price-Framework

    QUESTION: How do I start a project?
    LABEL:howtostartbcpproject
    ANSWER:
    <p>
        See <a href="PATHTODOC/START.LINKEXT">How to start a new project</a>.
    </p>

    QUESTION: What types of plugins can I add and how do I do this?
    LABEL:howtoaddplugins
    ANSWER:
    <p>
        See the <a href="PATHTODOC/modules.LINKEXT">doxygen documentation</a> for a list of
        plugin types. There is a <a href="PATHTODOC/index.LINKEXT#HOWTOADD">HowTo</a> for each of them.
    </p>

    QUESTION: When should I implement a constraint handler, when should I implement a separator?
    LABEL:conshdlrvsseparator
    ANSWER:
    <p>
        This depends on whether you want to add constraints or only cutting planes. The main
        difference is that constraints can be &quot;model constraints&quot;, while cutting planes are only
        additional LP rows that strengthen the LP relaxation.
        A model constraint is a constraint that is important for the feasibility of the integral
        solutions. If you delete a model constraint, some infeasible integral vectors would
        suddenly become feasible in the reduced model.
        A cutting plane is redundant w.r.t. integral solutions. The set of feasible integral
        vectors does not change if a cutting plane is removed. You can, however, relax this
        condition slightly and add cutting planes that do cut off feasible solutions, as long as
        at least one of the optimal solutions remains feasible.
    </p>
    <p>
      You want to use a constraint handler in the following cases:
    </p>
    <ol>
        <li>
            Some of your feasibility conditions can not be expressed by existing constraint types
            (e.g., linear constraints), or you would need too many of them. For example, the
            &quot;nosubtour&quot; constraint in the TSP is equivalent to exponentially many linear constraints.
            Therefore, it is better to implement a &quot;nosubtour&quot; constraint handler that can inspect
            solutions for subtours and generate subtour elimination cuts and others (e.g., comb
            inequalities) to strengthen the LP relaxation.</li>
            <li>Although you can express your feasibility condition by a reasonable number of existing
            constraint types, you can represent and process the condition in a more efficient way. For
            example, it may be that you can, due to your structural knowledge, implement a stronger or
            faster domain propagation or find tighter cutting planes than what one could do with the
            sum of the individual &quot;simple&quot; constraints that model the feasibility condition.
        </li>
    </ol>
    <p>
        You want to use a cutting plane separator in the following cases:
    </p>
    <ol>
        <li>
            You have a general purpose cutting plane procedure that can be applied to any MIP. It
            does not use problem specific knowledge. It only looks at the LP, the integrality
            conditions, and other deduced information like the implication graph.</li>
            <li>You can describe your feasibility condition by a set C of constraints of existing type
            (e.g., linear constraints). The cuts you want to separate are model specific, but apart
            from these cuts, there is nothing you can gain by substituting the set C of constraints
            with a special purpose constraint. For example, the preprocessing and the domain
            propagation methods for the special purpose constraint would do basically the same as what
            the existing constraint handler does with the set C of constraints. In this case, you
            don't need to implement the more complex constraint handler. You add constraints of
            existing type to your problem instance in order to produce a valid model, and you enrich
            the model by your problem specific cutting plane separator to make the solving process
            faster. You can easily evaluate the performance impact of your cutting planes by enabling
            and disabling the separator.
        </li>
    </ol>
    <p>
        Note that a constraint handler is defined by the type of constraints that it manages. For
        constraint handlers, always think in terms of constraint programming. For example, the
        &quot;nosubtour&quot; constraint handler in the TSP example
        (see "ConshdlrSubtour.cpp" in the directory "scip/examples/TSP/src/")
        manages &quot;nosubtour&quot; constraints, which demand
        that in a given graph no feasible solution can contain a tour that does not contain all
        cities. In the usual TSP problem, there is only one &quot;nosubtour&quot; constraint, because there
        is only one graph for which subtours have to be ruled out.
        The &quot;nosubtour&quot; constraint handler has various ways of enforcing the &quot;nosubtour&quot; property
        of the solutions. A simple way is to just check each integral solution candidate (in the
        CONSCHECK, CONSENFOLP, and CONSENFOPS callback methods) for subtours. If there is a subtour, the
        solution is rejected. A more elaborate way includes the generation of &quot;subtour elimination
        cuts&quot; in the CONSSEPALP callback method of the constraint handler. Additionally, the
        constraint handler may want to separate other types of cutting planes like comb
        inequalities in its CONSSEPALP callback.
    </p>

    QUESTION: Can I remove unnecessary display columns or&mdash;even better&mdash;add my own ones?
      Can I change the statistics displayed at the end of solving?
    LABEL:toggledisplaycolumns
    ANSWER:
    <p>
        Setting the status of a display column to 0 turns it off. E.g., type <code>set display memused status 0</code> in the
        interactive shell to disable the memory information column, or include the line <code>SCIPsetIntParam(scip,
        &quot;display/memused/status&quot;, 0)</code> into your source code.  Adding your own display column can be done
        by calling the <code>SCIPincludeDisp()</code> method, see the <a href="PATHTODOC/DISP.LINKEXT">doxygen
        documentation</a>.<br> The statistic display, which is shown by <code>display statistics</code> and
        <code>SCIPprintStatistics()</code>, respectively, cannot be changed.
    </p>

    QUESTION: What do LP-rows look like in SCIP?
    LABEL:lprows
    ANSWER:
    <p>
        Each row is of the form <i>lhs</i> &le; &Sigma;(<i>val</i>[<i>j</i>]&middot;<i>col</i>[<i>j</i>]) + <i>const</i>
        &le; <i>rhs</i>.  For now, <i>val</i>[<i>j</i>]&middot;<i>col</i>[<i>j</i>] can be interpreted as
        <i>a</i><sub><i>ij</i></sub>&middot;<i>x</i><sub><i>j</i></sub> (for the difference between columns and variables
        see <a href="#columnsvsvariables">here</a>).  The constant is essentially needed for collecting the influence of presolving
        reductions like variable fixings and aggregations.<br> The <i>lhs</i> and <i>rhs</i> may take infinite values: a
        less-than inequality would have <i>lhs</i> = -&#8734;, and a greater-than inequality would have <i>rhs</i> =
        +&#8734;.  For equations <i>lhs</i> is equal to <i>rhs</i>.  An infinite left hand side can be recognized by
        <code>SCIPisInfinity(scip, -lhs)</code>, an infinite right hand side can be recognized by
        <code>SCIPisInfinity(scip, rhs)</code>.
    </p>

    QUESTION: How do I get the data of the current LP-relaxation?
    LABEL:lprelaxationdata
    ANSWER:
    <p>
        You can get all rows in the current LP-relaxation by calling <code>SCIPgetLPRowsData()</code>. The methods
        <code>SCIProwGetConstant()</code>, <code>SCIProwGetLhs()</code>, <code>SCIProwGetRhs()</code>,
        <code>SCIProwGetVals()</code>, <code>SCIProwGetNNonz()</code>, <code>SCIProwGetCols()</code> then give you
        information about each row, see <a href="#lprows">previous question</a>.
    </p>
    <p>
        You get a columnwise representation by
        calling <code>SCIPgetLPColsData()</code>. The methods <code>SCIPcolGetLb()</code> and <code>SCIPcolGetUb()</code>
        give you the locally valid bounds of a column in the LP relaxation of the current branch-and-bound-node.
    </p>
    <p>
        If you are interested in global information, you have to call <code>SCIPcolGetVar()</code> to get the variable
        associated to a column (see <a href="#columnsvsvariables">next question</a>), which you can ask for global bounds via
        <code>SCIPvarGetLbGlobal()</code> and <code>SCIPvarGetUbGlobal()</code> as well as the type of the variable
        (binary, general integer, implicit integer, or continuous) by calling <code>SCIPvarGetType()</code>.  For more
        information, also see <a href="#searchdocumentation">this question</a>.
    </p>

    QUESTION: What is the difference between columns and variables, rows and constraints?
    LABEL:columnsvsvariables
    ANSWER:
    <p>
        The terms columns and rows always refer to the representation in the current LP-relaxation, variables and
        constraints to your global Constraint Integer Program.<br> Each column has an associated variable, which it
        represents, but not every variable must be part of the current LP-relaxation. E.g., it could be already fixed,
        aggregated to another variable, or be priced out if a column generation approach was implemented.
    </p>
    <p>
        Each row has either been added to the LP by a constraint handler or by a cutting plane separator.  A constraint handler is able
        to, but does not need to, add one or more rows to the LP as a linear relaxation of each of its constraints.  E.g.,
        in the usual case (i.e. without using dynamic rows) the linear constraint handler adds one row to the LP for each
        linear constraint.
    </p>

    QUESTION: Are the variables and rows sorted in any particular order?
    LABEL:variableandrowsorting
    ANSWER:
    <p>
        The variable array which you get by <code>SCIPgetVars()</code> is internally sorted by variable types.
        The ordering is binary, integer, implicit integer and continuous variables, i.e., the binary variables are stored at
        position [0,...,nbinvars-1], the general integers at [nbinvars,...,nbinvars+nintvars-1], and so on. It holds that
        nvars = nbinvars + ninitvars + nimplvars + ncontvars.  There is no further sorting within these sections, as well as
        there is no sorting for the rows.  But each column and each row has a unique index, which can be obtained by
        <code>SCIPcolGetIndex()</code> and <code>SCIProwGetIndex()</code>, respectively.
    </p>

    QUESTION: What is an implicit integer variable?
    LABEL:implicitinteger
    ANSWER:
    <p>

        A variable <code>v</code> is implicit integer if it is guaranteed to take an integer
        solution value in every optimal solution to every remaining subproblem after
        fixing all integer variables of the problem.
        Implicit integer variables are represented by the
        variable type <code>SCIP_VARTYPE_IMPLINT</code>.
        Note that continuous as well as integer variables can be declared
        implicit integer.
    </p>
    <p>
        The solver benefits from the presence of implicit integrality
        in several ways: Implict integer variables can be treated
        like continuous variables for branching because it is not necessary to
        enforce integrality. They can be treated like integer variables
        to yield stronger propagations, better coefficients in cuts, etc.
        <br/>
        Another advantage of this definition is that it allows heuristics to know
        that if a feasible point has integer values for all integer variables,
        then either all implicit integer variables have integer values or the
        value of an implicit integer variable can be assigned to an integer
        without worsening the objective value.
    </p>
    <p>
        Currently, SCIP identifies implicit integer variables via feasibility
        reasoning and optimality reasoning during presolving.
        <br/>
        As an example of feasibility reasoning, consider the constraint
        <code>x + y = 1</code> where both variables are integer.
        From this constraint, either one of them could be declared implicit
        integer.
        This is because fixing one to an integer value forces the other to be
        integer as well.
        Note that you must not declare both variables implicit integer, since
        the reasoning depends on the other variable still being of integer.
        type
        <br/>
        As an example of optimality reasoning, consider the problem <code>max
        x</code> subject to <code>x + y <= 10</code> and
        <code>y</code> has to be integer.
        After fixing <code>y</code> to any integer value, the optimal value of
        <code>x</code> will be <code>10 - y</code> which is an integer.
        Hence, <code>x</code> can be declared implicit integer.
        Note, however, that if the constraint is <code>2*x + y <= 10</code>, then we
        cannot conclude that <code>x</code> is implicit integer.
    </p>

    QUESTION: When should I use which of the numerical comparison functions?
    LABEL:feasibilitycomparison
    ANSWER:
    <p>
        There are various numerical comparison functions available, each of them using a different
        epsilon in its comparisons. Let's take the equality comparison as an example. There are
        the following methods available: <code>SCIPisEQ(), SCIPisSumEQ(), SCIPisFeasEQ(), SCIPisRelEQ(),
        SCIPisSumRelEQ()</code>.
    </p>
    <ul>
        <li>
            <code>SCIPisEQ()</code> should be used to compare two single values that are either results of a simple
            calculation or are input data. The comparison is done w.r.t. the &quot;numerics/epsilon&quot; parameter, which is
            1e-9 in the default settings.
        </li>
        <li>
            <code>SCIPisSumEQ()</code> should be used to compare the results of two scalar products or other &quot;long&quot;
            sums of values. In these sums, numerical inaccuracy can occur due to cancellation of digits in the addition of
            values with opposite sign. Therefore, <code>SCIPisSumEQ()</code> uses a relaxed equality tolerance of
            &quot;numerics/sumepsilon&quot;, which is 1e-6 in the default settings.
        </li>
        <li>
            <code>SCIPisFeasEQ()</code> should be used to check the feasibility of some result, for example after you have
            calculated the activity of a constraint and compare it with the left and right hand sides. The feasibility is
            checked w.r.t. the &quot;numerics/feastol&quot; parameter, and equality is defined in a relative fashion in
            contrast to absolute differences. That means, two values are considered to be equal if their difference divided by
            the larger of their absolute values is smaller than &quot;numerics/feastol&quot;. This parameter is 1e-6 in the
            default settings.
        </li>
        <li>
            <code>SCIPisRelEQ()</code> can be used to check the relative difference between two values, just like what
            <code>SCIPisFeasEQ()</code> is doing. In contrast to <code>SCIPisFeasEQ()</code> it uses
            &quot;numerics/epsilon&quot; as tolerance.
        </li>
        <li>
            <code>SCIPisSumRelEQ()</code> is the same as <code>SCIPisRelEQ()</code> but uses &quot;numerics/sumepsilon&quot;
            as tolerance.  It should be used to compare two results of scalar products or other &quot;long&quot; sums.
        </li>
    </ul>

    QUESTION: How do I solve an LP inside my SCIP plugin?
    LABEL:howtosolvelps
    ANSWER:
    <p>
        If the LP is only a slightly modified version of the LP relaxation - changed variable bounds or objective
        coefficients - then you can use SCIP's diving mode: methods <code>SCIPstartDive()</code>,
        <code>SCIPchgVarLbDive()</code>, <code>SCIPsolveDiveLP()</code>, etc.
    </p>
    <p>
        Alternatively, SCIP's probing mode allows for a tentative depth first search in the tree and can solve the LP
        relaxations at each node: methods <code>SCIPstartProbing()</code>, <code>SCIPnewProbingNode()</code>,
        <code>SCIPfixVarProbing()</code>, etc. However, you cannot change objective coefficients or enlarge variable bounds
        in probing mode.
    </p>
    <p>
        If you need to solve a separate LP, creating a sub-SCIP is not recommended because of the overhead involved
        and because dual information is not accessible (compare <a href="#scipaslpsolver">here</a>). Instead you can use SCIP's LP
        interface. For this you should include <code>lpi/lpi.h</code> and call the methods provided therein.
        Note that the LPI can be used independently from SCIP.
    </p>

    QUESTION: Can I write my own symmetry handling plugin for SCIP?
    LABEL:customsymmetryhandling
    ANSWER:
    <p>
        Yes, you can write your own symmetry handling plugin. To avoid conflicts with the internal symmetry handling methods
        of SCIP, you should deactivate SCIP's symmetry handling routines by calling
        <code>SCIP_CALL( SCIPsetIntParam(scip, "misc/usesymmetry", 0) )</code>.
    </p>

    QUESTION: What is the difference between sepastore and cutpool, and when should one add a cut to one or the other?
    LABEL:sepastorecutpool
    ANSWER:
    <p>
        Both, a sepastore and a cutpool, are data structures that can hold cuts.
        However, their main difference is how they are used by SCIP.
    </p>
    <p>
        In each separation round, cutting planes are added to SCIP's internal separation storage, that is, SCIP's
        sepastore.
        The cuts are added to the sepastore with <code>SCIPaddRow()</code>.
        Before the cuts from the sepastore are added to the current relaxation, they are filtered through the
        cutselectors.
        Note that by adding cuts with <code>SCIPaddRow()</code> one has the option to force the cut.
        This means that the cut is not going to be filtered out by the cutselectors.
        Moreover, if in a separation round all cutting planes are forced, then the cutselectors are not called.
        After each separation round, all cutting planes in the sepastore are removed.
    </p>
    <p>
        Cutting planes are mainly generated by constraint handlers and separators.
        In addition to adding cuts to SCIP with <code>SCIPaddRow()</code>, they can also add cuts with
        <code>SCIPaddPoolCut()</code> (although only when they are globally valid).
        The difference is that a cut added with <code>SCIPaddPoolCut()</code> does not go to the sepastore, but to
        SCIP's global cutpool.
        In each separation round, the global cutpool can then also add cuts to SCIP's sepastore.
    </p>
    <p>
        If a cut in the global cutpool is not added to the sepastore (e.g. because it is not efficacious enough),
        its age is increased. If its age reaches <code>separating/cutagelimit</code>, then the cut is removed from the
        cutpool. As soon as a cut from the cutpool is added to the sepastore, its age counter goes down to 0 and its
        age remains 0 as long as the cut is in the LP relaxation.
        In particular, this means that cuts from the global cutpool added to the sepastore are not removed from the
        global cutpool.
        This might make sense because of the following reasons.
        Even if the cut makes it to the sepastore, it does not mean it is going to enter the LP
        relaxation, because it might be filtered out by a cutselector.
        Furthermore, if the cut enters the LP it can still age out of the LP (e.g. because it is not active in enough
        consecutive LP relaxations), but the cut might still be interesting in other parts of the search tree.
        Thus, it makes sense to add cuts to the global cutpool that are known to be strong or expensive to generate.
    </p>
    <p>
        Another difference between sepastore and cutpool is that any plugin can create its own cutpool, while only the
        SCIP core can create a sepastore.
    </p>
    <p>
        As a summary, the purpose of the global cutpool is to store globally valid cuts that can be reused in later
        separation rounds, while the purpose of the sepastore is to collect the cuts that are to be added in a single
        separation round.
        In each separation round, constraint handlers and separators can add cuts to the global cutpool, and
        contraint handlers, separators and the global cutpool can add cuts directly to the sepastore.
        Furthermore, locally valid cuts can only be added to the sepastore and expensive globally valid cuts might be
        better suited for the global cutpool.
    </p>

SECTION: Specific questions about Column Generation and Branch-And-Price with SCIP

    QUESTION: What can I expect when using SCIP as a Branch-Cut-and-Price framework?
    LABEL:whattoexpect
    ANSWER:
    <p>
        If you want to use SCIP as a branch-and-price framework, you normally need to implement a reader to read in your
        problem data and build the problem, a pricer to generate new columns, and a branching rule to do the branching
        (see also  <a href="#howtostorebranchingdecisions">this question</a> to see how to store branching decisions, if needed).
        SCIP takes care about everything else,
        for example the branch-and-bound tree management and LP solving including storage of warmstart bases. Moreover,
        many of SCIP's primal heuristics will be used and can help improve your primal bound.
        However, this also comes with a few restrictions: You are not allowed to change the objective function coefficients
        of variables during the solving process, because that means that previously computed dual bounds might have to be updated.
        This prevents the use of dual variable stabilization techniques based on a (more or less strict) bounding box in the dual.
        We are working on making this possible and recommend to use a weighted sum stabilization approach until then.
        Another point that SCIP does for you is the dynamic removal of columns from the LP due to aging (see also the next two questions).
        However, due to the way simplex bases are stored in SCIP, columns can only be removed at the same node where they were created.
    </p>

    QUESTION: Why are not all variables in the LP?
    LABEL:wherearethevariables
    ANSWER:
    <p>
        With <code>SCIPgetLPColsData()</code> you can obtain the columns of the current LP relaxation. It is correct that
        not all variables are necessarily part of the current LP relaxation. In particular, in branch-and-price the
        variables generated at one node in the tree are not necessarily included in the LP relaxation of a different node
        (e.g., if the other node is not a descendant of the first node). But even if you are still at the same node or at
        a descendant node, SCIP can remove columns from the LP, if they are 0 in the LP relaxation. This dynamic column
        deletion can be avoided by setting the "removable" flag to FALSE in the <code>SCIPcreateVar()</code> call.
    </p>

    QUESTION: I only implemented one pricer, why is there a second one, called variable pricer?
    LABEL:variablepricer
    ANSWER:
    <p>
        As described in the <a href="#wherearethevariables">previous question</a>, it may happen, that some variables are not in the
        current LP relaxation. Nevertheless, these variables still exist, and SCIP can calculate their reduced costs and
        add them to the LP again, if necessary. This is the job of the variable pricer. It is called before all other
        pricers.
    </p>

    QUESTION: How can I store branching decisions?
    LABEL:howtostorebranchingdecisions
    ANSWER:
    <p>
        This is a very common problem in Branch-And-Price, which you can deal nicely with using SCIP.
        There are basically three different options.
        The first one is to add binary variables to the problem that encode branching decisions. Then constraints should
        be added that enforce the corresponding branching decisions in the subtrees.
    </p>
    <p>
        If you have complex pricer data like a graph and need to update it after each branching decision,
        you should introduce "marker constraints" that are added to the branching nodes and store
        all the information needed (see the <a href="#pricerandnodedata">next question</a>).
    </p>
    <p>
        The third way is to use an event handler, which is described <a href="#eventhdlrduringbranching">here</a>.
    </p>

    QUESTION: I want to store some information at the nodes and update my pricer's data structures
                    when entering a new node. How can I do that?
    LABEL:pricerandnodedata
    ANSWER:
    <p>
        This can be done by creating a new constraint handler with constraint data that can store the information and
        do/undo changes in the pricer's data structures.
    <p>
        Once you have such a constraint handler, just create constraints of this type and add them to the child nodes of
        your branching by <code>SCIPaddConsNode()</code>. Make sure to set the "stickingatnode" flag to TRUE in order to
        prevent SCIP from moving the constraint around in the tree.
    </p>
    </p>
        In general, all methods of the constraint handler (check, enforcing, separation, ...) should be empty (which means
        that they always return the status SCIP_FEASIBLE for the fundamental callbacks), just as if all constraints of this type
        are always feasible. The important callbacks are the CONSACTIVE and CONSDEACTIVE methods for communicating the
        constraints along the active path to your pricer, and the CONSDELETE callback for deleting data of constraints at nodes
        which became obsolete.
    <p>
        The CONSACTIVE method is always called when a node is entered on which the constraint has been added. Here, you
        need to apply the changes to your pricing data structures. The CONSDEACTIVE method will be called if the node is
        left again. Since the CONSACTIVE and CONSDEACTIVE methods of different constraints are always called in a
        stack-like fashion, this should be exactly what you need.
    </p>
    <p>
        All data of a constraint need to be freed by implementing an appropriate CONSDELETE callback.
    </p>
    <p>
        If you need to fix variables for enforcing your branching decision, this can be done in the propagation callback
        of the constraint handler. Since, in general, each node is only propagated once, in this case you will have to check
        in your CONSACTIVE method whether new variables were added after your last propagation of this node. If this is
        the case, you will have to mark this node for repropagation by <code>SCIPrepropagateNode()</code>.
    </p>
    <p>
        You can look into the constraint handler of the coloring problem (examples/Coloring/src/cons_storeGraph.c) to get
        an example of a constraint handler that does all these things.
    </p>

    QUESTION: How can an event handler help me with my branching?
    LABEL:eventhdlrduringbranching
    ANSWER:
    <p>
        An event handler can watch for events like local bound changes on variables. So, if your
        pricer wants to be informed whenever a local bound of a certain variable changes, add an
        event handler, catch the corresponding events of the variable, and in the event handler's
        execution method adjust the data structures of your pricer accordingly.
    </p>

    QUESTION: How can I add locally valid variables to the problem in my branch-and-price code?
    LABEL:localvariables
    ANSWER:
    <p>
        Variables in SCIP are always added globally. If you want to add them locally, because they are forbidden
        in another part of the branch-and-bound-tree, you should ensure that they are locally fixed to 0
        in all subtrees where they are not valid. A description of how this can be done is given <a href="#pricerandnodedata">here</a>.
    </p>

    QUESTION: My pricer generates the same column twice. How can I solve this problem?
    LABEL:doublecolumns
    ANSWER:
    <p>
        First check whether your pricing is correct. Are there upper bounds on variables that you have forgotten to take
        into account? If your pricer cannot cope with variable bounds other than 0 and infinity, you have to mark
        all constraints containing priced variables as modifiable, and you may have to disable reduced cost
        strengthening by setting propagating/rootredcost/freq to -1.
    </p>
    <p>
        If your pricer works correctly and makes sure that the same column is added at most once in one pricing round, this
        behavior is probably caused by the PRICER_DELAY property of your pricer.
    </p>
    <p>
        If it is set to FALSE, the following may have happened: The variable pricer (see <a href="#variablepricer">this question</a>)
        found a variable with negative dual feasibility that was not part of the current LP relaxation and added it to the
        LP. In the same pricing round, your own pricer found the same column and created a new variable for it. This might
        happen, since your pricer uses the same dual values as the variable pricer. To avoid this behavior, set
        PRICER_DELAY to TRUE, so that the LP is reoptimized after the variable pricer added variables to the LP. You can
        find some more information about the PRICER_DELAY property at <a
        href="PATHTODOC/PRICER.LINKEXT#PRICER_PROPERTIES">How to add variable pricers </a>.
    </p>

    QUESTION: Which default plugins should be deactivated in order to get a working branch-and-price code?
    LABEL:problematicplugins
    ANSWER:
    <p>
        In most cases you should deactivate separators since cutting planes that are added to your master problem may
        destroy your pricing problem. Additionally, it may be necessary to deactivate some presolvers, mainly the dual
        fixing presolver. This can be done by not including these plugins into SCIP, namely by not calling
        <code>SCIPincludeSepaXyz()</code> and <code>SCIPincludePresolXyz()</code> in your own plugins-including
        files. Alternatively, you can set the parameters maxrounds and maxroundsroot to zero for all separators and
        maxrounds to zero for the presolvers.
    </p>

    QUESTION: What are the lazy bounds for variables in SCIP and what do I need them for?
    LABEL:whatarelazybounds
    ANSWER:
    <p>
        In many Branch-and-Price applications, you have binary variables, but you do not want to impose
        upper bounds on these variables in the LP relaxation, because the upper bound is already implicitly enforced
        by the problem constraints and the objective. If the upper bounds are explicitly added to the LP,
        they lead to further dual variables, which may be hard to take into account in the pricing problem.
    </p>
    <p>
        There are two possibilities for how to solve this problem. First, you could change the binary variables
        to general integer variables, if this does not change the problem. However, if you use special linear
        constraints like set partitioning/packing/covering, you can only add binary variables to these constraints.
    </p>
    <p>
        In order to still allow the usage of these types of constraints in a branch-and-price approach, the
        concept of lazy bounds was introduced in SCIP 2.0.
        For each variable, you can define lazy upper and lower bounds, i.e. bounds, that are implicitly enforced by
        constraints and objective. SCIP adds variable bounds to the LP only if the bound is tighter than the
        corresponding lazy bound.
        Note that lazy bounds are explicitly put into and removed from the LP when starting and ending diving mode,
        respectively. This is needed because changing the objective in diving might reverse the implicitly enforced
        bounds.
    </p>
    <p>
        For instance, if you have set partitioning constraints in your problem, you can define variables contained in these
        constraints as binary and set the lazy upper bound to 1, which allows you to use the better propagation methods
        of the setppc constraint handler compared to the linear constraint handler without taking care about upper
        bounds on variables in the master.
    </p>

    QUESTION: Can I stop the pricing process before the master problem is solved to optimality?
    LABEL:terminatepricing
    ANSWER:
    <p>
        In a column generation approach, you usually have to solve the master problem to optimality; otherwise,
        its objective function value is not a valid dual bound. However, there is a way in SCIP to
        stop the pricing process earlier, called "early branching".
    </p>
    <p>
        The reduced cost pricing method of a pricer has a result pointer that should be set each time the method is called.
        In the usual case that the pricer either adds a new variable or ensures that there are no further
        variables with negative dual feasibility, the result pointer should be set to SCIP_SUCCESS.
        If the pricer aborts pricing without creating a new variable, but there might exist additional
        variables with negative dual feasibility, the result pointer should be set to SCIP_DIDNOTRUN.
        In this case, the LP solution will not be used as a lower bound.
        Typically, early branching goes along with the computation of a Lagrangian bound in each pricing iteration.
        The pricer store store this valid lower bound in the <code>lowerbound pointer</code> in order to update the lower
        bound of the current node.
        Since SCIP 3.1, it is even possible to state that pricing should be stopped early even though new variables were created
        in the last pricing round. For this, the pricer has to set the <code>stopearly</code> pointer to TRUE.
    </p>

    QUESTION: SCIP does not stop although my gap is below 1.0 and all variables are binary and have objective coefficient 1. What can I do?
    LABEL:integralobj
    ANSWER:
    <p>
	SCIP tries to detect whether the objective function values of all solutions must be integral or the problem
	can be scaled such that the former holds. If this is the case, solving will be stopped as soon as the absolute gap
	is below 1.0 (scaled).
    </p>
    <p>

	However, the detection does not work in case of branch-and-price, because SCIP cannot know whether any of the newly
	created variables would violate this property. For this case, there is the possibility to inform SCIP that
	all newly created variables will be integer and have an integer objective coefficient by calling
	<code>SCIPsetObjIntegral()</code>. This knowledge will then be exploited by SCIP for bounding.
    </p>

    QUESTION: How can I delete variables?
    LABEL:howtodeletevariables
    ANSWER:
    <p>
        SCIP features the functionality to delete variables from the problem when performing branch-and-price.
        This feature is still in a beta status and can be activated by switching the parameters
        <code>pricing/delvars</code> and <code>pricing/delvarsroot</code> to TRUE in order to allow deletion
        of variables at the root node and at all other nodes, respectively.
        Furthermore, variables have to be marked to be deletable by <code>SCIPvarMarkDeletable()</code>, which has to be done
        before adding the variable to the problem. Then, after a node of the branch-and-bound-tree is processed,
        SCIP automatically deletes variables from the problem that were created at the current node and whose corresponding
        columns were already removed from the LP. Note that due to the way SCIP stores basis information, it is not possible to
        completely delete a variable that was created at another node than the current node.
        You might want to change the parameters <code>lp/colagelimit</code>, <code>lp/cleanupcols</code>, and <code>lp/cleanupcolsroot</code>,
        which have an impact on when and how fast columns are removed from the LP.
    </p>
    <p>
        Constraint handlers support a new callback function that deletes variables from constraints in which they were marked to be deleted.
        Thus, when using automatic variable deletion, you should make sure that all used constraint handlers implement this callback.
        By now, the linear, the set partitioning/packing/covering and the knapsack constraint handler support this callback, which should
        be sufficient for most branch-and-price applications. Note that set covering constraints can be used instead of logicor constraints.
    </p>
    <p>
        Instead of deleting a variable completely, you can also remove it from the problem by either fixing the variable to zero
        using <code>SCIPfixVar()</code>, which fixes the variable globally or using <code>SCIPchgVarUbNode()</code> and
        <code>SCIPchgVarLbNode()</code>, which changes the bounds only for the current subtree.
    </p>

    QUESTION: How do I branch on constraints?
    LABEL:howtobranchonconstraints
    ANSWER:
    <p>
        Constraint-based branching is rather straightforward to implement in
        SCIP.  You have to add a new branching rule that uses the methods
        SCIPcreateChild() and SCIPaddConsNode() in its branching callbacks.
        A very good example for this is the Ryan/Foster branching rule that has
        been implemented in the binpacking example from the <a href="PATHTODOC/EXAMPLES.LINKEXT">examples section</a>.
    </p>
    <p>
        Sometimes it might be more appropriate to implement a constraint
        handler instead of a branching rule. This is the case if, e.g., the added constraints alone
        do NOT ensure integrality of the integer variables, or if you still want to use the available branching rules.
        In the ENFOLP callback of your constraint handler, the
        branching really happens. The integrality constraint
        handler calls the branching rules within the ENFOLP callback. Give your constraint handler a positive enforcement priority
        to trigger your constraint branching before the integrality constraint handler and perform the constraint branching.
    </p>

SECTION: Specific questions about the copy functionality in SCIP

    QUESTION: What is <code>SCIPcopy()</code>?
    LABEL:scipcopy
    ANSWER:
    <p>
        The functionality of copying a SCIP model was added in SCIP version 2.0.0. It gives the possibility to
        generate a copy of the current SCIP model. This functionality is of interest, for example, in large
        neighborhood heuristics (such as heur_rens.c). They can now easily copy the complete problem and fix a certain
        set of variables to work on a reasonable copy of the original problem.
    </p>
    <p>
        Since SCIP version 4.0.0, the additional copying method <code>SCIPcopyConsCompression()</code> is available,
        which expects as additional argument a list of variables that should be fixed in the problem copy. These will be
        fixed right away at creation, so that all constraints may treat those variables as constants to potentially
        reduce the memory required to store the problem copy.
    </p>
    QUESTION: When should I use <code>SCIPcopy()</code> instead of <code>SCIPcopyConsCompression()</code>?
    LABEL:comparecopyandconscompression
    ANSWER:
    <p>
        This, of course, depends on the problem copy's intended use. The large neighborhood search heuristics such as, e.g.,
        heur_rens.c, usually create a problem copy in which they fix a number of variables and solve the remaining, smaller
        subproblem only once. In this case, it makes sense to use <code>SCIPcopyConsCompression()</code> that treats
        fixed variables as constants at constraint creation time to save memory.
    </p>
    <p>
        For a more general use of the problem copy such as resolving with different objective functions or multiple solves
        for different sets of fixed variables, you should clearly use <code>SCIPcopy()</code> because this is beyond the
        scope of a compressed copy.
    </p>

    QUESTION: How do I get a copy of a variable or a constraint?
    LABEL:howtocopyvariablesandconstraints
    ANSWER:
    <p>
        For the variables and constraints there are the methods <code>SCIPgetVarCopy()</code> and
        <code>SCIPgetConsCopy()</code> which provide a copy for a variable or a constraint, respectively.
    </p>

    QUESTION: What does the <code>valid</code> pointer in the copy callback of the constraint handler and variable pricer mean?
    LABEL:useofvalidpointer
    ANSWER:
    <p>
        SCIP would like to know if the copied problem is a valid copy.
        A problem copy is called valid if it is valid in both the primal and the dual sense, i.e., if
        <ul>
            <li>it is a relaxation of the source problem</li>
            <li>it does not enlarge the feasible region.</li>
        </ul>
        If this is the case, all reductions made in the copy can be transferred to the
        original instance. The problem defining objects in SCIP are the constraint handlers and the variable pricers.
    </p>
    <p>
       A constraint handler may choose to not copy a constraint and still declare the resulting copy as valid. Therefore, it must ensure
       the feasibility of any solution to the problem copy in the original (source) space.
    </p>
