Using the descent direction in a method of centres algorithm for solving multi-objective programming problems

Interior-point methods, particularly the cutting-plane strategy, have emerged as interesting techniques in optimization. The main idea of the cutting-plane method is to cut off parts of the feasible set and shrink it by removing the points where optimality is surely not attained. The aim of this study is to improve the convergence speed of a newly developed modified cutting-plane method for multi-objective optimization problems. The effectiveness of the proposed approach is emphasized by its ability rapidly to shrink the feasible space, strengthen the optimal solution search method, and at the same time minimize the computational overhead. Additionally, it is demonstrated that the method is capable of achieving well-distributed efficient solutions on the efficient frontier by purposefully assigning weight vectors. The experimental analysis carried out confirms the effectiveness of the suggested method and offers a new promising perspective for addressing multi-objective optimization challenges.