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Optimizing energy efficiency in unrelated parallel machine scheduling problem through reinforcement learning

INFORMATION SCIENCES 2025年 693卷

作者： Bernal, Christian Perez Salido, Miguel A. Moya, Carlos March Univ Politecn Valencia Valencia Spain

The industrial sector plays a significant role in global energy consumption and greenhouse gas emissions. To reduce this environmental impact, it's crucial to implement energy-efficient manufacturing systems that utilize sustainable materials and optimize energy usage. This can lead to benefits such as reduced carbon footprints and cost savings. In recent years, metaheuristic approaches have been focused on minimizing energy consumption within the unrelated parallel machine scheduling problem (UPMSP). Traditional methods often overlook complex factors like release dates, due dates, and job setup times. This research introduces a novel algorithm that integrates reinforcement learning (RL) with a genetic algorithm (GA) to address this gap. The proposed RLGA algorithm, rooted in the dynamic field of evolutionary reinforcement learning, breaks down policies into smaller components to isolate essential parameters for problem-solving. Through comprehensive analysis, hyperparameters that influence optimal results are identified, facilitating automated hyperparameter selection and optimization. The expert system takes into account problem characteristics such as machine or job saturation, job overlap, and the maximum values of target variables, allowing instances to be grouped into clusters. These clusters are solved using a genetic algorithm with varying combinations of mutation and crossover hyperparameters. The most suitable approach for each cluster is determined by analyzing the results, and this configuration of hyperparameters is applied iteratively to optimize the solution search. The effectiveness of RLGA is evaluated across benchmark instances with different complexities, machine sets, jobs, and constraints. Comprehensive comparisons against existing methods highlight the superior performance and efficiency of RLGA in optimizing energy use and solution quality. Experimental results show that RLGA outperforms well-known solvers like CPO, CPLEX, OR-tools, and Gecode

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OPERATIONAL RESEARCH 2023年第3期23卷 46页

作者： Sarac, Tugba Ozcelik, Feristah Ertem, Mehmet Eskisehir Osmangazi Univ Eskisehir Turkiye

unrelated parallel machine scheduling problem (UPM) is widely studied in the scheduling literature because of its extensive application area in the industry. Since it has a stochastic nature, several studies handled the problem as stochastic. However, most of the studies that have considered the problem as stochastic focused only on the case of stochastic processing times. Whereas, especially in industries where setup times are sequence and machine-dependent, these are often stochastic, as well. Although this situation has been ignored in the literature for a long time, it has been examined only in a few studies. In this study, for the first time, an exact solution method is proposed to solve UPM with stochastic sequence-dependent setup times (SDSTs). For the considered problem, a two-stage stochastic programming method is proposed. A mathematical model and a genetic algorithm are developed for the stochastic problem. The effectiveness of the proposed solution approaches is demonstrated using randomly generated test problems. The test results demonstrate the importance of considering the SDSTs as stochastic.

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7th International Conference on Logistics and Supply Chain Management (LSCM)

作者： Arani, Mohammad Dastmard, Mousaalreza Momenitabar, Mohsen Liu, Xian Univ Arkansas Dept Syst Engn Little Rock AR 72204 USA Sapienza Univ Rome Lazio Dept Informat Engn Elect & Telecommun Rome Italy North Dakota State Univ Dept Transportat Logist & Finance Fargo ND 58105 USA

ISBN: (纸本)9783030897437;9783030897420

In this paper, we studied a real-world example of an unrelated parallel machine scheduling problem in which the Just-in-Time (JIT) inventory system, includingWork-in-Process and Finished Goods inventories, is the center of interest. The presented Simulated Annealing Algorithm tackling the combinatorial problem is a part of the expert and intelligent production system that assists a Decision Maker in perceiving his/her decision's outcome in advance. Precisely noted, the problem statement is novel since the integration of inventory systems (Work-in-Process and Finished Goods), and renewable and non-renewable resources engaged in manufacturing are taken into account. The undertaken manufacturing system could be attributed to the direct influence of the management strategy of the JIT inventory system not only to reduce the inventory level but also to minimize the earliness and tardiness cost responding to due dates. Moreover, the conventional parameters are reflected in the problem description and solution methodology. In conclusion, the results are remarkable in two terms, the first is to obtain better production planning in considerably less time, and secondly, a cost-benefit analysis tool to contrast the JIT approach with the earliest possible completion time criterion. Finally, possible research directions are suggested for future studies.

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Bi-objective unrelated parallel machine scheduling problem under availability and energy constraints 10

Bi-objective unrelated parallel machine scheduling problem u...

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10th International Conference on Control, Decision and Information Technologies (CoDIT)

作者： Touat, Meriem Benatchba, Karima Haned, Annis-Sahnoune Aghelinejad, Mohammad-Mohsen Univ Technol Troyes Comp Sci & Digital Soc LIST3N Troyes France Ecole Natl Super Informat ESI Lab Methodes Concept Syst LMCS Algiers Algeria

ISBN: (纸本)9798350373981;9798350373974

The objective of this study is to address a scheduling issue arising in production workshops, specifically dealing with unrelated parallel machine scheduling integrating flexible and periodic maintenance interventions. machines, while operational, consume varying amounts of energy based on their state: idle states consume less energy than active ones. Additionally, energy consumption is influenced by both the production job and the specific machine. Our goal is to minimize two functions: the first pertains to reducing production and maintenance earliness/tardiness, while the second focuses on minimizing energy consumption. To address this problem, a Mixed Integer Linear Program (MILP) is proposed. The epsilon-constrained method is employed for computing the Pareto front, and further adaptation involves applying the Multi-Objective Simulated Annealing algorithm (MOSA) to handle instances of substantial size. The proposed MILP model demonstrates the ability to accurately determine the Pareto front for up to 30 production jobs and 2 machines on literature benchmarks within a timeframe of less than 1 hour. Moreover, the computed metrics proves the effectiveness of the proposed MOSA.

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A bi-objective mathematical model for an unrelated parallel machine scheduling problem with job-splitting

JOURNAL OF THE FACULTY OF ENGINEERING AND ARCHITECTURE OF GA...

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JOURNAL OF THE FACULTY OF ENGINEERING AND ARCHITECTURE OF GAZI UNIVERSITY 2022年第4期37卷 2293-2307页

作者： Sarac, Tugba Tutumlu, Busra Eskisehir Osmangazi Univ Fac Engn & Architecture Ind Enginering Dept TR-26480 Eskisehir Turkey Kutahya Dumlupinar Univ Fac Engn Ind Enginering Deparment TR-43100 Kutahya Turkey

Studies dealing with parallel machine scheduling problems generally assume that jobs are not split. However, splitting of jobs can offer opportunities such as delivering the jobs on time or evenly distributing the jobs to the machines. In this study, two different multi-objective mathematical models are proposed for the unrelated parallel machine scheduling problem without and with job-splitting. The first model is for the unrelated parallel machine scheduling problem without job-splitting and it was developed based on the model proposed by Sarac and Tutumlu [1]. In the second model, in which the jobs can split, besides the machines to which the jobs will be assigned and their order, it is also determined how the jobs will split and in which ratios the jobs will be processed on which machines. The objectives of both models are to minimize the completion time of the last job and the number of machines to be used. Multi-objective models were transformed into a single-objective structure with the epsilon constraint method. Randomly generated test problems were solved with the proposed models using the GAMS/Cplex solver, and the results were compared. Considering the problems for which the optimum solution is obtained, the first model found a solution in an average of 85% less time than the model in the literature [1], and the second model shortens the completion time of the last job in an average of 14%. In addition, a mathematical heuristic algorithm is proposed for solving large-size problems.

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A mix integer programming model and solution approach to determine the optimum machine number in the unrelated parallel machine scheduling problem

JOURNAL OF THE FACULTY OF ENGINEERING AND ARCHITECTURE OF GA...

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JOURNAL OF THE FACULTY OF ENGINEERING AND ARCHITECTURE OF GAZI UNIVERSITY 2022年第1期37卷 329-345页

作者： Sarac, Tugba Tutumlu, Busra Eskisehir Osmangazi Univ Ind Engn Dept TR-26480 Eskisehir Turkey Kutahya Dumlupinar Univ Ind Engn Dept TR-43100 Kutahya Turkey

It is assumed that all machines will be used in studies dealing with parallel machine scheduling problems. However, for some businesses having special processes, where large furnaces with very intense energy consumption are used during commissioning, it can be very critical to complete jobs using the least number of furnaces. In addition, for many businesses, doing their jobs with fewer machines creates opportunities for unused machines to be rented to another company or to accept additional jobs as much as the capacity of idle machines. For this reason, in this study, the assumption that all machines will be used has been removed and a mathematical model has been proposed that will decide both which machines will be used and which jobs will be produced in which order on these machines, for the unrelated parallel machine scheduling problem with sequence and machine dependent setup times and machine eligibility restriction. The objectives of the considered problem are minimizing the number of machines to be used and the completion time of the last job. The objective functions of the proposed multi-objective mathematical model are scalarized using the weighted sum method. In order to show the solution performance of the mathematical model, randomly generated test problems were solved with GAMS / CPLEX. To solve the large problems, a local search algorithm and a genetic algorithm have been proposed due to the lack of feasible solutions with GAMS / CPLEX. In the large-scale problem, when all weight pairs are taken into account, genetic algorithm is more successful than local search algorithm an average of 25.64% in terms of solution quality and 50.31% in terms of time.

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A matheuristic algorithm for multi-objective unrelated parallel machine scheduling problem

JOURNAL OF THE FACULTY OF ENGINEERING AND ARCHITECTURE OF GA...

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JOURNAL OF THE FACULTY OF ENGINEERING AND ARCHITECTURE OF GAZI UNIVERSITY 2023年第3期38卷 1953-1966页

作者： Sarac, Tugba Ozcelik, Feristah Eskisehir Osmangazi Univ Fac Engn & Architecture Dept Ind Engn TR-26480 Eskisehir Turkiye

machine scheduling problems are one of the basic manufacturing problems. Thus, there are a lot of study in the literature. In most of these studies, the problem is considered as single objective. Although the single objective approach makes it easier to solve problems theoretically, it is often not possible to provide realistic solutions because almost all real-life problems have multi-objective properties. It is aimed to close this gap in the literature by using the multi-objective programming method that emerged as a powerful solution approach. The objectives are minimizing the makespan and minimizing the total tardiness. A matheuristic algorithm is developed for solving the considered problem. The performance of the algorithm is compared with the results of the augmented e-constraint method. With the proposed matheuristic algorithm, both a solution time advantage is obtained and dominant solutions that could not be obtained with the augmented e-constraint method are reached.

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Modified whale optimization algorithm for solving unrelated parallel machine scheduling problems

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SOFT COMPUTING 2021年第14期25卷 9545-9557页

作者： Al-qaness, Mohammed A. A. Ewees, Ahmed A. Abd Elaziz, Mohamed Wuhan Univ State Key Lab Informat Engn Surveying Mapping & R Wuhan 430079 Peoples R China Univ Bisha Dept E Syst Bisha 61922 Saudi Arabia Damietta Univ Dept Comp Dumyat 34511 Egypt Zagazig Univ Dept Math Fac Sci Zagazig 44519 Egypt Tomsk Polytech Univ Sch Comp Sci & Robot Tomsk Russia

unrelated parallel machine scheduling problem (UPMSP) with sequence-dependent setup times is considered a hot topic among the researchers, as it presents more complexity to be able to find an optimal solution. Many efforts have been made to solve UPMSP problems and established their performances. Therefore, in this study, a new method is introduced to address UPMSP problems with sequence-dependent and machine-dependent setup time. Our proposed method utilizes two meta-heuristic techniques, the whale optimization algorithm (WOA) and the firefly algorithm (FA), by combining their features to perform this task. The hybrid model is called WOAFA. For more detail, the operators of the FA are employed to improve the exploitation ability of the WOA by serving as a local search. Moreover, the quality of the proposed WOAFA method is tested by comparing with well-known meta-heuristic algorithms over six machines and six jobs, namely (2, 4, 6, 8, 10, and 12 machines) and (20, 40, 60, 80, 100, and 120 jobs).

关键词： Whale optimization algorithm Firefly algorithm Meta-heuristic unrelated parallel machine scheduling problem Local search

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Development of lower bounds for the scheduling of setup tasks in serial production lines

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EUROPEAN JOURNAL OF INDUSTRIAL ENGINEERING 2013年第5期7卷 558-576页

作者： Pessan, Cedric Neron, Emmanuel Haouari, Mohamed Univ Tours Polytech Tours Equipe Ordonnancement & Conduite Lab InformatERLCNRS 6305EA 2101 F-37200 Tours France Ecole Polytech Tunisie Combinatorial Optimizat Res Grp ROI La Marsa 2078 Tunisia Ozyegin Univ Dept Ind Engn Istanbul Turkey

Efficient production resettings are necessary to achieve production flexibility. For this reason, it is of primary importance to reduce the setup time required to switch the production from one product type to another, and more generally to minimise the loss of production during these resetting phases. In this paper, we investigate the problem of scheduling operations within a production resetting that arises at the ball bearing factories of the SKF group. In the case of full serial production lines, improving the setup times amount to minimising the time spent prior to restarting production. We show that the problem of scheduling operations within a production resetting can be modelled as an unrelated parallel machine scheduling problem, and we propose several lower bounds. The first one is an extension of the improved energetic reasoning to the unrelated parallel machine problem. The second one is based on a preemptive relaxation that includes valid inequalities. We report the results of computational experiments that were carried out on both industrial and generated instances and that provide evidence of the efficacy of the proposed lower bounds.

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A combined approach for analysing heuristic algorithms

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JOURNAL OF HEURISTICS 2019年第4-5期25卷 591-628页

作者： Corstjens, Jeroen Dang, Nguyen Depaire, Benoit Caris, An De Causmaecker, Patrick UHasselt Res Grp Logist Agoralaan B-3590 Diepenbeek Belgium Katholieke Univ Leuven CODeS Imec ITEC Etienne Sabbelaan 53 7659 B-8500 Kortrijk Belgium

When developing optimisation algorithms, the focus often lies on obtaining an algorithm that is able to outperform other existing algorithms for some performance measure. It is not common practice to question the reasons for possible performance differences observed. These types of questions relate to evaluating the impact of the various heuristic parameters and often remain unanswered. In this paper, the focus is on gaining insight in the behaviour of a heuristic algorithm by investigating how the various elements operating within the algorithm correlate with performance, obtaining indications of which combinations work well and which do not, and how all these effects are influenced by the specific problem instance the algorithm is solving. We consider two approaches for analysing algorithm parameters and components-functional analysis of variance and multilevel regression analysis-and study the benefits of using both approaches jointly. We present the results of a combined methodology that is able to provide more insights than when the two approaches are used separately. The illustrative case studies in this paper analyse a large neighbourhood search algorithm applied to the vehicle routing problem with time windows and an iterated local search algorithm for the unrelated parallel machine scheduling problem with sequence-dependent setup times.

关键词： Functional analysis of variance fANOVA Multilevel regression Algorithm performance Vehicle routing problem with time windows Large neighbourhood search Iterated local search unrelated parallel machine scheduling problem

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