Augmented ɛ-constraint-based matheuristic methodology for Bi-objective production scheduling problems

IF 2.5 Q2 ENGINEERING, INDUSTRIAL
Jiaxin Fan
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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.

Abstract Image

基于增量ɛ约束的双目标生产调度问题数学启发式方法论
数学启发式是一种优化方法,它整合了数学方法和启发式方法,以解决难以解决的组合优化问题,其中一个常见的框架是插入混合整数线性规划(MILP)模型,作为进化算法的局部搜索函数。然而,由于数学程序设计公式只试图找到目标值最佳的解决方案,因此在要求帕累托最优解集的多目标场景中,例如车辆路线问题和生产调度问题,很少采用数学启发式方法。在这种情况下,ɛ约束似乎是一种很有前途的方法,它通过将选定目标视为约束条件,将多目标问题转化为单目标问题。首先,提出了一种基于ɛ约束的增强型数学启发式方法(ɛ-MH),将ɛ约束的思想应用于嵌入式 MILP 模型,从而通过求解一组 MILP 模型,进一步改进元启发式得到的帕累托前沿。随后,研究人员提出了四种加速策略,以减轻重复求解数学公式所带来的计算负担,这也意味着利用ɛ-MH 优势的最佳方案。最后,讨论了几个现实世界中的双目标调度问题,介绍了所提方法的潜在应用。
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来源期刊
IET Collaborative Intelligent Manufacturing
IET Collaborative Intelligent Manufacturing Engineering-Industrial and Manufacturing Engineering
CiteScore
9.10
自引率
2.40%
发文量
25
审稿时长
20 weeks
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).
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