Multi Objective Optimization With Multiple Spatially Distributed Surrogates

Abstract

In engineering design optimization, evaluation of a single solution (design) often requires running one or more computationally expensive simulations. Surrogate assisted optimization (SAO) approaches have long been used for solving such problems, in which approximations/surrogates are used in lieu of computationally expensive simulations during the course of search. Existing SAO approaches often use the same type of approximation model to represent all objectives and constraints in all regions of the search space. The selection of a type of surrogate model over another is nontrivial and an a priori choice limits flexibility in representation. In this paper, we introduce a multiobjective evolutionary algorithm (EA) with multiple adaptive spatially distributed surrogates. Instead of a single global surrogate, local surrogates of multiple types are constructed in the neighborhood of each offspring solution and a multiobjective search is conducted using the best surrogate for each objective and constraint function. The proposed approach offers flexibility of representation by capitalizing on the benefits offered by various types of surrogates in different regions of the search space. The approach is also immune to illvalidation since approximated and truly evaluated solutions are not ranked together. The performance of the proposed surrogate assisted multiobjective algorithm (SAMO) is compared with baseline nondominated sorting genetic algorithm II (NSGAII) and NSGAII embedded with global and local surrogates of various types. The performance of the proposed approach is quantitatively assessed using several engineering design optimization problems. The numerical experiments demonstrate competence and consistency of SAMO.