Abstract
Evolutionary multi-objective optimization aims to provide a representative subset of the Pareto front to decision makers. In practice, however, decision makers are usually interested in only a particular part of the Pareto front of the multi-objective optimization problem. This is particularly true when the number of objectives becomes large. Over the past decade, preference-based multi-objective optimization has attracted increasing attention from both academia and industry due to its significance in both theory and practice. Significant progress has been made in evolutionary multi-objective optimization and multi-criteria decision communities, although many open issues still remain to be addressed. This paper provides a concise review on preference-based multi-objective optimization, including various preference modeling methods and existing preference-based optimization methods, as well as a brief discussion of the main future challenges.
Highlights
Most real-world optimization problems in science, engineering and even daily life need to take into account multiple and often conflicting criteria [1,2]
A set of Pareto optimal solutions exists for the multi-objective optimization problems (MOPs) is descried in Eq (1), the set of x∗ is called as Pareto set (PS), and their corresponding objective vectors F(x∗) are called as Pareto front (PF)
It is helpful for decision markers (DMs) to make their decisions if the whole Pareto optimal set is already known, because the whole set can provide an overall picture of the distribution of Pareto optimal solutions
Summary
Most real-world optimization problems in science, engineering and even daily life need to take into account multiple and often conflicting criteria [1,2]. It was shown that Pareto-based MOEAs fail to solve manyobjective optimization problems (MaOPs) that are defined to be MOPs with more than three objectives [11], mainly due to the fact that the dominance comparison becomes less effective when the number of objectives increases for a limited population size [12]. Preferences can be involved in different stages of multi-objective optimization algorithms, and preferencebased optimization methods can be classified into three categories: a priori, interactive, and a posteriori methods [28] It is unclear which preferences are able to effectively incorporated into MOEAs, and in many cases the user does not have a clear preference when little knowledge about the problem is available.
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