A survey on handling computationally expensive multiobjective optimization problems with evolutionary algorithms

Abstract

Evolutionary algorithms are widely used for solving multiobjective optimization problems but are often criticized because of a large number of function evaluations needed. Approximations, especially function approximations, also referred to as surrogates or metamodels are commonly used in the literature to reduce the computation time. This paper presents a survey of 45 different recent algorithms proposed in the literature between 2008-2016 to handle computationally expensive multiobjective optimization problems. Several algorithms are discussed based on what kind of an approximation such as problem, function or fitness approximation they use. Most emphasis is given to function approximation based algorithms. We also compare these algorithms based on different criteria such as metamodelling technique and evolutionary algorithm used, type and dimensions of the problem solved, handling constraints, training time and the type of evolution control. Furthermore, we identify and discuss some promising elements and major issues among algorithms in the literature related to using an approximation and numerical settings used. In addition, we discuss selecting an algorithm to solve a given computationally expensive mmultiobjective optimization problem based on the dimensions in both objective and decision spaces and the computation budget available.

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

“…As per the survey on computationally expensive multiobjective optimization problems [9], Kriging has been frequently used for surrogate techniques, mainly because it is able to deliver uncertainty information of the approximated values, which is very useful in managing surrogates [24]. In this work, we use uncertainty information from Kriging models to update the surrogates, which will be further discussed in the next section.…”

“…As pointed out in [9], little work has been reported on using SAEAs for solving computationally expensive problems having more than three objectives. During the years 2008-2015, only three algorithms [6], [38], [41] have been tested on multi-objective benchmark problems with more than three objectives.…”

“…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].…”

“…For this reason, the number of decision variables SAEAs have handled is by far up to 50. According to a recent survey [9], only seven SAEAs have been tested on optimization problems with more than 20 decision variables and six of them were benchmarks. Note that SAEAs using neural networks as the surrogate were tested on more than 20 variables, while SAEAs using Kriging models as the surrogate have been used to solve problems with up to eight decision variables.…”

On Constraint Handling in Surrogate-Assisted Evolutionary Many-Objective Optimization

“…Such problems are usually handled using surrogates, which are approximate functions that replace the computationally expensive ones. For overviews of surrogate-assisted evolutionary algorithms (SAEAs) for single and multiobjective optimization, see [1,2]. Surrogate-assisted evolutionary algorithms for many-objective optimization have not received much attention but recently a novel Kriging-assisted evolutionary algorithm for manyobjective optimization called K-RVEA [3] has been proposed.…”