Hybridization of Interval CP and Evolutionary Algorithms for Optimizing Difficult Problems

Abstract : The only rigorous approaches for achieving a numerical proof of optimality in global optimization are interval-based methods that interleave branching of the search-space and pruning of the subdomains that cannot contain an optimal solution. State-of-the-art solvers generally integrate local optimization algorithms to compute a good upper bound of the global minimum over each subspace. In this document, we propose a cooperative framework in which interval methods cooperate with evolutionary algorithms. The latter are stochastic algorithms in which a population of candidate solutions iteratively evolves in the search-space to reach satisfactory solutions. Within our cooperative solver Charibde, the evolutionary algorithm and the interval-based algorithm run in parallel and exchange bounds, solutions and search-space in an advanced manner via message passing. A comparison of Charibde with state-of-the-art interval-based solvers (GlobSol, IBBA, Ibex) and NLP solvers (Couenne, BARON) on a benchmark of difficult COCONUT problems shows that Charibde is highly competitive against non-rigorous solvers and converges faster than rigorous solvers by an order of magnitude.
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Submitted on : Thursday, June 25, 2015 - 11:47:33 AM
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Charlie Vanaret, Jean-Baptiste Gotteland, Nicolas Durand, Jean-Marc Alliot. Hybridization of Interval CP and Evolutionary Algorithms for Optimizing Difficult Problems. 21st International Conference on Principles and Practice of Constraint Programming (CP 2015), Aug 2015, Cork, Ireland. ⟨hal-01168096⟩

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