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A reliable hybrid solver for nonconvex optimization

Abstract : Nonconvex and highly multimodal optimization problems represent a challenge both for stochastic and deterministic global optimization methods. The former (metaheuristics) usually achieve satisfactory solutions but cannot guarantee global optimality, while the latter (generally based on a spatial branch and bound scheme [1], an exhaustive and non-uniform partitioning method) may struggle to converge toward a global minimum within reasonable time. The partitioning process is exponential in the number of variables, which prevents the resolution of large instances. The performances of the solvers even dramatically deteriorate when using reliable techniques, namely techniques that cope with rounding errors.In this paper, we present a fully reliable hybrid algorithm named Charibde (Cooperative Hybrid Algorithm using Reliable Interval-Based methods and Dierential Evolution) [2] that reconciles stochastic and deterministic techniques. An Evolutionary Algorithm (EA) cooperates with intervalbased techniques to accelerate convergence toward the global minimum and prove the optimality of the solution with user-defined precision. Charibde may be used to solve continuous, nonconvex, constrained or bound-constrained problems involving factorable functions.
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Charlie Vanaret, Jean-Baptiste Gotteland, Nicolas Durand, Jean-Marc Alliot. A reliable hybrid solver for nonconvex optimization. META’2014, 5th International Conference on Metaheuristics and Nature Inspired Computing, Oct 2014, Marrakech, Morocco. ⟨hal-01293547⟩

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