Pub Date : 2026-06-01Epub Date: 2026-01-20DOI: 10.1016/j.cor.2026.107407
Sabine Münch, Stephen Raach
We study the problem of maximizing a monotone increasing submodular function over a set of weighted elements subject to a knapsack constraint. Although this problem is NP-hard, some applications require exact solutions, as approximate solutions are often insufficient in practice. To address this need, we propose an exact branch-and-bound algorithm tailored for the submodular knapsack problem and introduce several acceleration techniques to enhance its efficiency. We evaluate these techniques on artificial instances of three benchmark problems as well as on instances derived from real-world data. We compare the proposed solver with two solvers by Sakaue and Ishihata (2018) as well as with a branch-and-cut algorithm implemented using Gurobi that solves a binary linear reformulation of the submodular knapsack problem, demonstrating that our methods are highly successful.
{"title":"An exact solver for submodular knapsack problems","authors":"Sabine Münch, Stephen Raach","doi":"10.1016/j.cor.2026.107407","DOIUrl":"10.1016/j.cor.2026.107407","url":null,"abstract":"<div><div>We study the problem of maximizing a monotone increasing submodular function over a set of weighted elements subject to a knapsack constraint. Although this problem is NP-hard, some applications require exact solutions, as approximate solutions are often insufficient in practice. To address this need, we propose an exact branch-and-bound algorithm tailored for the submodular knapsack problem and introduce several acceleration techniques to enhance its efficiency. We evaluate these techniques on artificial instances of three benchmark problems as well as on instances derived from real-world data. We compare the proposed solver with two solvers by Sakaue and Ishihata (2018) as well as with a branch-and-cut algorithm implemented using Gurobi that solves a binary linear reformulation of the submodular knapsack problem, demonstrating that our methods are highly successful.</div></div>","PeriodicalId":10542,"journal":{"name":"Computers & Operations Research","volume":"190 ","pages":"Article 107407"},"PeriodicalIF":4.3,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146186535","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This study addresses the Multi-Depot Periodic Capacitated Arc Routing Problem with Intermediate Facilities (MDPCARPIF), considering a fleet of homogenous vehicles. A novel optimization model is proposed to formulate the problem, minimizing the total cost of vehicle deployment and travelled distances. Due to the NP-hard nature of the problem, Adaptive Large Neighbourhood Search (ALNS) and Parallel Adaptive Large Neighbourhood Search (PALNS) are utilized to tackle large-sized instances. However, CPLEX solver/GAMS software is used to treat small-sized instances. The results demonstrate that in 7 out of 10 small-sized instances where the CPLEX solver obtains the optimal solution, both the ALNS and PALNS reach the optimal solution. In the remaining three instances, the proposed algorithms achieve average gaps of 0.83% and 0.53% relative to the optimal solutions, respectively. Furthermore, for 25 large-sized instances, the proposed algorithms attain average relative gaps of 1.75% and 0.05%, respectively, when compared to the best solution found across all algorithm runs. Considering the solution quality and computational time, the proposed PALNS algorithm reveals its acceptable applicability for real-world waste collection planning by municipal authorities.
{"title":"Multi-depot periodic capacitated arc routing problem with intermediate facilities for waste collection","authors":"Alireza Saberi , Mahdi Alinaghian , Mohammad Reza Asadi , Erfan Babaee Tirkolaee","doi":"10.1016/j.cor.2026.107412","DOIUrl":"10.1016/j.cor.2026.107412","url":null,"abstract":"<div><div>This study addresses the Multi-Depot Periodic Capacitated Arc Routing Problem with Intermediate Facilities (MDPCARPIF), considering a fleet of homogenous vehicles. A novel optimization model is proposed to formulate the problem, minimizing the total cost of vehicle deployment and travelled distances. Due to the NP-hard nature of the problem, Adaptive Large Neighbourhood Search (ALNS) and Parallel Adaptive Large Neighbourhood Search (PALNS) are utilized to tackle large-sized instances. However, CPLEX solver/GAMS software is used to treat small-sized instances. The results demonstrate that in 7 out of 10 small-sized instances where the CPLEX solver obtains the optimal solution, both the ALNS and PALNS reach the optimal solution. In the remaining three instances, the proposed algorithms achieve average gaps of 0.83% and 0.53% relative to the optimal solutions, respectively. Furthermore, for 25 large-sized instances, the proposed algorithms attain average relative gaps of 1.75% and 0.05%, respectively, when compared to the best solution found across all algorithm runs. Considering the solution quality and computational time, the proposed PALNS algorithm reveals its acceptable applicability for real-world waste collection planning by municipal authorities.</div></div>","PeriodicalId":10542,"journal":{"name":"Computers & Operations Research","volume":"190 ","pages":"Article 107412"},"PeriodicalIF":4.3,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146186537","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-06-01Epub Date: 2026-02-11DOI: 10.1016/j.cor.2026.107428
Alexandre Jesus , Arthur Corrêa , Miguel Vieira , Catarina Marques , Cristóvão Silva , Samuel Moniz
This paper introduces PRISMA, a hybrid multi-agent Deep Reinforcement Learning (DRL) framework for solving the Flexible Job-shop Scheduling Problem (FJSP). It uses Constraint Programming (CP) solutions to pretrain decentralized policies and to guide exploration during training. Although DRL can generate fast solutions for large combinatorial problems, it often fails to match the quality of optimization methods, motivating the integration with hybrid frameworks. The growing interest in embedding domain knowledge into learning algorithms has produced several hybrid formulations, yet their potential remains underexplored, particularly in multi-agent settings. PRISMA combines supervised and reinforcement learning within a multi-agent framework, where CP solutions are used to (i) learn expert decisions through imitation learning, and (ii) train an auxiliary network that guides DRL training via reward shaping. A shared graph network is adopted for transferring system-level knowledge into machine-level observations, enabling fast and consistent inference from enriched local embeddings. To the best of our knowledge, PRISMA introduces the first expert-derived guidance mechanism for the FJSP and is among the earliest to apply imitation learning within a multi-agent formulation. By combining both modules, it strengthens the bridge between optimization and learning-based methods, where such dual integrations remain scarce. Experimental results show faster convergence and higher solution quality than state-of-the-art DRL models. PRISMA achieves an average optimality gap of 6.74%, corresponding to a 50% relative improvement over the single-agent baseline, while reducing inference time. These findings reinforce the value of merging optimization accuracy with the flexibility of multi-agent DRL for efficient scheduling.
{"title":"Enhancing multi-agent deep reinforcement learning for flexible job-shop scheduling through constraint programming","authors":"Alexandre Jesus , Arthur Corrêa , Miguel Vieira , Catarina Marques , Cristóvão Silva , Samuel Moniz","doi":"10.1016/j.cor.2026.107428","DOIUrl":"10.1016/j.cor.2026.107428","url":null,"abstract":"<div><div>This paper introduces <em>PRISMA</em>, a hybrid multi-agent Deep Reinforcement Learning (DRL) framework for solving the Flexible Job-shop Scheduling Problem (FJSP). It uses Constraint Programming (CP) solutions to pretrain decentralized policies and to guide exploration during training. Although DRL can generate fast solutions for large combinatorial problems, it often fails to match the quality of optimization methods, motivating the integration with hybrid frameworks. The growing interest in embedding domain knowledge into learning algorithms has produced several hybrid formulations, yet their potential remains underexplored, particularly in multi-agent settings. <em>PRISMA</em> combines supervised and reinforcement learning within a multi-agent framework, where CP solutions are used to (i) learn expert decisions through imitation learning, and (ii) train an auxiliary network that guides DRL training via reward shaping. A shared graph network is adopted for transferring system-level knowledge into machine-level observations, enabling fast and consistent inference from enriched local embeddings. To the best of our knowledge, <em>PRISMA</em> introduces the first expert-derived guidance mechanism for the FJSP and is among the earliest to apply imitation learning within a multi-agent formulation. By combining both modules, it strengthens the bridge between optimization and learning-based methods, where such dual integrations remain scarce. Experimental results show faster convergence and higher solution quality than state-of-the-art DRL models. <em>PRISMA</em> achieves an average optimality gap of 6.74%, corresponding to a 50% relative improvement over the single-agent baseline, while reducing inference time. These findings reinforce the value of merging optimization accuracy with the flexibility of multi-agent DRL for efficient scheduling.</div></div>","PeriodicalId":10542,"journal":{"name":"Computers & Operations Research","volume":"190 ","pages":"Article 107428"},"PeriodicalIF":4.3,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146186541","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-06-01Epub Date: 2026-01-24DOI: 10.1016/j.cor.2026.107410
Zongxing He , Zeqiang Zhang , Shuai Chen , Yu Zhang , Silu Liu
Reasonable positions of material loading and unloading points are the key factors to reduce material handling costs and improve material efficiency in manufacturing workshops. In response to the assumption of overlapping material handling points in current loop layout studies, this study proposes a unidirectional loop layout problem that considers the positions of material handling points between facilities. A mixed-integer linear programming model is constructed with the optimization objective of minimizing material handling costs. Recognizing the computational complexity of solving the problem, an adaptive hybrid algorithm of genetic algorithm and simulated annealing algorithm is proposed to obtain a better layout for the large-scale problem. For the problem characteristics, an efficient encoding and decoding strategy is designed to generate good initial solutions at the initial stage of the algorithm. The genetic algorithm is improved by combining adaptive crossover, adaptive mutation and nested simulated annealing algorithm, and a double threshold stopping criterion is used to remove the number of redundant cycles to improve the performance of the proposed algorithm. Finally, the proposed algorithm is applied to solve some benchmark instances, and the results are analysed to verify the efficiency and stability of the proposed algorithm. And the proposed algorithm is successfully applied to the security door production workshop to provide an improved layout scheme.
{"title":"Mathematical modelling and an effective algorithm for unidirectional loop layout problem with fixed loading and unloading points","authors":"Zongxing He , Zeqiang Zhang , Shuai Chen , Yu Zhang , Silu Liu","doi":"10.1016/j.cor.2026.107410","DOIUrl":"10.1016/j.cor.2026.107410","url":null,"abstract":"<div><div>Reasonable positions of material loading and unloading points are the key factors to reduce material handling costs and improve material efficiency in manufacturing workshops. In response to the assumption of overlapping material handling points in current loop layout studies, this study proposes a unidirectional loop layout problem that considers the positions of material handling points between facilities. A mixed-integer linear programming model is constructed with the optimization objective of minimizing material handling costs. Recognizing the computational complexity of solving the problem, an adaptive hybrid algorithm of genetic algorithm and simulated annealing algorithm is proposed to obtain a better layout for the large-scale problem. For the problem characteristics, an efficient encoding and decoding strategy is designed to generate good initial solutions at the initial stage of the algorithm. The genetic algorithm is improved by combining adaptive crossover, adaptive mutation and nested simulated annealing algorithm, and a double threshold stopping criterion is used to remove the number of redundant cycles to improve the performance of the proposed algorithm. Finally, the proposed algorithm is applied to solve some benchmark instances, and the results are analysed to verify the efficiency and stability of the proposed algorithm. And the proposed algorithm is successfully applied to the security door production workshop to provide an improved layout scheme.</div></div>","PeriodicalId":10542,"journal":{"name":"Computers & Operations Research","volume":"190 ","pages":"Article 107410"},"PeriodicalIF":4.3,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146096064","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-06-01Epub Date: 2026-02-08DOI: 10.1016/j.cor.2026.107425
Zian Zhao , Hong Zhou , Jiepeng Wang , Boyan Nie
As a new service-oriented paradigm, cloud manufacturing (CMfg) virtualizes distributed manufacturing resources into services orchestrated via cloud platforms to fulfill individualized production demands. With the increasing need for mass customization and ever-shortening production cycles, higher flexibility and efficiency in CMfg resource assignment and task scheduling become particularly essential. Within this context, the integrated optimization of CMfg tasks planning and scheduling is receiving increased attention. Among the existing studies on this problem, however, it is usually assumed that either a single fixed routing or a predefined set of alternative process routes is given in advance, overlooking the possibility of gaining better solutions by optimizing the process routes in task planning with consideration of the resource heterogeneity and availability. Another common assumption is that the task is processed as a whole, which may result in lower scheduling flexibility. To address these issues, this paper integrates routing optimization with lot streaming scheduling at the sublot level, instead of task level, and incorporates two flexibility-enhancing mechanisms: variable sublots and intermingling. In dealing with the high solving complexity, a knowledge-based matheuristic driven by dueling Q-learning is proposed, in which eight MILP-based optimization strategies are designed, each targeting a core subproblem. A knowledge-based pruning strategy is elaborated for targeted improvement, while the dueling Q-learning mechanism adaptively guides the selection of MILP-based strategies. The effectiveness and efficiency of the proposed approach are verified through extensive experiments based on the Kim benchmark, with its practical applicability and advantages being demonstrated through a real-world industrial case.
{"title":"A knowledge-based matheuristic driven by dueling Q-learning for integrated task planning and lot-streaming scheduling in cloud manufacturing","authors":"Zian Zhao , Hong Zhou , Jiepeng Wang , Boyan Nie","doi":"10.1016/j.cor.2026.107425","DOIUrl":"10.1016/j.cor.2026.107425","url":null,"abstract":"<div><div>As a new service-oriented paradigm, cloud manufacturing (CMfg) virtualizes distributed manufacturing resources into services orchestrated via cloud platforms to fulfill individualized production demands. With the increasing need for mass customization and ever-shortening production cycles, higher flexibility and efficiency in CMfg resource assignment and task scheduling become particularly essential. Within this context, the integrated optimization of CMfg tasks planning and scheduling is receiving increased attention. Among the existing studies on this problem, however, it is usually assumed that either a single fixed routing or a predefined set of alternative process routes is given in advance, overlooking the possibility of gaining better solutions by optimizing the process routes in task planning with consideration of the resource heterogeneity and availability. Another common assumption is that the task is processed as a whole, which may result in lower scheduling flexibility. To address these issues, this paper integrates routing optimization with lot streaming scheduling at the sublot level, instead of task level, and incorporates two flexibility-enhancing mechanisms: variable sublots and intermingling. In dealing with the high solving complexity, a knowledge-based matheuristic driven by dueling Q-learning is proposed, in which eight MILP-based optimization strategies are designed, each targeting a core subproblem. A knowledge-based pruning strategy is elaborated for targeted improvement, while the dueling Q-learning mechanism adaptively guides the selection of MILP-based strategies. The effectiveness and efficiency of the proposed approach are verified through extensive experiments based on the Kim benchmark, with its practical applicability and advantages being demonstrated through a real-world industrial case.</div></div>","PeriodicalId":10542,"journal":{"name":"Computers & Operations Research","volume":"190 ","pages":"Article 107425"},"PeriodicalIF":4.3,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146186540","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-06-01Epub Date: 2026-01-30DOI: 10.1016/j.cor.2026.107415
Amir M. Fathollahi-Fard , Zhiwu Li
Redesigning a closed-loop supply chain (CLSC) network is essential for enhancing efficiency and resilience in high-growth industries such as the tire industry. A CLSC integrates forward and reverse flows, to create a complex network structure. This study formulates a mixed-integer programming model to support strategic and tactical decisions, including facility openings and closures and capacity reconfiguration, while ensuring balanced demand flow. To solve this complex network design problem efficiently, an adaptive large neighborhood search (ALNS) algorithm is developed, incorporating customized destruction–construction operators and linear relaxation. The algorithm’s performance is evaluated on 64 test instances of varying sizes and compared with an exact solver. Results show that the ALNS achieves optimal solutions for small to medium-sized cases and maintains average optimality gaps around 10% with high computational efficiency. Sensitivity analyses highlight the significant influence of redesign costs, capacity flexibility, and market demand on network structure and total cost. From a managerial perspective, the findings underscore the importance of investing in capacity expansion and flexible infrastructure to achieve a cost-effective resilient CLSC network design.
{"title":"Adaptive large neighborhood search algorithm for redesigning a closed-loop supply chain network considering capacity configurations","authors":"Amir M. Fathollahi-Fard , Zhiwu Li","doi":"10.1016/j.cor.2026.107415","DOIUrl":"10.1016/j.cor.2026.107415","url":null,"abstract":"<div><div>Redesigning a closed-loop supply chain (CLSC) network is essential for enhancing efficiency and resilience in high-growth industries such as the tire industry. A CLSC integrates forward and reverse flows, to create a complex network structure. This study formulates a mixed-integer programming model to support strategic and tactical decisions, including facility openings and closures and capacity reconfiguration, while ensuring balanced demand flow. To solve this complex network design problem efficiently, an adaptive large neighborhood search (ALNS) algorithm is developed, incorporating customized destruction–construction operators and linear relaxation. The algorithm’s performance is evaluated on 64 test instances of varying sizes and compared with an exact solver. Results show that the ALNS achieves optimal solutions for small to medium-sized cases and maintains average optimality gaps around 10% with high computational efficiency. Sensitivity analyses highlight the significant influence of redesign costs, capacity flexibility, and market demand on network structure and total cost. From a managerial perspective, the findings underscore the importance of investing in capacity expansion and flexible infrastructure to achieve a cost-effective resilient CLSC network design.</div></div>","PeriodicalId":10542,"journal":{"name":"Computers & Operations Research","volume":"190 ","pages":"Article 107415"},"PeriodicalIF":4.3,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146186536","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-06-01Epub Date: 2026-02-03DOI: 10.1016/j.cor.2026.107414
Yunfan Yang , Yuchuan Song , Qi Lei , Weifei Guo , Haoming Yu , Lianghua Fan
The flexible job shop scheduling problem with consistent sublots (FJSP-CS) is a typical lot streaming scheduling problem in the discrete production mode, which can effectively improve production efficiency by splitting appropriate sublots. In this paper, a knowledge-driven co-evolutionary algorithm (KDCA) is proposed to address FJSP-CS for minimizing makespan, based on a methodology combining heuristics and metaheuristics. Considering the characteristics of FJSP-CS, KDCA is designed based on genetic algorithm (GA) and gene expression programming (GEP), where GA is adopted to optimize the consistent lot-splitting problem, and GEP is adopted to evolve composite dispatching rules for addressing the scheduling problem. In KDCA, a hybrid initialization method based on chaotic mapping is designed to ensure the quality and diversity of the initial population. Then, a probabilistic model based on three quantifiable lot-splitting knowledge is established to guide the search process of KDCA. On this basis, knowledge-driven mutation and local search operators are designed to improve the local search capability. Additionally, a knowledge-driven catastrophe operator is developed to avoid premature convergence. Finally, numerical experiments based on widely used FJSP-CS instances are conducted to verify the effectiveness of the proposed operators and the superior performance of KDCA. Experimental results demonstrate that KDCA can obtain better solutions compared to several state-of-the-art algorithms in over 70% instances.
{"title":"Knowledge-driven co-evolutionary algorithm for flexible job shop scheduling problem with consistent sublots","authors":"Yunfan Yang , Yuchuan Song , Qi Lei , Weifei Guo , Haoming Yu , Lianghua Fan","doi":"10.1016/j.cor.2026.107414","DOIUrl":"10.1016/j.cor.2026.107414","url":null,"abstract":"<div><div>The flexible job shop scheduling problem with consistent sublots (FJSP-CS) is a typical lot streaming scheduling problem in the discrete production mode, which can effectively improve production efficiency by splitting appropriate sublots. In this paper, a knowledge-driven co-evolutionary algorithm (KDCA) is proposed to address FJSP-CS for minimizing makespan, based on a methodology combining heuristics and metaheuristics. Considering the characteristics of FJSP-CS, KDCA is designed based on genetic algorithm (GA) and gene expression programming (GEP), where GA is adopted to optimize the consistent lot-splitting problem, and GEP is adopted to evolve composite dispatching rules for addressing the scheduling problem. In KDCA, a hybrid initialization method based on chaotic mapping is designed to ensure the quality and diversity of the initial population. Then, a probabilistic model based on three quantifiable lot-splitting knowledge is established to guide the search process of KDCA. On this basis, knowledge-driven mutation and local search operators are designed to improve the local search capability. Additionally, a knowledge-driven catastrophe operator is developed to avoid premature convergence. Finally, numerical experiments based on widely used FJSP-CS instances are conducted to verify the effectiveness of the proposed operators and the superior performance of KDCA. Experimental results demonstrate that KDCA can obtain better solutions compared to several state-of-the-art algorithms in over 70% instances.</div></div>","PeriodicalId":10542,"journal":{"name":"Computers & Operations Research","volume":"190 ","pages":"Article 107414"},"PeriodicalIF":4.3,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146186538","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-06-01Epub Date: 2026-02-06DOI: 10.1016/j.cor.2026.107413
Muhammad Waqas Aslam , Zeqiang Zhang , Kaleem Ullah Qasim
In high stakes manufacturing sectors, facility layout design plays a crucial role in enhancing both efficiency and adaptability, particularly under the human centric framework of modern industrial systems. Traditional heuristic and constraint based approaches to the double row facility layout problem often fall short in addressing the continuous reconfigurations required in dynamic production environments. Multimodal Vision Large Language Models (VLLMs) have recently emerged as powerful tools that integrate visual and textual modalities, enabling machines to perceive, reason, and act more effectively. Advanced models such as CLIP, Claude, and GPT-4V demonstrate these capabilities. This paper proposes a novel framework for solving DRFLP using the CORTEX-V VLLM. Unlike conventional methods, our approach leverages zero-shot initialization spatial reasoning to interpret visual layouts, material flow matrices, and constraint sets generating optimized, constraint compliant configurations without task specific retraining. A key contribution lies in structured prompt engineering combined with tool augmented inference, facilitating iterative layout refinement. Our method achieves a 32.0% reduction in material handling cost from 27,381.79 to 18,616.66, within only three optimization iterations. By embedding operational constraints directly into the model’s reasoning process, the framework ensures both feasibility and efficiency. This work introduces a scalable, interpretable, and intelligent solution for facility planning, offering industrial engineers a practical tool for designing adaptive, next generation manufacturing systems.
{"title":"CORTEX-V: A cognitive reasoning toolkit for vision-based, cost-efficient layout optimization","authors":"Muhammad Waqas Aslam , Zeqiang Zhang , Kaleem Ullah Qasim","doi":"10.1016/j.cor.2026.107413","DOIUrl":"10.1016/j.cor.2026.107413","url":null,"abstract":"<div><div>In high stakes manufacturing sectors, facility layout design plays a crucial role in enhancing both efficiency and adaptability, particularly under the human centric framework of modern industrial systems. Traditional heuristic and constraint based approaches to the double row facility layout problem often fall short in addressing the continuous reconfigurations required in dynamic production environments. Multimodal Vision Large Language Models (VLLMs) have recently emerged as powerful tools that integrate visual and textual modalities, enabling machines to perceive, reason, and act more effectively. Advanced models such as CLIP, Claude, and GPT-4V demonstrate these capabilities. This paper proposes a novel framework for solving DRFLP using the CORTEX-V VLLM. Unlike conventional methods, our approach leverages zero-shot initialization spatial reasoning to interpret visual layouts, material flow matrices, and constraint sets generating optimized, constraint compliant configurations without task specific retraining. A key contribution lies in structured prompt engineering combined with tool augmented inference, facilitating iterative layout refinement. Our method achieves a 32.0% reduction in material handling cost from 27,381.79 to 18,616.66, within only three optimization iterations. By embedding operational constraints directly into the model’s reasoning process, the framework ensures both feasibility and efficiency. This work introduces a scalable, interpretable, and intelligent solution for facility planning, offering industrial engineers a practical tool for designing adaptive, next generation manufacturing systems.</div></div>","PeriodicalId":10542,"journal":{"name":"Computers & Operations Research","volume":"190 ","pages":"Article 107413"},"PeriodicalIF":4.3,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146186539","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-05-01Epub Date: 2026-01-21DOI: 10.1016/j.cor.2026.107397
Thomas Pammer , Markus Sinnl
The single row facility layout problem (SRFLP) is a well-studied NP-hard combinatorial optimization problem with applications in manufacturing and logistics systems. In the SRFLP, a set of facilities with lengths is given, as well as weights between each pair of facilities. The facilities must be arranged on a line, such that the sum of the weighted center-to-center distances is minimized. In this work, we introduce a novel matheuristic approach that integrates exact optimization into a metaheuristic framework based on simulated annealing to effectively solve large-scale SRFLP instances. Specifically, we propose the window approach matheuristic, which allows to solve subsegments of the layout to optimality using mixed-integer programming while preserving the ordering of facilities outside the window. To the best of our knowledge, this constitutes the first matheuristic approach specifically designed for the SRFLP. We evaluate the performance of our method on the widely-used benchmark instance sets from literature. The computational results demonstrate that our matheuristic improves the best-known solution values for 13 of 70 instances, and matches the best-known solution values for the remaining 57 instances, outperforming current state-of-the-art metaheuristics.
{"title":"A matheuristic for solving the single row facility layout problem","authors":"Thomas Pammer , Markus Sinnl","doi":"10.1016/j.cor.2026.107397","DOIUrl":"10.1016/j.cor.2026.107397","url":null,"abstract":"<div><div>The single row facility layout problem (SRFLP) is a well-studied NP-hard combinatorial optimization problem with applications in manufacturing and logistics systems. In the SRFLP, a set of facilities with lengths is given, as well as weights between each pair of facilities. The facilities must be arranged on a line, such that the sum of the weighted center-to-center distances is minimized. In this work, we introduce a novel matheuristic approach that integrates exact optimization into a metaheuristic framework based on simulated annealing to effectively solve large-scale SRFLP instances. Specifically, we propose the window approach matheuristic, which allows to solve subsegments of the layout to optimality using mixed-integer programming while preserving the ordering of facilities outside the window. To the best of our knowledge, this constitutes the first matheuristic approach specifically designed for the SRFLP. We evaluate the performance of our method on the widely-used benchmark instance sets from literature. The computational results demonstrate that our matheuristic improves the best-known solution values for 13 of 70 instances, and matches the best-known solution values for the remaining 57 instances, outperforming current state-of-the-art metaheuristics.</div></div>","PeriodicalId":10542,"journal":{"name":"Computers & Operations Research","volume":"189 ","pages":"Article 107397"},"PeriodicalIF":4.3,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146035849","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-05-01Epub Date: 2026-01-19DOI: 10.1016/j.cor.2025.107375
A. Fois , L. Insolia , L. Consolini , F. Laurini , M. Locatelli , M. Riani
Clusterwise Linear Regression (CLR) combines classical linear regression with cluster analysis to model heterogeneous data. It overcomes the limitations of a single global model by simultaneously partitioning the data points into distinct clusters and fitting each cluster separately. However, since the underlying point-to-cluster assignments are unknown, the estimation process typically leads to a computationally challenging combinatorial problem. In this work, we introduce a new reformulation of the CLR problem under Gaussian assumptions, and propose a probabilistic branch-and-bound algorithm called pclustreg. This algorithm gives, with high probability, solutions that are at least as good as the (unknown) ground truth in terms of log-likelihood, bridging the gap between existing likelihood-based heuristic and global methods. Moreover, by limiting the number of expanded nodes, it can also be used as an effective heuristic algorithm. We highlight the performance of pclustreg on both synthetic and real-world datasets, comparing it against the state-of-the-art likelihood-based heuristic method, and show that it achieves comparable or better results both in terms of solution accuracy and computing times.
{"title":"Clusterwise linear regression using a probabilistic branch and bound algorithm under Gaussianity","authors":"A. Fois , L. Insolia , L. Consolini , F. Laurini , M. Locatelli , M. Riani","doi":"10.1016/j.cor.2025.107375","DOIUrl":"10.1016/j.cor.2025.107375","url":null,"abstract":"<div><div>Clusterwise Linear Regression (CLR) combines classical linear regression with cluster analysis to model heterogeneous data. It overcomes the limitations of a single global model by simultaneously partitioning the data points into distinct clusters and fitting each cluster separately. However, since the underlying point-to-cluster assignments are unknown, the estimation process typically leads to a computationally challenging combinatorial problem. In this work, we introduce a new reformulation of the CLR problem under Gaussian assumptions, and propose a probabilistic branch-and-bound algorithm called <span>pclustreg</span>. This algorithm gives, with high probability, solutions that are at least as good as the (unknown) ground truth in terms of log-likelihood, bridging the gap between existing likelihood-based heuristic and global methods. Moreover, by limiting the number of expanded nodes, it can also be used as an effective heuristic algorithm. We highlight the performance of <span>pclustreg</span> on both synthetic and real-world datasets, comparing it against the state-of-the-art likelihood-based heuristic method, and show that it achieves comparable or better results both in terms of solution accuracy and computing times.</div></div>","PeriodicalId":10542,"journal":{"name":"Computers & Operations Research","volume":"189 ","pages":"Article 107375"},"PeriodicalIF":4.3,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146074708","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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