Augmented Lagrangian Weighted Chebyshev Method for Constrained Multiobjective Optimization

This document focuses primarily on addressing multi-objective optimization issues using an augmented Lagrange method to derive a set of non-dominated solutions. The proposed technique involves transforming the initial multiobjective optimization problem into a scalar parametric problem via the weighted Chebyshev approach. This transformed function is then applied within the augmented Lagrange framework. By adhering to well-defined assumptions, the algorithm’s initial output consists of feasible sequences that satisfy problem constraints. Moreover, the document establishes that any limit point of these sequences represents a Pareto optimal solution, indicating an optimal trade-off among diverse objectives. To practically execute the proposed algorithm, a dedicated secondary algorithm is introduced to solve the sub-problem within the primary algorithm. The second algorithm incorporates the Steepest Descent method and a Max-type non-monotone line search technique. The document presents results that validate the correct configuration of the linear search method in the second algorithm. Additionally, while adhering to rigorous assumptions, it is shown that any limit point produced by this second algorithm is a Pareto-critical point. To assess the method’s efficiency and performance, numerical validations are conducted by solving various test problems. The obtained numerical outcomes effectively demonstrate the algorithm’s competence in generating high-quality solutions for multiobjective optimization problems subject to constraints.