# Hybridization of Interval CP and Evolutionary Algorithms for Optimizing Difficult Problems Source: [Hybridization of Interval CP and Evolutionary Algorithms for Optimizing Difficult Problems]() Collection index: [llms.txt]() Data updated: 2026-06-05T05:00:47.746Z Authors: Charlie Vanaret, Jean-Baptiste Gotteland, Nicolas Durand, Jean-Marc Alliot Published: 2015-10-16T15:18:42.000Z ## 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. ## Recorded benchmark results A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. - [Global Optimization on COCONUT (ex6\_2\_6)](): Global Optimization; COCONUT (ex6\_2\_6); Best Upper Bound: -0.000002603. - [Global Optimization on COCONUT (ex6\_2\_11)](): Global Optimization; COCONUT (ex6\_2\_11); Best Upper Bound: -0.000002673. - [Global Optimization on COCONUT ex2\_1\_7](): Global Optimization; COCONUT ex2\_1\_7; Best Upper Bound: -4150.410133929. - [Global Optimization on COCONUT (ex6\_2\_8)](): Global Optimization; COCONUT (ex6\_2\_8); Best Upper Bound: -0.02700635. - [Global Optimization on COCONUT ex6\_2\_9](): Global Optimization; COCONUT ex6\_2\_9; Best Upper Bound: -0.034066185. - [Global Optimization on COCONUT ex6\_2\_12](): Global Optimization; COCONUT ex6\_2\_12; Best Upper Bound: 0.28919474. - [Global Optimization on COCONUT ex7\_3\_5](): Global Optimization; COCONUT ex7\_3\_5; Best Upper Bound: 1.206716992. - [Constrained Optimization on COCONUT difficult constrained problems](): Constrained Optimization; COCONUT difficult constrained problems; Convergence Time (s): 0.2. - [Global Optimization on COCONUT (ex2\_1\_9)](): Global Optimization; COCONUT (ex2\_1\_9); Best Upper Bound: -0.3750000075. - [Global Optimization on COCONUT (ex7\_2\_3)](): Global Optimization; COCONUT (ex7\_2\_3); Best Upper Bound: 7049.248020529. - [Global Optimization on COCONUT (ex14\_1\_7)](): Global Optimization; COCONUT (ex14\_1\_7); Best Upper Bound: 1e-8. - [Global Optimization on COCONUT ex14\_2\_7](): Global Optimization; COCONUT ex14\_2\_7; Best Upper Bound: 8e-9. ## Original sources and implementation [Original paper]() [PDF]()