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This paper proposes a Petri net based mathematical programming approach to combinatorial optimization, in which we generate integer linear programming problems from Petri net models instead of the direct mathematical formulation. We treat two types of combinatorial optimization problems, ordinary problems and time-dependent problems. Firstly, we present autonomous Petri net modeling for ordinary optimization problems, where we obtain fundamental constraints derived from Petri net properties and additional problem-specific ones. Secondly, we propose a colored timed Petri net modeling approach to time-dependent problems, where we generate variables and constraints for time management and for resolving conflicts. Our Petri net approach can drastically reduce the difficulty of the mathematical formulation in a sense that (1) the Petri net modeling does not require deep knowledge of mathematical programming and technique of integer linear model formulations, (2) our automatic formulation allows us to generate large size of integer linear programming problems, and (3) the Petri net modeling approach is flexible for input parameter changes of the original problem.

- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E102-A No.2 pp.389-398

- Publication Date
- 2019/02/01

- Publicized

- Online ISSN
- 1745-1337

- DOI
- 10.1587/transfun.E102.A.389

- Type of Manuscript
- Special Section PAPER (Special Section on Mathematical Systems Science and its Applications)

- Category

Morikazu NAKAMURA

University of the Ryukyus

Takeshi TENGAN

Meio University

Takeo YOSHIDA

University of the Ryukyus

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Morikazu NAKAMURA, Takeshi TENGAN, Takeo YOSHIDA, "A Petri Net Approach to Generate Integer Linear Programming Problems" in IEICE TRANSACTIONS on Fundamentals,
vol. E102-A, no. 2, pp. 389-398, February 2019, doi: 10.1587/transfun.E102.A.389.

Abstract: This paper proposes a Petri net based mathematical programming approach to combinatorial optimization, in which we generate integer linear programming problems from Petri net models instead of the direct mathematical formulation. We treat two types of combinatorial optimization problems, ordinary problems and time-dependent problems. Firstly, we present autonomous Petri net modeling for ordinary optimization problems, where we obtain fundamental constraints derived from Petri net properties and additional problem-specific ones. Secondly, we propose a colored timed Petri net modeling approach to time-dependent problems, where we generate variables and constraints for time management and for resolving conflicts. Our Petri net approach can drastically reduce the difficulty of the mathematical formulation in a sense that (1) the Petri net modeling does not require deep knowledge of mathematical programming and technique of integer linear model formulations, (2) our automatic formulation allows us to generate large size of integer linear programming problems, and (3) the Petri net modeling approach is flexible for input parameter changes of the original problem.

URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E102.A.389/_p

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@ARTICLE{e102-a_2_389,

author={Morikazu NAKAMURA, Takeshi TENGAN, Takeo YOSHIDA, },

journal={IEICE TRANSACTIONS on Fundamentals},

title={A Petri Net Approach to Generate Integer Linear Programming Problems},

year={2019},

volume={E102-A},

number={2},

pages={389-398},

abstract={This paper proposes a Petri net based mathematical programming approach to combinatorial optimization, in which we generate integer linear programming problems from Petri net models instead of the direct mathematical formulation. We treat two types of combinatorial optimization problems, ordinary problems and time-dependent problems. Firstly, we present autonomous Petri net modeling for ordinary optimization problems, where we obtain fundamental constraints derived from Petri net properties and additional problem-specific ones. Secondly, we propose a colored timed Petri net modeling approach to time-dependent problems, where we generate variables and constraints for time management and for resolving conflicts. Our Petri net approach can drastically reduce the difficulty of the mathematical formulation in a sense that (1) the Petri net modeling does not require deep knowledge of mathematical programming and technique of integer linear model formulations, (2) our automatic formulation allows us to generate large size of integer linear programming problems, and (3) the Petri net modeling approach is flexible for input parameter changes of the original problem.},

keywords={},

doi={10.1587/transfun.E102.A.389},

ISSN={1745-1337},

month={February},}

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TY - JOUR

TI - A Petri Net Approach to Generate Integer Linear Programming Problems

T2 - IEICE TRANSACTIONS on Fundamentals

SP - 389

EP - 398

AU - Morikazu NAKAMURA

AU - Takeshi TENGAN

AU - Takeo YOSHIDA

PY - 2019

DO - 10.1587/transfun.E102.A.389

JO - IEICE TRANSACTIONS on Fundamentals

SN - 1745-1337

VL - E102-A

IS - 2

JA - IEICE TRANSACTIONS on Fundamentals

Y1 - February 2019

AB - This paper proposes a Petri net based mathematical programming approach to combinatorial optimization, in which we generate integer linear programming problems from Petri net models instead of the direct mathematical formulation. We treat two types of combinatorial optimization problems, ordinary problems and time-dependent problems. Firstly, we present autonomous Petri net modeling for ordinary optimization problems, where we obtain fundamental constraints derived from Petri net properties and additional problem-specific ones. Secondly, we propose a colored timed Petri net modeling approach to time-dependent problems, where we generate variables and constraints for time management and for resolving conflicts. Our Petri net approach can drastically reduce the difficulty of the mathematical formulation in a sense that (1) the Petri net modeling does not require deep knowledge of mathematical programming and technique of integer linear model formulations, (2) our automatic formulation allows us to generate large size of integer linear programming problems, and (3) the Petri net modeling approach is flexible for input parameter changes of the original problem.

ER -