title: Optimization algorithm for single objective, mixed integer, constrained programming?
body: <p>I have an optimization problem that can hardly be solved by analytic nor numeric solvers, as I'm not able to provide the derivatives for it. Therefore im looking for a solution using heuristic or genetic algorithms.</p>
  
  <p>My problem consists of the following:</p>
  
  <ul>
  <li>single objective</li>
  <li>large scale, but app. less than 10.000 variables</li>
  <li>mixed integer (MIP) (variables mainly decimals, a few are boolean/integer variables)</li>
  <li>constrained (variable-boundary constraints, equality and inequality constraints, app. the same amount as variables)</li>
  </ul>
  
  <p>So my questions are:</p>
  
  <ol>
  <li><p>Is there a paper that takes all the points into account (especially mixed integer programming) in a heuristic/genetic algorithm?</p></li>
  <li><p>Is there a good way to achieve mixed integer programming in a heuristic/genetic algorithm?</p></li>
  <li><p>How does one handle equality constraints in a heuristic/genetic algorithm the best way?</p></li>
  <li><p>Are there any (open source) libraries out there that could be promising?</p></li>
  </ol>
  
  <hr>
  
  <p>My expirience so far with my problem implementing in the <a href="http://moeaframework.org" rel="nofollow">MOEA-Framework</a> using the algorithmtypes <em>NSGAII</em> (and some of its derivatives) or a plain stupid random number generator is that, when using equality constraints or a MIP problem, the GA does not find a solution, even not when allowing alot of generations and a large populationsize for a really small problem.</p>