DMS and MultiGLODS: black-box optimization benchmarking of two direct search methods on the bbob-biobj test suite

Direct Multisearch (DMS) and MultiGLODS are two derivative-free solvers for approximating the entire set of Pareto-optimal solutions of a multiobjective (blackbox) problem. They both follow the search/poll step approach of direct search methods, employ Pareto dominance to avoid aggregating objectives, and have theoretical limit guarantees. Although the original publications already compare the two algorithms empirically with a variety of multiobjective solvers, an analysis on their scaling behavior with dimension was missing. Here, we run the publicly available implementations on the bbob-biobj test suite of the COCO platform and by investigating their performances in more detail, observe (i) a small defect in the default initialization of DMS, (ii) for both algorithms a decrease in relative performance to other algorithms of the original studies (even matching the performance of random search for MultiGLODS in higher dimension), and (iii) consequently, an under-performance to previously untested stochastic solvers from the evolutionary computation field, especially when the dimension is higher.