Petri net representation and reachability analysis of 0-1 integer linear programming problems

被引：4

作者：

Kodama, Akito ^{[1
]}

Nishi, Tatsushi ^{[1
]}

机构：

[1] Osaka Univ, Dept Syst Innovat, Div Math Sci Social Syst, Grad Sch Engn Sci, 1-3 Machikaneyama, Toyonaka, Osaka 5608531, Japan

来源：

INFORMATION SCIENCES | 2017年 / 400卷

关键词：

Discrete event systems; Petri net; 0-1 integer linear programming problem; Optimal transition firing sequence problems; Reachability analysis; AGV systems; AUTOMATED GUIDED VEHICLES; FLEXIBLE MANUFACTURING SYSTEMS; OPTIMAL SUPERVISORY CONTROL; DEADLOCK PREVENTION POLICY; DECOMPOSITION APPROACH; AGV SYSTEMS; AVOIDANCE; SIPHONS; MODEL;

D O I：

10.1016/j.ins.2017.03.014

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

In this paper, we investigate a general algorithm for converting the 0-1 integer linear programming problem (0-1IP) into an optimal transition firing sequence problem (OFSP) of a Petri net (PN). The general 0-1IP can be visualized graphically and then analyzed using the PN theory after application of our proposed conversion algorithm. The proposed algorithm is applied to a traveling salesman problem, a vehicle routing problem and an automated guided vehicles (AGV) routing problem. A PN reduction technique is employed to reduce the size of the PN. Valid inequalities are derived using reachability analysis of the converted PN model. These inequalities are imposed on the original 0-1IP. Computational results show that the total computational time for solving an AGVRP with the valid inequalities derived using the reachability analysis is significantly reduced. (C) 2017 Elsevier Inc. All rights reserved.

引用

页码：157 / 172

页数：16

共 50 条

[21] Nonlinear separation of data via mixed 0-1 Integer and Linear Programming
Kim, Kwangsoo
Ryoo, Hong Seo
APPLIED MATHEMATICS AND COMPUTATION, 2007, 193 (01) : 183 - 196
[22] 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
[23] An approximation algorithm for quadratic cost 0-1 mixed integer programming problems
Mukai, K
Tatsumi, K
Fukushima, M
ELECTRONICS AND COMMUNICATIONS IN JAPAN PART III-FUNDAMENTAL ELECTRONIC SCIENCE, 1999, 82 (06): : 9 - 17
[24] FURTHER COMMENTS ON APPLICATION OF 0-1 INTEGER PROGRAMMING TO MULTITARGET TRACKING PROBLEMS
LEHTOMAKI, NA
IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 1980, 25 (04) : 856 - 856
[25] Approximation algorithm for quadratic cost 0-1 mixed integer programming problems
Mukai, Kumiko
Tatsumi, Keiji
Fukushima, Masao
Electronics and Communications in Japan, Part III: Fundamental Electronic Science (English translation of Denshi Tsushin Gakkai Ronbunshi), 1999, 82 (06): : 9 - 16
[26] Finding sparse representation of quantized frame coefficients using 0-1 integer programming
Ryen, T
Aase, SO
Husoy, JH
ISPA 2001: PROCEEDINGS OF THE 2ND INTERNATIONAL SYMPOSIUM ON IMAGE AND SIGNAL PROCESSING AND ANALYSIS, 2001, : 541 - 544
[27] NONLINEAR MULTIPRODUCT CVP ANALYSIS WITH 0-1 MIXED INTEGER PROGRAMMING
TSAI, WH
LIN, TM
ENGINEERING COSTS AND PRODUCTION ECONOMICS, 1990, 20 (01): : 81 - 91
[28] 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
[29] 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):
[30] A 0-1 integer linear programming approach to schedule outages of nuclear power plants
Jost, V.
Savourey, D.
JOURNAL OF SCHEDULING, 2013, 16 (06) : 551 - 566

← 1 2 3 4 5 →