{"title":"Augmented ɛ-constraint-based matheuristic methodology for Bi-objective production scheduling problems","authors":"Jiaxin Fan","doi":"10.1049/cim2.12120","DOIUrl":null,"url":null,"abstract":"<p>Matheuristic is an optimisation methodology that integrates mathematical approaches and heuristics to address intractable combinatorial optimisation problems, where a common framework is to insert mixed integer linear programming (MILP) models as local search functions for evolutionary algorithms. However, since a mathematical programming formulation only tries to find the solution with the best objective value, matheuristics are rarely adopted to multi-objective scenarios asking for a set of Pareto optimal solutions, for example, vehicle routing problems and production scheduling problems. In this situation, the <i>ɛ</i>-constraint, which transforms multi-objective problems into single-objective formulations by considering selected objectives as constraints, seems to be a promising approach. First, an augmented <i>ɛ</i>-constraint-based matheuristic methodology (<i>ɛ</i>-MH) is proposed to apply the idea of <i>ɛ</i>-constraint to embedded MILP models, so that Pareto fronts obtained by meta-heuristics can be further improved by solving a set of MILP models. Afterwards, four speed-up strategies are developed to alleviate the computational burden resulting from repeatedly solving mathematical formulations, which also imply preferable scenarios for taking advantages of the <i>ɛ</i>-MH. Finally, several real-world bi-objective scheduling problems are discussed to present potential applications for the proposed methodology.</p>","PeriodicalId":33286,"journal":{"name":"IET Collaborative Intelligent Manufacturing","volume":"6 4","pages":""},"PeriodicalIF":2.5000,"publicationDate":"2024-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1049/cim2.12120","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"IET Collaborative Intelligent Manufacturing","FirstCategoryId":"1085","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1049/cim2.12120","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"ENGINEERING, INDUSTRIAL","Score":null,"Total":0}
引用次数: 0
Abstract
Matheuristic is an optimisation methodology that integrates mathematical approaches and heuristics to address intractable combinatorial optimisation problems, where a common framework is to insert mixed integer linear programming (MILP) models as local search functions for evolutionary algorithms. However, since a mathematical programming formulation only tries to find the solution with the best objective value, matheuristics are rarely adopted to multi-objective scenarios asking for a set of Pareto optimal solutions, for example, vehicle routing problems and production scheduling problems. In this situation, the ɛ-constraint, which transforms multi-objective problems into single-objective formulations by considering selected objectives as constraints, seems to be a promising approach. First, an augmented ɛ-constraint-based matheuristic methodology (ɛ-MH) is proposed to apply the idea of ɛ-constraint to embedded MILP models, so that Pareto fronts obtained by meta-heuristics can be further improved by solving a set of MILP models. Afterwards, four speed-up strategies are developed to alleviate the computational burden resulting from repeatedly solving mathematical formulations, which also imply preferable scenarios for taking advantages of the ɛ-MH. Finally, several real-world bi-objective scheduling problems are discussed to present potential applications for the proposed methodology.
期刊介绍:
IET Collaborative Intelligent Manufacturing is a Gold Open Access journal that focuses on the development of efficient and adaptive production and distribution systems. It aims to meet the ever-changing market demands by publishing original research on methodologies and techniques for the application of intelligence, data science, and emerging information and communication technologies in various aspects of manufacturing, such as design, modeling, simulation, planning, and optimization of products, processes, production, and assembly.
The journal is indexed in COMPENDEX (Elsevier), Directory of Open Access Journals (DOAJ), Emerging Sources Citation Index (Clarivate Analytics), INSPEC (IET), SCOPUS (Elsevier) and Web of Science (Clarivate Analytics).