Difficulty Adjustable and Scalable Constrained Multi-objective Test Problem Toolkit
Zhun Fan, Wenji Li, Xinye Cai, Hui Li, Caimin Wei, Qingfu Zhang,, Kalyanmoy Deb, Erik D. Goodman

TL;DR
This paper introduces a flexible toolkit for creating constrained multi-objective optimization problems with adjustable difficulty levels, aiding the development and benchmarking of algorithms for real-world constrained scenarios.
Contribution
It proposes a classification scheme for problem difficulty and develops a scalable toolkit to generate customizable constrained multi-objective problems for research.
Findings
Different algorithms perform better on specific difficulty types.
The toolkit enables systematic evaluation of MOEAs on constrained problems.
Current algorithms have limitations in solving complex constrained scenarios.
Abstract
Multi-objective evolutionary algorithms (MOEAs) have progressed significantly in recent decades, but most of them are designed to solve unconstrained multi-objective optimization problems. In fact, many real-world multi-objective problems contain a number of constraints. To promote research on constrained multi-objective optimization, we first propose a problem classification scheme with three primary types of difficulty, which reflect various types of challenges presented by real-world optimization problems, in order to characterize the constraint functions in constrained multi-objective optimization problems (CMOPs). These are feasibility-hardness, convergence-hardness and diversity-hardness. We then develop a general toolkit to construct difficulty-adjustable and scalable CMOPs (DAS-CMOPs, or DAS-CMaOPs when the number of objectives is greater than three) with three types of…
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