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          <h1 id="project_title">Constraint Relationships</h1>
          <h2 id="project_tagline">A utility library for constraint relationships on top of the MiniZinc/MiniSearch toolchain as well as native utils for JaCoP.</h2>

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          <p><a href="http://www.isse.uni-augsburg.de/"><img src="images/isse.png" style = "width: 150px; height: auto;"  alt="Constraint Relationships indicate priorities over constraints"></a></p>

        <h1>
<a id="what-are-constraint-relationships-about" class="anchor" href="#what-are-constraint-relationships-about" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>Optimization with Preferences</h1>

<p><img src="images/cr-o.png" style="float: right; margin: 10px; " alt="Constraint Relationships indicate priorities over constraints"></p>

<p>Many combinatorial optimization problems are conveniently expressed using a constraint-based modeling language. They are then solved by powerful constraint programming or mathematical programming solvers.</p>

<p>We provide support for over-constrained problems or problems where desirable properties can be modeled as optional (soft) constraints. Importance is expressed only by means of relations between constraints (see <a href="http://www.isse.uni-augsburg.de/software/constraint-relationships/constraint-relationships.pdf">this 1 slide</a> to get an idea). Our library extensions are built on top of <a href="http://www.minizinc.org/">MiniZinc</a> that facilitates modeling combinatorial optimization problems for various solvers. The library includes:</p>

<ul>
<li>Convenient expression of soft constraint problems using constraint relationships</li>
<li>Automatic translation to weighted CSP</li>
<li>Generic search heuristics</li>
<li>Consistency checks of the specified relationships</li>
</ul>

<h2>
<a id="quick-example" class="anchor" href="#quick-example" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>Quick Example</h2>

<pre><code>% A really simplistic over-constrained model
% X: {x,y,z} D_i = {1,2,3}, i in X
%    * c1: x + 1 = y 
%    * c2: z = y + 2
%    * c3: x + y &lt;= 3
% -------------------------------------------

% import libraries as bundle for a quick start
include "minisearch.mzn"; % include the search minisearch lite
include "soft_constraints/minisearch_bundle.mzn";

var 1..3: x; 
var 1..3: y;
var 1..3: z;

% read as "soft constraint c1 is satisfied iff x + 1 = y"
constraint x + 1 = y &lt;-&gt; satisfied[1];
constraint z = y + 2 &lt;-&gt; satisfied[2];
constraint x + y &lt;= 3 &lt;-&gt; satisfied[3];

% soft constraint data specific to this model
nScs = 3; % number of soft constraints

% Constraint Relationships: 
%    c1
%  c2  c3
% -----------------------------------------
% three soft constraints c1, c2, c3
%    c2 less imp than c1,
%    c3 less imp than c1,  

nCrEdges = 2;
crEdges = [| 2, 1 | 3, 1 |];

% uses a specific branch-and-bound search to perform optimization
solve 
:: seq_search( [
    % generic soft constraint search heuristic 
    int_search([satisfied[mostImpFirst[i]] | i in SOFTCONSTRAINTS], 
               input_order, indomain_max, complete),
    % problem-specific heuristic
    int_search([x,y,z], input_order, indomain_max, complete)] )


search time_limit(3000, strictlyBetterBAB(violatedScs)) /\ 
       if hasSol() then print() 
       else print("No solution found\n") endif;

output ["Obj: \(penSum) by violating {\(violatedScs) } : " ++
        " x -&gt; \(x), y  -&gt; \(y), z -&gt; \(z)"];
</code></pre>

<h2>
<a id="download-and-installation" class="anchor" href="#download-and-installation" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>Download and Installation</h2>

<h3>
<a id="quickest-start" class="anchor" href="#quickest-start" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>Quickest start:</h3>

<ol>
<li>Download and install the newest MiniZinc IDE version from <a href="http://www.minizinc.org/">http://www.minizinc.org/</a>
</li>
<li>Download <a href="http://www.isse.uni-augsburg.de/software/constraint-relationships/soft_constraints.zip">soft_constraints.zip</a> and unpack it</li>
<li>Locate the directory "./share/minizinc/std" of your MiniZinc installation</li>
<li>Copy the directory "soft_constraints" into "./share/minizinc/std"</li>
<li>Run the above code (smallexample_minizinc.mzn in <a href="http://www.isse.uni-augsburg.de/software/constraint-relationships/codeexamples.zip">codeexamples.zip</a>)</li>
</ol>

<h3>
<a id="slightly-slower-start" class="anchor" href="#slightly-slower-start" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>Slightly slower start:</h3>

<ol>
<li>Build MiniSearch according to the instructions at <a href="http://www.minizinc.org/minisearch/">MiniSearch</a>
</li>
<li>Download <a href="http://www.isse.uni-augsburg.de/software/constraint-relationships/soft_constraints.zip">soft_constraints.zip</a> and unpack it</li>
<li>Locate the directory "./share/minizinc/std" of your MiniSearch installation</li>
<li>Copy the directory "soft_constraints" into "./share/minizinc/std"</li>
<li>Run the above code (smallexample.mzn in <a href="http://www.isse.uni-augsburg.de/software/constraint-relationships/codeexamples.zip">codeexamples.zip</a>) to see custom search and variable ordering heuristics in action.</li>
</ol>

<h3>
<a id="after-starting" class="anchor" href="#after-starting" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>After starting:</h3>

<p>Have a look at these case studies to get a better idea. We will continously improve these pages, but for starters please refer to the slides.</p>

<ol>
<li><a href="http://www.isse.uni-augsburg.de/software/constraint-relationships/Case-Studies.zip">Case Studies</a></li>
<li><a href="images/step-by-step.zip"> Step-by-step conversion of a MiniZinc problem</a> </li>
<li>Language Features (coming soon)</li>
</ol>

<h2>
<a id="citing" class="anchor" href="#citing" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>Citing</h2>

<p>If you plan to use constraint relationships in your research, please consider citing </p>

<pre><code>
@INPROCEEDINGS{Schiendorfer13,
  author = {Alexander Schiendorfer and
            Jan-Philipp Steghöfer and
            Alexander Knapp and
            Florian Nafz and
            Wolfgang Reif},
  title = {{Constraint Relationships for Soft Constraints}},
  editor = {Max Bramer and
            Miltos Petridis},
  booktitle = {Proc. 33\textsuperscript{rd} SGAI Int. Conf.
               Innovative Techniques and Applications of Artificial Intelligence (AI'13)},
  publisher = {Springer},
  year = {2013},
  pages = {241-255},
  nolanguage = {English}
}

</code></pre>

<h2>
<a id="authors-and-contributors" class="anchor" href="#authors-and-contributors" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>Authors and Contributors</h2>

<ul>
<li>Alexander Schiendorfer (<a href="https://github.com/Alexander-Schiendorfer" class="user-mention">@Alexander-Schiendorfer</a>)</li>
<li>Alexander Knapp </li>
</ul>

<h2>
<a id="support-or-contact" class="anchor" href="#support-or-contact" aria-hidden="true"><span aria-hidden="true" class="octicon octicon-link"></span></a>Support or Contact</h2>

<p>For general information and support please contact <a href="https://github.com/Alexander-Schiendorfer" class="user-mention">@Alexander-Schiendorfer</a>. </p>
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