A Novel Neural Network Model and Two New Algorithms for Solving Multiobjective Linear Optimization Problems

Abstract

In this article, the Pareto front of multiobjective linear optimization problems (MLOPs) is approximated via a new neural network (NN) model. Karush-Kuhn-Tucker (KKT) optimality conditions for multiobjective linear optimization problems are applied to construct this neural network model. Compared with the available models in the literature, the proposed approach employs the KKT optimality conditions of the main MLOP, not a scalarized problem related to the MLOP. The stability of the suggested NN model in the sense of Lyapunov, is proved. Also, it is shown that the proposed NN is globally convergent to an efficient solution of the main MLOP. Moreover, we present two algorithms to attain some nondominated points with equidistant distribution throughout the Pareto front of bi-objective and three-objective optimization problems. In the suggested algorithms we apply some filters to attain a uniform approximation of the Pareto front. Illustrative results are provided to clarify the validity and performance of the introduced model for different categories of MLOPs. Numerical results satisfy the presented theoretical aspects. In order to have a comparison with other methods, three indicators, including Hypervolume (HV), Spacing, and Even distribution (EV), are utilized. Finally, we apply the proposed idea for the sustainable development of a multinational company in automotive engineering.