An exact scalarization method with multiple reference points for bi-objective integer linear optimization problems

被引:4
|
作者
Aliano Filho, Angelo [1 ]
Moretti, Antonio Carlos [2 ]
Pato, Margarida Vaz [3 ,4 ]
de Oliveira, Washington Alves [5 ]
机构
[1] Fed Technol Univ Parana, Acad Dept Math, Apucarana, Brazil
[2] Univ Estadual Campinas, Inst Math Stat & Sci Computat, Campinas, Brazil
[3] Univ Lisbon, ISEG, Lisbon, Portugal
[4] Univ Lisbon, CMAFcIO, Lisbon, Portugal
[5] Univ Estadual Campinas, Sch Appl Sci, Limeira, Brazil
关键词
Bi-objective optimization problems; Integer linear optimization; Exact scalarization methods; NORMAL-BOUNDARY INTERSECTION; LOT-SIZING PROBLEM; PROGRAMMING APPROACH; CONSTRAINT METHOD; ALGORITHM; EFFICIENT; SET; APPROXIMATION; METAHEURISTICS; GENERATION;
D O I
10.1007/s10479-019-03317-9
中图分类号
C93 [管理学]; O22 [运筹学];
学科分类号
070105 ; 12 ; 1201 ; 1202 ; 120202 ;
摘要
This paper presents an exact scalarization method to solve bi-objective integer linear optimization problems. This method uses diverse reference points in the iterations, and it is free from any kind of a priori chosen weighting factors. In addition, two new adapted scalarization methods from literature and the modified Tchebycheff method are studied. Each one of them results in different ways to obtain the Pareto frontier. Computational experiments were performed with random real size instances of two special problems related to the manufacturing industry, which involve lot sizing and cutting stock problems. Extensive tests confirmed the very good performance of the new scalarization method with respect to the computational effort, the number of achieved solutions, the ability to achieve different solutions, and the spreading and spacing of solutions at the Pareto frontier.
引用
收藏
页码:35 / 69
页数:35
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