Do We Really Need to Use Constraint Violation in Constrained Evolutionary Multi-Objective Optimization?

TL;DR

This paper investigates whether constraint violation is essential in constrained evolutionary multi-objective optimization algorithms, especially when constraint functions are unknown, and finds that it may not be crucial for performance.

Contribution

The study develops variants of existing algorithms that replace constraint violation with a crisp value and evaluates their performance.

Findings

Performance is not significantly affected without using constraint violation.

Algorithms with crisp constraint values perform comparably to traditional methods.

Constraint violation may not be necessary in scenarios with unknown constraint formulations.

Abstract

Constraint violation has been a building block to design evolutionary multi-objective optimization algorithms for solving constrained multi-objective optimization problems. However, it is not uncommon that the constraint violation is hardly approachable in real-world black-box optimization scenarios. It is unclear that whether the existing constrained evolutionary multi-objective optimization algorithms, whose environmental selection mechanism are built upon the constraint violation, can still work or not when the formulations of the constraint functions are unknown. Bearing this consideration in mind, this paper picks up four widely used constrained evolutionary multi-objective optimization algorithms as the baseline and develop the corresponding variants that replace the constraint violation by a crisp value. From our experiments on both synthetic and real-world benchmark test problems, we find that the performance of the selected algorithms have not been significantly influenced when the constraint violation is not used to guide the environmental selection.