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<p>Constrained multi-objective optimization problems (CMOPs) frequently arise in real-world engineering tasks where multiple conflicting objectives must be optimized under complex feasibility conditions. This study introduces the ranking-based constrained multi-objective equilibrium optimizer (RB-CMOEO), an enhanced variant of the Equilibrium Optimizer designed for CMOPs. The algorithm integrates three complementary mechanisms: a composite ranking scheme combining objective performance, total Constraint Violation, and the Number of Violated Constraints; an adaptive penalty mechanism that dynamically adjusts constraint sensitivity during evolution; and a dual-archive strategy that maintains both feasible and near-feasible solutions to balance exploration and exploitation. The proposed algorithm is rigorously evaluated using two well-known benchmark suites, MW and LIR-CMOP, as well as 12 real-world constrained engineering problems (RCEPs). Performance is assessed through standard multi-objective indicators, including Hypervolume, Spacing, Spread, and Inverted Generational Distance, with statistical validation via the Friedman test. The proposed RB-CMOEO demonstrates superior performance, achieving up to <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(14.2\%\)</EquationSource> </InlineEquation> higher hypervolume, a <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(47.6\%\)</EquationSource> </InlineEquation> reduction in Spacing, and an <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(8.9\%\)</EquationSource> </InlineEquation> improvement in Spread compared to state-of-the-art algorithms, confirming its effectiveness in enhancing convergence and maintaining Pareto diversity across benchmark and RCEPs.</p>

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A constrained multi-objective equilibrium optimizer algorithm for constrained optimization problems

  • 期刊论文

  • 发表日期：

    2026年6月30日

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  • Fatemeh BahraniPour,
  • Mohammad Farshi,
  • Sepehr Ebrahimi Mood

摘要

Constrained multi-objective optimization problems (CMOPs) frequently arise in real-world engineering tasks where multiple conflicting objectives must be optimized under complex feasibility conditions. This study introduces the ranking-based constrained multi-objective equilibrium optimizer (RB-CMOEO), an enhanced variant of the Equilibrium Optimizer designed for CMOPs. The algorithm integrates three complementary mechanisms: a composite ranking scheme combining objective performance, total Constraint Violation, and the Number of Violated Constraints; an adaptive penalty mechanism that dynamically adjusts constraint sensitivity during evolution; and a dual-archive strategy that maintains both feasible and near-feasible solutions to balance exploration and exploitation. The proposed algorithm is rigorously evaluated using two well-known benchmark suites, MW and LIR-CMOP, as well as 12 real-world constrained engineering problems (RCEPs). Performance is assessed through standard multi-objective indicators, including Hypervolume, Spacing, Spread, and Inverted Generational Distance, with statistical validation via the Friedman test. The proposed RB-CMOEO demonstrates superior performance, achieving up to \(14.2\%\) higher hypervolume, a \(47.6\%\) reduction in Spacing, and an \(8.9\%\) improvement in Spread compared to state-of-the-art algorithms, confirming its effectiveness in enhancing convergence and maintaining Pareto diversity across benchmark and RCEPs.