An Efficient Neuro-Dynamic Network for Constructing the Pareto Front of Convex Multiobjective Optimization Problems

Abstract

This article introduces an effective neural network model for addressing convex multiobjective optimization problems, developed using the Karush–Kuhn–Tucker optimality conditions for multiobjective optimization problems. The proposed model is shown to be stable in the sense of Lyapunov and globally convergent to efficient solutions of the original problem. Additionally, a novel algorithm is presented to achieve a uniform approximation of the Pareto frontier. The approach's validity and effectiveness are demonstrated through experimental multiobjective problems. For a thorough comparison with other methods, four metrics including purity, uniformity, coverage, and spacing indicators are used, focusing on the positioning of the non-dominated points. Extensive numerical tests highlight the proposed algorithm's substantial advantages.