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

Ruiqing Sun, Dawei Feng, Sheng Qi, Xing Zhou, Lianghao Li, Bo Ding, Yijie Wang, Rui Wang, Huaimin Wang

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.

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

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.

Paper Structure

This paper contains 23 sections, 5 equations, 5 figures, 4 tables, 4 algorithms.

Table of Contents

  1. Introduction
  2. Related Works
  3. Single-Stage, Single-Task CMOEAs
  4. Multi-Stage, Single-Task CMOEAs
  5. Single-Stage, Multi-Task CMOEAs
  6. Multi-Stage, Multi-Task CMOEAs
  7. PROPOSED ALGORITHM
  8. Framework of RCCMO
  9. Key functions in RCCMO
  10. Update Probe
  11. Update Constraint-Specific Populations
  12. Determine Target Constraint and Priority
  13. Experimental Studies
  14. Experimental Settings
  15. Experimental Results
  16. ...and 8 more sections

Figures (5)

  • Figure 1: Three types of constraint priority situations based on their geometric relationships with the final CPF.
  • Figure 2: Flowchart of the proposed RCCMO
  • Figure 3: Working principle of Probe population: used to detect constraints that hinder the main population from further evolving towards the Pareto optimal direction.
  • Figure 4: A step-by-step example demonstrating the constraint prioritizing mechanism in RCCMO.
  • Figure 5: Comparison of the performance and running time of RCCMO under different interval parameter $V$.