Operator Preserving Optimum Method for Solving Multiobjective Optimization Problems

Abstract

In this work, we introduce an algorithm leveraging an optimality-preserving operator to address multi-objective optimization challenges. Following a comprehensive review of prior research, we formalize the methodology through an operator designed to retain optimal solutions in multi-objective settings without relying on scalarization techniques. Under explicitly stated conditions, we establish that all solutions produced by our framework correspond to Pareto optimal outcomes for the original problem. To validate the algorithm’s efficacy, we assess its performance using benchmark problems widely recognized in the literature. Quantitative metrics are employed to measure its behavior, and the results are bench marked against those of a prominent evolutionary algorithm, NSGA-II, serving as a reference standard.