On the occasion of the 5th anniversary of my doctoral defense in Toulouse (France), I finally completed the English translation of my dissertation, entitled “Hybridization of interval methods and evolutionary algorithms for solving difficult optimization problems“.
My rigorous solver Charibde combines an interval branch and contract algorithm with an evolutionary algorithm in a parallel fashion ; the two algorithms exchange bounds, solutions and domains via message passing, in order to intensify the pruning of the search space. Charibde proved competitive with interval-based solvers GlobSol, IBBA and Ibex on a subset of difficult COCONUT problems. I also provided new optimality results for highly multimodal problems for which few (even approximate) solutions are known. Finally, I presented the first numerical proof of optimality for the open Lennard-Jones problem with five atoms. State-of-the-art interval-based solvers did not converge within reasonable time, while exhaustive solvers BARON and Couenne produced erroneous results.