A mixed 0-1 linear programming formulation for the exact solution of the minimum linear arrangement problem

被引：12
|
作者：
Amaral, Andre R. S. [1 ]
机构：
[1] Univ Fed Espirito Santo, Dept Informat, BR-29060900 Vitoria, ES, Brazil
来源：
OPTIMIZATION LETTERS | 2009年 / 3卷 / 04期
关键词：
Vertex ordering problems; Minimum linear arrangement; Integer programming; QUADRATIC ASSIGNMENT PROBLEM; ALGORITHM; LINEARIZATION; GRAPHS;
D O I：
10.1007/s11590-009-0130-0
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：
We are concerned with the exact solution of a graph optimization problem known as minimum linear arrangement (MinLA). Define the length of each edge of a graph with respect to a linear ordering of the graph vertices. Then, the MinLA problem asks for a vertex ordering that minimizes the sum of edge lengths. MinLA has several practical applications and is NP-Hard. We present a mixed 0-1 linear programming formulation of the problem, which led to fast optimal solutions for dense graphs of sizes up to n = 23.
引用
收藏
页码：513 / 520
页数：8
相关论文
共 50 条
  • [1] A mixed 0-1 linear programming formulation for the exact solution of the minimum linear arrangement problem
    André R. S. Amaral
    Optimization Letters, 2009, 3 : 513 - 520
  • [2] Continuous solution to linear 0-1 programming
    Li, Yan-Yan
    Li, Xing-Si
    Dalian Ligong Daxue Xuebao/Journal of Dalian University of Technology, 2009, 49 (02): : 299 - 302
  • [3] An improved integer linear programming formulation for the closest 0-1 string problem
    Arbib, Claudio
    Servilio, Mara
    Ventura, Paolo
    COMPUTERS & OPERATIONS RESEARCH, 2017, 80 : 94 - 100
  • [4] CONVERTING 0-1 POLYNOMIAL PROGRAMMING PROBLEM TO A 0-1 LINEAR PROGRAM
    GLOVER, F
    WOOLSEY, E
    OPERATIONS RESEARCH, 1974, 22 (01) : 180 - 182
  • [5] Linear programming for the 0-1 quadratic knapsack problem
    Billionnet, A
    Calmels, F
    EUROPEAN JOURNAL OF OPERATIONAL RESEARCH, 1996, 92 (02) : 310 - 325
  • [6] A 0-1 LINEAR-PROGRAMMING FORMULATION FOR SOLVING AN EQUIPMENT REPLACEMENT-PROBLEM
    BECTOR, CR
    HAWALESHKA, O
    GILL, A
    INTERNATIONAL JOURNAL OF SYSTEMS SCIENCE, 1992, 23 (12) : 2393 - 2399
  • [7] SEQUENTIAL APPROACH TO 0-1 LINEAR-PROGRAMMING PROBLEM
    CHRISTOFIDES, N
    TRYPIA, M
    SIAM JOURNAL ON APPLIED MATHEMATICS, 1976, 31 (02) : 271 - 285
  • [8] Adjacency Variables Formulation for the Minimum Linear Arrangement Problem
    Gueye, Serigne
    Michel, Sophie
    Moeini, Mahdi
    OPERATIONS RESEARCH AND ENTERPRISE SYSTEMS, ICORES 2014, 2015, 509 : 95 - 107
  • [9] Links between linear bilevel and mixed 0-1 programming problems
    Audet, C
    Hansen, P
    Jaumard, B
    Savard, G
    JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 1997, 93 (02) : 273 - 300
  • [10] Links between linear bilevel and mixed 0-1 programming problems
    Ecl. des Hautes Etudes Commerciales, GERAD, Département MQ, Montréal, Que., Canada
    不详
    J. Optim. Theory Appl., 2 (273-300):
12345