joint work with Cheikh Touré, Nikolaus Hansen, Dimo Brockhoff
We present a new multi-objective optimization solver, COMO-CMA-ES that aim at converging towards p points of the Pareto set solution of a multi-objective problem. Denoting n the search space dimension, the solver approaches the p × n-dimensional problem of finding p solutions maximizing the hypervolume by a dynamic subspace optimization. Each subspace optimization is performed with the CMA-ES solver. We show empirically that COMO-CMA-ES converges linearly on bi-convex-quadratic problems and that it has better performance than the MO-CMA-ES, NSGA-II and SMS-EMOA algorithms.
joint work with Sébastien Le Digabel, Jean Bigeon
Derivative-free multiobjective optimization involves the presence of two or more conflicting objective functions, considered as blackboxes for which no derivative information is available. This talk describes a new extension of the Mesh Adaptive Direct Search (MADS) algorithm, called MADMS. This algorithm keeps a list of non-dominated points which converges to the Pareto front. As for the single-objective MADS algorithm, this method is built around an optional search step and a poll step. Convergence results and promising computational experiments will be described.
joint work with Maria do Carmo Brás
Polynomial interpolation or regression models are an important tool in Derivative-free Optimization, acting as surrogates of the real function. In this work we propose the use of these models in a multiobjective framework, namely the one of Direct Multisearch. Previously evaluated points are used to build quadratic polynomial models, which are minimized in an attempt of generating nondominated points of the true function, defining a search step for the algorithm. We will detail the proposed methodology and report compelling numerical results, stating its competitiveness.