Constrained Multiobjective Optimization: Test Problem Construction and Performance Evaluations

Constrained multiobjective optimization abounds in practical applications and is gaining growing attention in the evolutionary computation community. Artificial test problems are critical to the progress in this research area. Nevertheless, many of them lack important characteristics, such as scalab...

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Vydáno v:IEEE transactions on evolutionary computation Ročník 25; číslo 1; s. 172 - 186
Hlavní autoři: Zhou, Yuren, Xiang, Yi, He, Xiaoyu
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York IEEE 01.02.2021
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Témata:
Algorithms
Benchmark testing
Constraint optimization
Constraints
Convergence
Evolutionary algorithms
Evolutionary computation
Hardness
Hyperspaces
local search
Maintenance engineering
multi/many-objective optimization
Multiple objective analysis
Optimization
Pareto optimization
Performance evaluation
Shape
ISSN:1089-778X, 1941-0026
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Shrnutí:Constrained multiobjective optimization abounds in practical applications and is gaining growing attention in the evolutionary computation community. Artificial test problems are critical to the progress in this research area. Nevertheless, many of them lack important characteristics, such as scalability and variable dependencies, which may be essential in benchmarking modern evolutionary algorithms. This article first proposes a new framework for constrained test problem construction. This framework splits a decision vector into position and distance variables and forces their optimal values to lie on a nonlinear hypersurface such that the interdependencies can be introduced among the position ones and among the distance ones individually. In this framework, two kinds of constraints are designed to introduce convergence-hardness and diversity-hardness, respectively. The first kind introduces infeasible barriers in approaching the optima, and at the same time, makes the position and distance variables interrelate with each other. The second kind restricts the feasible optimal regions such that different shapes of Pareto fronts can be obtained. Based on this framework, we construct 16 scalable and constrained test problems covering a variety of difficulties. Then, in the second part of this article, we evaluate the performance of some state of the art on the proposed test problems, showing that they are quite challenging and there is room for further enhancement of the existing algorithms. Finally, we discuss in detail the source of difficulties presented in these new problems.
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ISSN:1089-778X
1941-0026
DOI:10.1109/TEVC.2020.3011829