Derivative-Free Optimization: Lifting Single-Objective to Multi-Objective Algorithm

Abstract

Most of the derivative-free optimization (DFO) algorithms rely on a comparison function able to compare any pair of points with respect to a black-box objective function. Recently, new dedicated derivative-free optimization algorithms have emerged to tackle multi-objective optimization problems and provide a Pareto front approximation to the user. This work aims at reusing single objective DFO algorithms (such as Nelder-Mead) in the context of multi-objective optimization. Therefore we introduce a comparison function able to compare a pair of points in the context of a set of non-dominated points. We describe an algorithm, MOGEN, which initializes a Pareto front approximation composed of a population of instances of single-objective DFO algorithms. These algorithms use the same introduced comparison function relying on a shared Pareto front approximation. The different instances of single-objective DFO algorithms are collaborating and competing to improve the Pareto front approximation. Our experiments comparing MOGEN with the state-of the-art Direct Multi-Search algorithm on a large set of benchmarks shows the practicality of the approach, allowing to obtain high quality Pareto fronts using a reasonably small amount of function evaluations.