The objective that freed me: a multi-objective local search approach for continuous single-objective optimization

Abstract

Single-objective continuous optimization can be challenging, especially when dealing with multimodal problems. This work sheds light on the effects that multi-objective optimization may have in the single-objective space. For this purpose, we examine the inner mechanisms of the recently developed sophisticated local search procedure SOMOGSA. This method solves multimodal single-objective continuous optimization problems based on first expanding the problem with an additional objective (e.g., a sphere function) to the bi-objective domain and subsequently exploiting local structures of the resulting landscapes. Our study particularly focuses on the sensitivity of this multiobjectivization approach w.r.t. (1) the parametrization of the artificial second objective, as well as (2) the position of the initial starting points in the search space. As SOMOGSA is a modular framework for encapsulating local search, we integrate Nelder–Mead local search as optimizer in the respective module and compare the performance of the resulting hybrid local search to its original single-objective counterpart. We show that the SOMOGSA framework can significantly boost local search by multiobjectivization. Hence, combined with more sophisticated local search and metaheuristics, this may help solve highly multimodal optimization problems in the future.

Analytical and Comparative Study for Optimization Problems

“…Specific techniques are only relevant to certain kinds of functions, such as uni-modal functions, with only one maximum (or minimum) within the parameter range under study. The function need not be continuous as a result [22]. An single-objective optimization (SOP) problem (SOPP) has an objective function of (f(x ⃗ )) that should be maximized or minimized and a number of the constraints (g(x ⃗ )).…”