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.

内点法（interior-point method），尤其是割平面策略（cutting-plane strategy），现已成为优化领域中颇具研究价值的技术手段。割平面法的核心思路是通过移除那些显然无法取得最优解的点，切割可行域（feasible set）的一部分并逐步缩小其范围。本研究旨在提升一种新近提出的改进型割平面法在多目标优化问题（multi-objective optimization problems）中的收敛速度。该所提方法的优势体现在其能够快速缩小可行空间、强化最优解搜索流程，同时最大限度降低计算开销。此外，研究证明该方法可通过针对性地设置权重向量（weight vectors），在有效前沿（efficient frontier）上获得分布均匀的高效解。所开展的实验分析验证了所提方法的有效性，也为解决多目标优化难题提供了全新的、极具前景的研究视角。