Hybridization of Interval CP and Evolutionary Algorithms for Optimizing Difficult Problems

TL;DR

This paper introduces Charibde, a hybrid solver combining interval methods and evolutionary algorithms, which significantly improves the efficiency of solving difficult global optimization problems.

Contribution

It presents a novel cooperative framework where interval and evolutionary algorithms work together in parallel, enhancing convergence speed and robustness.

Findings

Charibde outperforms state-of-the-art interval-based solvers.

Charibde converges faster than rigorous solvers by an order of magnitude.

The approach is highly competitive against non-rigorous solvers.

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.