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

Akito Kodama, Tatsushi Nishi

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)157-172
Number of pages16
JournalInformation Sciences
Volume400-401
DOIs
Publication statusPublished - Aug 1 2017
Externally publishedYes

Keywords

  • 0–1 integer linear programming problem
  • AGV systems
  • Discrete event systems
  • Optimal transition firing sequence problems
  • Petri net
  • Reachability analysis

ASJC Scopus subject areas

  • Software
  • Control and Systems Engineering
  • Theoretical Computer Science
  • Computer Science Applications
  • Information Systems and Management
  • Artificial Intelligence

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