The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. ex. Some numerals are expressed as "XNUMX".
Copyrights notice
The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. Copyrights notice
이 논문은 조합 최적화에 대한 Petri net 기반 수학적 프로그래밍 접근 방식을 제안합니다. 여기서는 직접적인 수학적 공식 대신 Petri net 모델에서 정수 선형 계획법 문제를 생성합니다. 우리는 두 가지 유형의 조합 최적화 문제, 즉 일반적인 문제와 시간 종속 문제를 다룹니다. 먼저, 일반적인 최적화 문제에 대한 자율 페트리 넷 모델링을 제시합니다. 여기서는 페트리 넷 속성과 추가 문제별 속성에서 파생된 기본 제약 조건을 얻습니다. 둘째, 시간 종속 문제에 대한 컬러 시간 제한 페트리 넷 모델링 접근 방식을 제안합니다. 여기서 시간 관리 및 충돌 해결을 위한 변수와 제약 조건을 생성합니다. 우리의 Petri net 접근 방식은 (1) Petri net 모델링에는 수학적 프로그래밍과 정수 선형 모델 공식화 기술에 대한 깊은 지식이 필요하지 않으며, (2) 자동 공식화를 통해 다음을 생성할 수 있다는 점에서 수학적 공식화의 어려움을 대폭 줄일 수 있습니다. 대규모 정수 선형 계획법 문제 및 (3) Petri net 모델링 접근 방식은 원래 문제의 입력 매개변수 변경에 유연합니다.
Morikazu NAKAMURA
University of the Ryukyus
Takeshi TENGAN
Meio University
Takeo YOSHIDA
University of the Ryukyus
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부
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
부
@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},}
부
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 -