A New Global Scalarization Method for Multiobjective Optimization with an Arbitrary Ordering Cone  

作　　者：El-Desouky Rahmo Marcin Studniarski 

机构地区：[1]Department of Mathematics, Faculty of Science, Taif University, Khurma, Kingdom of Saudi Arabia [2]Mathematics Department, Faculty of Science, Mansoura University, Mansoura, Egypt [3]Faculty of Mathematics and Computer Science, University of Lódé , Lódé , Poland

出　　处：《Applied Mathematics》2017年第2期154-163,共10页应用数学（英文）

摘　　要：We propose a new scalarization method which consists in constructing, for a given multiobjective optimization problem, a single scalarization function, whose global minimum points are exactly vector critical points of the original problem. This equivalence holds globally and enables one to use global optimization algorithms (for example, classical genetic algorithms with “roulette wheel” selection) to produce multiple solutions of the multiobjective problem. In this article we prove the mentioned equivalence and show that, if the ordering cone is polyhedral and the function being optimized is piecewise differentiable, then computing the values of a scalarization function reduces to solving a quadratic programming problem. We also present some preliminary numerical results pertaining to this new method.We propose a new scalarization method which consists in constructing, for a given multiobjective optimization problem, a single scalarization function, whose global minimum points are exactly vector critical points of the original problem. This equivalence holds globally and enables one to use global optimization algorithms (for example, classical genetic algorithms with “roulette wheel” selection) to produce multiple solutions of the multiobjective problem. In this article we prove the mentioned equivalence and show that, if the ordering cone is polyhedral and the function being optimized is piecewise differentiable, then computing the values of a scalarization function reduces to solving a quadratic programming problem. We also present some preliminary numerical results pertaining to this new method.

关 键 词：MULTIOBJECTIVE Optimization SCALARIZATION Function Generalized JACOBIAN VECTOR CRITICAL Point 

分 类 号：O1[理学—数学]