Ranking Constraints via Topological Dual-Directional Search in Evolutionary Multi-Objective Optimization

TL;DR

This paper introduces RCCMO, a novel evolutionary algorithm that prioritizes constraints based on their geometric roles to improve solutions for constrained multi-objective problems.

Contribution

RCCMO employs a geometric constraint prioritization and dual-directional search, significantly enhancing performance over existing algorithms in CMOPs.

Findings

RCCMO outperforms seven state-of-the-art algorithms on benchmark and real-world CMOPs.

The algorithm effectively identifies and exploits constraints that shape the Pareto front.

Specialized mechanisms accelerate convergence and reduce heuristic errors.

Abstract

Existing evolutionary algorithms for Constrained Multi-objective Optimization Problems (CMOPs) typically treat all constraints uniformly, overlooking their distinct geometric relationships with the true Constrained Pareto Front (CPF). In reality, constraints play different roles: some directly shape the final CPF, some create infeasible obstacles, while others are irrelevant. To exploit this insight, we propose a novel algorithm named RCCMO, which sequentially performs unconstrained exploration, single-constraint exploitation, and full-constraint refinement. The core innovation of RCCMO lies in a constraint prioritization method derived from these geometric insights, seamlessly coupled with a unique dual-directional search mechanism. Specifically, RCCMO first prioritizes constraints that constitute the final CPF, approaching them from the evolutionary direction (optimizing objectives) to locate the CPF directly shaped by single-constraint boundaries. Subsequently, for constraints that merely hinder the population's progress, RCCMO searches from the anti-evolutionary direction (targeting the infeasible boundaries where hindering constraints intersect with the CPF) to effectively discover how these constraints obstruct and form the final CPF. Meanwhile, irrelevant constraints are intentionally bypassed. Furthermore, a series of specialized mechanisms are proposed to accelerate the algorithm's execution, reduce heuristic misjudgments, and dynamically adjust search directions in real time. Extensive experiments on 5 benchmark test suites and 29 real-world CMOPs demonstrate that RCCMO significantly outperforms seven state-of-the-art algorithms.