A decomposition method for optimal firing sequence problems for first-order hybrid petri nets

Tatsushi Nishi; Kenichi Shimatani; Masahiro Inuiguchi

doi:10.1109/ICSMC.2009.5345896

A decomposition method for optimal firing sequence problems for first-order hybrid petri nets

Tatsushi Nishi, Kenichi Shimatani, Masahiro Inuiguchi

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

2 Citations (Scopus)

Abstract

In this paper, we propose a general decomposition method for transition firing sequence problems for first order hybrid Petri Nets. The optimal transition firing sequence problem for first-order hybrid Petri Nets is formulated as a mixed integer programming problem. We propose a Lagrangian relaxation method for solving optimal transition firing sequence problems. The hybrid Petri Net is decomposed into several subnets in which the optimal firing sequence for each subnet is easily solved. The optimality of solution can be evaluated by duality gap derived by Lagrangian relaxation method. The proposed method is applied to a small-scale example. Computational experiments demonstrate the validity of the proposed formulation.

Original language	English
Title of host publication	Proceedings 2009 IEEE International Conference on Systems, Man and Cybernetics, SMC 2009
Pages	2854-2859
Number of pages	6
DOIs	https://doi.org/10.1109/ICSMC.2009.5345896
Publication status	Published - 2009
Externally published	Yes
Event	2009 IEEE International Conference on Systems, Man and Cybernetics, SMC 2009 - San Antonio, TX, United States Duration: Oct 11 2009 → Oct 14 2009

Publication series

Name	Conference Proceedings - IEEE International Conference on Systems, Man and Cybernetics
ISSN (Print)	1062-922X

Conference

Conference	2009 IEEE International Conference on Systems, Man and Cybernetics, SMC 2009
Country/Territory	United States
City	San Antonio, TX
Period	10/11/09 → 10/14/09

Keywords

Decomposition
Firing sequence problem
First-order hybrid petri nets
Lagrangian relaxation
Optimization

ASJC Scopus subject areas

Electrical and Electronic Engineering
Control and Systems Engineering
Human-Computer Interaction

Access to Document

10.1109/ICSMC.2009.5345896

Cite this

Nishi, T., Shimatani, K., & Inuiguchi, M. (2009). A decomposition method for optimal firing sequence problems for first-order hybrid petri nets. In Proceedings 2009 IEEE International Conference on Systems, Man and Cybernetics, SMC 2009 (pp. 2854-2859). [5345896] (Conference Proceedings - IEEE International Conference on Systems, Man and Cybernetics). https://doi.org/10.1109/ICSMC.2009.5345896

A decomposition method for optimal firing sequence problems for first-order hybrid petri nets. / Nishi, Tatsushi; Shimatani, Kenichi; Inuiguchi, Masahiro.

Proceedings 2009 IEEE International Conference on Systems, Man and Cybernetics, SMC 2009. 2009. p. 2854-2859 5345896 (Conference Proceedings - IEEE International Conference on Systems, Man and Cybernetics).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Nishi, T, Shimatani, K & Inuiguchi, M 2009, A decomposition method for optimal firing sequence problems for first-order hybrid petri nets. in Proceedings 2009 IEEE International Conference on Systems, Man and Cybernetics, SMC 2009., 5345896, Conference Proceedings - IEEE International Conference on Systems, Man and Cybernetics, pp. 2854-2859, 2009 IEEE International Conference on Systems, Man and Cybernetics, SMC 2009, San Antonio, TX, United States, 10/11/09. https://doi.org/10.1109/ICSMC.2009.5345896

Nishi T, Shimatani K, Inuiguchi M. A decomposition method for optimal firing sequence problems for first-order hybrid petri nets. In Proceedings 2009 IEEE International Conference on Systems, Man and Cybernetics, SMC 2009. 2009. p. 2854-2859. 5345896. (Conference Proceedings - IEEE International Conference on Systems, Man and Cybernetics). doi: 10.1109/ICSMC.2009.5345896

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title = "A decomposition method for optimal firing sequence problems for first-order hybrid petri nets",

abstract = "In this paper, we propose a general decomposition method for transition firing sequence problems for first order hybrid Petri Nets. The optimal transition firing sequence problem for first-order hybrid Petri Nets is formulated as a mixed integer programming problem. We propose a Lagrangian relaxation method for solving optimal transition firing sequence problems. The hybrid Petri Net is decomposed into several subnets in which the optimal firing sequence for each subnet is easily solved. The optimality of solution can be evaluated by duality gap derived by Lagrangian relaxation method. The proposed method is applied to a small-scale example. Computational experiments demonstrate the validity of the proposed formulation.",

keywords = "Decomposition, Firing sequence problem, First-order hybrid petri nets, Lagrangian relaxation, Optimization",

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AB - In this paper, we propose a general decomposition method for transition firing sequence problems for first order hybrid Petri Nets. The optimal transition firing sequence problem for first-order hybrid Petri Nets is formulated as a mixed integer programming problem. We propose a Lagrangian relaxation method for solving optimal transition firing sequence problems. The hybrid Petri Net is decomposed into several subnets in which the optimal firing sequence for each subnet is easily solved. The optimality of solution can be evaluated by duality gap derived by Lagrangian relaxation method. The proposed method is applied to a small-scale example. Computational experiments demonstrate the validity of the proposed formulation.

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KW - First-order hybrid petri nets

KW - Lagrangian relaxation

KW - Optimization

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A decomposition method for optimal firing sequence problems for first-order hybrid petri nets

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Keywords

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