Surrogate Many Objective Optimization: Combining Evolutionary Search, $\epsilon$-Dominance and Connected Restarts

Abstract

Scaling multi-objective optimization (MOO) algorithms to handle many objectives is a significant computational challenge. This challenge exacerbates when the underlying objectives are computationally expensive, and solutions are desired within a limited number of expensive objective evaluations. A surrogate model-based optimization framework can be effective in MOO. However, most prior model-based algorithms are effective for 2–3 objectives. This study investigates the combined use of $\epsilon$-dominance, connected restarts and evolutionary search for efficient Many-objective optimization (MaOO). We built upon an existing surrogate-based evolutionary algorithm, GOMORS, and propose $\epsilon$-GOMORS, i.e., a surrogate-based iterative evolutionary algorithm that combines Radial Basis Functions and $\epsilon$-dominance-based evolutionary search, to propose new points for expensive evaluations in each algorithm iteration. Moreover, a novel connected restart mechanism is introduced to ensure that the optimization search does not get stuck in locally optimum fronts. $\epsilon$-GOMORS is applied to a few benchmark multi-objective problems and a watershed calibration problem, and compared against GOMORS, ParEGO, NSGA-III, Borg, $\epsilon$-NSGA-II and MOEA/D on a limited budget of 1000 evaluations. Results indicate that $\epsilon$-GOMORS converges more quickly than other algorithms and the variance of its performance across multiple trials, is also less than other algorithms.

This work was partially supported by the Singapore National Research Foundation, Prime Minister’s Office, Singapore under its Campus for Research Excellence and Technological Enterprise (CREATE) programme (E2S2-CREATE project CS-B) and by Prof. Shoemaker’s NUS startup grant.