Solving Convex Multi-Objective Optimization Problems via a Capable Neural Network Scheme

Abstract

A neural network architecture is constructed to solve Convex Multi-objective Programming Problem (CMPP). By using the weighted sum method, a single-objective optimization problem related to the CMPP is formulated, in which the scalar objective is summation of weighted original objective functions. The Pareto Optimal Solution (POS) is given by using different values of weights. A neural network framework is then designed for solving the obtained convex problem. Based on employing Lyapunov theory, the proposed model is established to be stable in the sense of Lyapunov and it is globally convergent to an exact optimal solution of the convex programming problem with different values of weights. The computer simulations shows the feasibility and the efficiency of the suggested model.