A Review of Techniques for Handling Expensive Functions in Evolutionary Multi-Objective Optimization

Abstract

Abstract. Evolutionary algorithms have been very popular for solving multiobjective optimization problems, mainly because of their ease of use, and their wide applicability. However, multi-objective evolutionary algorithms (MOEAs) tend to consume an important number of objective function evaluations, in order to achieve a reasonably good approximation of the Pareto front. This is a major concern when attempting to use MOEAs for real-world applications, since we can normally afford only a fairly limited number of fitness function evaluations in such cases. Despite these concerns, relatively few efforts have been reported in the literature to reduce the computational cost of MOEAs. It has been until relatively recently, that researchers have developed techniques to achieve an effective reduction of fitness function evaluations by exploiting knowledge acquired during the search. In this chapter, we analyze different proposals currently available in the specialized literature to deal with expensive functions in evolutionary multi-objective optimization. Additionally, we review some real-world applications of these methods, which can be seen as case studies in which such techniques led to a substantial reduction in the computational cost of the MOEA adopted. Finally, we also indicate some of the potential paths for future research in this area.

A Surrogate-Assisted Reference Vector Guided Evolutionary Algorithm for Computationally Expensive Many-Objective Optimization

“…A surrogate is also known as a metamodel in the literature, which can in part replace the computationally expensive objective functions. For more details about SAEAs, see [9], [24], [43].…”

Evolutionary algorithms and other metaheuristics in water resources: Current status, research challenges and future directions

“…There are a number of reviews of the use of these techniques in optimisation, including Jin (2005) and Knowles and Nakayama (2008), as well as a dedicated edited volume on "Computational Intelligence in Expensive Optimization Problems" (Tenne and Goh, 2010) (in particular, reviews by Shi and Rasheed (2010) and Santana-Quintero et al (2010) therein). In addition, Razavi et al (2012) presented an extensive review of surrogate modelling in water resources and recent developments and applications to environmental systems are also presented in a special issue on "Emulation techniques for the reduction and sensitivity analysis of complex environmental models" (see Ratto et al, 2012).…”

“…There are two problems to consider with SM: (i) choosing the best method for building a SM with data generated by the exact model (see Santana-Quintero et al, 2010) and (ii) choosing or developing MOEA schemes (or restructuring existing ones) that are able to use a SM instead of the exact model in the most efficient way. This is what is called "metamodel-enabled optimizers" by Razavi et al (2012), and is referred to as SM-based optimisation (SMBO) algorithms (SMBOA) in this paper.…”

Controller tuning using evolutionary multi-objective optimisation: Current trends and applications

“…Therefore stochastic approaches could face a problem, given the complexity to evaluate the fitness (performance) of an individual (design alternative); it could affect their exploration capabilities and hence, slow down its convergence properties. A review on the topic can be consulted in [49].…”