Karush-Kuhn-Tucker Optimality Based Local Search for Enhanced Convergence of Evolutionary Multi-Criterion Optimization Methods

Recent studies have used Karush-Kuhn-Tucker (KKT) optimality conditions to develop a KKT ProximityMeasure (KKTPM) for terminating amulti-objective optimization simulation run based on theoretical convergence of solutions. In addition to determining a suitable termination condition and due to their ability to provide a single measure for convergence to Pareto-optimal solutions, the developed KKTPM can also be applied more directly to enhance the performance of an optimization algorithm. In this paper, we integrate the KKTPM information with an evolutionary multi-objective optimization (EMO) algorithm to enhance its convergence properties to Pareto-optimal solutions. Specifically, we use KKTPM to identify poorly converged nondominated solutions in every generation and apply an achievement scalarizing function based local search procedure to improve their convergence. Simulations on both constrained and unconstrained multiple and many-objective optimization problems demonstrate that the hybrid algorithm significantly improves the overall convergence properties. This study brings evolutionary optimization closer to mainstream optimization field and should motivate researchers to utilize KKTPM measure further within EMO and other numerical optimization algorithms for improving their working behaviors.