Many-Objective Optimization with Limited Computing Budget

Abstract

Designers are increasingly being confronted with practical applications that require solution of optimization problems with more than three conflicting objectives. In recent years, a number of efficient algorithms have been proposed to deal with such problems, commonly referred to as many-objective optimization problems (MaOP). However, most such algorithms require evaluation of numerous solutions prior to convergence which may not be affordable for practical applications involving computationally expensive evaluations. While surrogates or approximations have long been used to deal with single-/multi-objective optimization problems involving expensive evaluations, they are not designed to deal with MaOPs which involve unique set of challenges. In this chapter, we introduce a surrogate-assisted optimization algorithm for many-objective optimization (SaMaO) which is capable of delivering converged and well distributed set of solutions within a limited computing budget. The proposed algorithm successfully combines features of state-of-the-art MaOPs and surrogate-assisted optimization strategies. The algorithm relies on principles of decomposition and adaption of reference vectors for effective search. The flexibility of function representation is offered through the use of multiple types of surrogate models. Furthermore, to efficiently deal with constrained MaOPs, marginally infeasible solutions are promoted during initial phases of the search. The performance of the proposed algorithm is objectively evaluated and compared with state-of-the-art approaches using three to ten objective DTLZ and WFG benchmarks, recently introduced minus DTLZ and minus WFG benchmarks and constrained C-DTLZ benchmarks. The results clearly highlight the competence of the proposed approach. The chapter also provides a summary of considerations that are important for practical applications and areas which need further development.