Max-max, max-min, min-max and min-min knapsack problems with a parametric constraint

被引：0
|
作者：
Halman, Nir [1 ]
Kovalyov, Mikhail Y. [2 ]
Quilliot, Alain [3 ]
机构：
[1] Bar Ilan Univ, Ramat Gan, Israel
[2] Natl Acad Sci Belarus, United Inst Informat Problems, Minsk, BELARUS
[3] Univ Blaise Pascal, UMR CNRS 6158, LIMOS, Bat ISIMA,Campus Cezeaux,BP 125, F-63173 Aubiere, France
来源：
4OR-A QUARTERLY JOURNAL OF OPERATIONS RESEARCH | 2023年 / 21卷 / 02期
基金：
以色列科学基金会;
关键词：
Knapsack problems; Parametric optimization; Polynomial algorithm; FPTAS; ALGORITHMS; COMPLEXITY; FPTAS;
D O I：
10.1007/s10288-022-00509-1
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：
Max-max, max-min, min-max and min-min optimization problems with a knapsack-type constraint containing a single numerical parameter are studied. The goal is to present optimal solutions for all possible values of the parameter. Algorithms with O (n log n) and O (n(2)) running times are proposed for the problems with a fixed parameter and for the general problem, respectively, where n is the number of items to be packed into the knapsack. The latter algorithm determines optimal solution values for all values of the parameter in O (n log(2) n) time. The problem of deciding whether there exists a single optimal solution for all values of the numerical parameter is proved to be NP-complete.
引用
收藏
页码：235 / 246
页数：12
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