A Memetic Algorithm Assisted by an Adaptive Topology RBF Network and Variable Local Models for Expensive Optimization Problems

A common practice in modern engineering is that of simulation-driven optimization. This implies replacing costly and lengthy laboratory experiments with computer experiments, i.e. computationally-intensive simulations which model real world physics with high fidelity. Due to the complexity of such simulations a single simulation run can require up to several hours of CPU time of a high-performance computer [45, 56, 61]. With computer experiments the simulation-driven optimization process is cast as a nonlinear optimization problem having three distinct features: There is typically no analytic expression for the relation between inputs (candidate designs) and outputs, i.e. it is a black-box function. Each simulation run is expensive so only a small number (∼ 200) of runs can be made. The underlying real-world physics and/or numerical solution often yield an inputs– output landscape which is multimodal and nonsmooth. A promising approach to tackle such problems is the surrogate-assisted memetic optimization. A memetic algorithm combines an evolutionary algorithm (EA) with an efficient local search so as to obtain both efficient exploration and exploitation during the optimization search [21, 65]. A surrogate-model is a computationally cheaper mathematical approximation of the expensive objective function and is used during the optimization search in lieu of the expensive function [2, 45] (in some references the term metamodel is used synonymously while ‘surrogate-model’ is reserved for a lower-fidelity simulation [42, 87]). Thus, using surrogate-models circumvents the problem of simulation cost and allows evaluation of many candidate designs. In this study we propose a surrogate-assisted memetic algorithm which builds upon recent advances in computational intelligence and optimization [9, 53, 60, 83–85, 94]. The proposed algorithm aims to address four open issues: Obtaining a global model with a small generalization error is too expensive: analysis has shown the number of sites required to achieve a fixed generalization error grows exponentially with the problem dimension [79]. To avoid allocating all function evaluations to the global model we employ a combination of global and local surrogate-models to achieve an efficient optimization search. O pe n A cc es s D at ab as e w w w .ite ch on lin e. co m