.png){kind=icon}
返回
Budgeting with bounded multiple-choice constraints
.png){kind=icon}
PRE
AI
DOI：10.1016/S0377-2217(99)00451-8.png)
.png){kind=icon}
原文求助.png){kind=icon}
分享.png){kind=icon}
收藏
摘要
En 中文
We consider a budgeting problem where a specified number of projects from some disjoint classes has to be selected such that the overall gain is largest possible, and such that the costs of the chosen projects do not exceed a fixed upper limit. The problem has several application in government budgeting, planning, and as relaxation from other combinatorial problems. It is demonstrated that the problem can be transformed to an equivalent multiple-choice knapsack problem through dynamic programming. A naive transformation however leads to a drastic increase in the number of variables, thus we propose an algorithm for the continuous problem based on Dantzig-Wolfe decomposition. A master problem solves a continuous multiple-choice knapsack problem knowing only some extreme points in each of the transformed classes. The individual subproblems find extreme points for each given direction, using a median search algorithm. An integer optimal solution is then derived by using the dynamic programming transformation to a multiple-choice knapsack problem for an expanding core. The individual classes are considered in an order given by their gradients, and the transformation to a multiple-choice knapsack problem is performed when needed. In this way, only a dozen of classes need to be transformed for standard instances from the literature. Computational experiments are presented, showing that the developed algorithm is orders of magnitude faster than a general LP/MIP algorithm. (C) 2001 Elsevier Science B.V. All rights reserved.
Keyword:
integer programming
Dantzig-Wolfe decomposition
dynamic programming
bounded multiple-choice knapsack problem
AI总结
对已上传原文的论文进行重点信息的提取，主要内容包括：简要概述、研究摘要、背景介绍、关键亮点、图文解析、展望与总结。
期刊
IF:
6
论文数:
2.2W
被引数:
6.4W
机构
暂无机构信息
.png){kind=icon}
