Pub Date : 2024-10-05DOI: 10.1016/j.cor.2024.106860
Clément Mommessin , Thomas Erlebach , Natalia V. Shakhlevich
Heuristics for Vector Bin Packing (VBP) play an important role in modern distributed computing systems and other applications aimed at optimizing the usage of multidimensional resources. In this paper we perform a systematic classification of heuristics for VBP, with the focus on construction heuristics. We bring together existing VBP algorithms and their tuning parameters, and propose new algorithms and new tuning parameters. For a less studied class of multi-bin algorithms, we explore their properties analytically, considering monotonic and anomalous behavior and approximation guarantees. For empirical evaluation, all algorithms are implemented as the Vectorpack library and assessed through extensive experiments. Our findings may serve as the basis for the development of more complex, hybrid algorithms, hyperheuristics and machine learning algorithms. The Vectorpack library can also be adjusted for addressing enhanced VBP problems with additional features, which arise in applications, especially those typical for modern distributed computing systems.
{"title":"Classification and evaluation of the algorithms for vector bin packing","authors":"Clément Mommessin , Thomas Erlebach , Natalia V. Shakhlevich","doi":"10.1016/j.cor.2024.106860","DOIUrl":"10.1016/j.cor.2024.106860","url":null,"abstract":"<div><div>Heuristics for Vector Bin Packing (VBP) play an important role in modern distributed computing systems and other applications aimed at optimizing the usage of multidimensional resources. In this paper we perform a systematic classification of heuristics for VBP, with the focus on construction heuristics. We bring together existing VBP algorithms and their tuning parameters, and propose new algorithms and new tuning parameters. For a less studied class of multi-bin algorithms, we explore their properties analytically, considering monotonic and anomalous behavior and approximation guarantees. For empirical evaluation, all algorithms are implemented as the <em>Vectorpack</em> library and assessed through extensive experiments. Our findings may serve as the basis for the development of more complex, hybrid algorithms, hyperheuristics and machine learning algorithms. The <em>Vectorpack</em> library can also be adjusted for addressing enhanced VBP problems with additional features, which arise in applications, especially those typical for modern distributed computing systems.</div></div>","PeriodicalId":10542,"journal":{"name":"Computers & Operations Research","volume":"173 ","pages":"Article 106860"},"PeriodicalIF":4.1,"publicationDate":"2024-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142441513","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-01DOI: 10.1016/j.cor.2024.106857
Vinicius Ferreira , Artur Pessoa , Thibaut Vidal
Influence propagation has been the subject of extensive study due to its important role in social networks, epidemiology, and many other areas. Understanding propagation mechanisms is critical to control the spread of fake news or epidemics. In this work, we study the problem of detecting the smallest group of users whose conversion achieves, through propagation, a certain influence level over the network, therefore giving valuable information on the propagation behavior in this network. We develop mixed integer programming algorithms to solve this problem. The core of our algorithm is based on new valid inequalities, cutting planes, and separation algorithms embedded into a branch-and-cut algorithm. We additionally introduce a light formulation relying on fewer variables than the literature formulations. Through extensive computational experiments, we observe that the proposed methods can optimally solve many previously-open benchmark instances, and otherwise achieve small optimality gaps. These experiments also provide various insights into the benefits of different mathematical formulations.
{"title":"Influence optimization in networks: New formulations and valid inequalities","authors":"Vinicius Ferreira , Artur Pessoa , Thibaut Vidal","doi":"10.1016/j.cor.2024.106857","DOIUrl":"10.1016/j.cor.2024.106857","url":null,"abstract":"<div><div>Influence propagation has been the subject of extensive study due to its important role in social networks, epidemiology, and many other areas. Understanding propagation mechanisms is critical to control the spread of fake news or epidemics. In this work, we study the problem of detecting the smallest group of users whose conversion achieves, through propagation, a certain influence level over the network, therefore giving valuable information on the propagation behavior in this network. We develop mixed integer programming algorithms to solve this problem. The core of our algorithm is based on new valid inequalities, cutting planes, and separation algorithms embedded into a branch-and-cut algorithm. We additionally introduce a light formulation relying on fewer variables than the literature formulations. Through extensive computational experiments, we observe that the proposed methods can optimally solve many previously-open benchmark instances, and otherwise achieve small optimality gaps. These experiments also provide various insights into the benefits of different mathematical formulations.</div></div>","PeriodicalId":10542,"journal":{"name":"Computers & Operations Research","volume":"173 ","pages":"Article 106857"},"PeriodicalIF":4.1,"publicationDate":"2024-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142445256","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 : 2024-09-28DOI: 10.1016/j.cor.2024.106854
Dario Bezzi , Andrea Corsini , Mauro Dell’Amico
In this work, we consider a real-life scheduling problem involving the production of off-road vehicles using a three-level assembly process, subject to precedence, machines, and resource constraints. This problem shares multiple characteristics with other scheduling problems such as the Parallel Machine Scheduling and Flexible Flow Shop Problems. However, it also comprises less investigated aspects such as a specific job precedence structure resulting in a directed rooted in-tree and a global resource constraint limiting the number of simultaneously active machines. We present a straightforward adaptation of a time-indexed mathematical formulation to the problem and introduce a new lower-bounding procedure. To solve the problem, we propose constructive heuristics based on classical priority rules and adaptations of job sequencing heuristics. We also propose CORE, a specialized approach tailored to leverage the problem structure. All the algorithms are extensively evaluated on two benchmark sets, various shop floor configurations, and eight real-life scenarios. Our results reveal the general effectiveness of job sequencing approaches and demonstrate the overall superiority of CORE.
{"title":"Lower and upper bounds for scheduling a real-life assembly problem with precedences and resource constraints","authors":"Dario Bezzi , Andrea Corsini , Mauro Dell’Amico","doi":"10.1016/j.cor.2024.106854","DOIUrl":"10.1016/j.cor.2024.106854","url":null,"abstract":"<div><div>In this work, we consider a real-life scheduling problem involving the production of off-road vehicles using a three-level assembly process, subject to precedence, machines, and resource constraints. This problem shares multiple characteristics with other scheduling problems such as the Parallel Machine Scheduling and Flexible Flow Shop Problems. However, it also comprises less investigated aspects such as a specific job precedence structure resulting in a directed rooted in-tree and a global resource constraint limiting the number of simultaneously active machines. We present a straightforward adaptation of a time-indexed mathematical formulation to the problem and introduce a new lower-bounding procedure. To solve the problem, we propose constructive heuristics based on classical priority rules and adaptations of job sequencing heuristics. We also propose CORE, a specialized approach tailored to leverage the problem structure. All the algorithms are extensively evaluated on two benchmark sets, various shop floor configurations, and eight real-life scenarios. Our results reveal the general effectiveness of job sequencing approaches and demonstrate the overall superiority of CORE.</div></div>","PeriodicalId":10542,"journal":{"name":"Computers & Operations Research","volume":"173 ","pages":"Article 106854"},"PeriodicalIF":4.1,"publicationDate":"2024-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142420292","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 : 2024-09-27DOI: 10.1016/j.cor.2024.106856
Jiaqi Wang , Bruce Golden , Jiří Mazurek
Pairwise comparisons constitute a fundamental part of many multiple-criteria decision-making methods designed to solve complex real-world problems. One of the pervasive features associated with the complexity of any problem is uncertainty. Experts are rarely able to consistently and accurately evaluate a set of alternatives under consideration due to time pressure, cognitive bias, the intricacy or intangible essence of the problem, a lack of requisite knowledge or experience, or other reasons. Interval pairwise comparisons (IPCs) allow for this uncertainty in a natural way; however, the problem of inconsistency (or infeasibility) may arise. That is, a set of interval comparisons may not allow experts to find a solution in the form of a priority vector. The aim of this paper is to provide a comparison of existing priority deriving methods for inconsistent (infeasible) IPCs via numerical examples and simulations. Our results indicate that the Interval Stretching Method is the best with respect to preserving original preferences. In addition, the question of the uniqueness of the solution is investigated for selected methods, with the Fuzzy Preference Programming method being the best in providing a unique solution. Since the majority of examined methods provide mostly non-unique solutions, modifying these methods in order to provide unique solutions might be a research direction worth considering in the future.
{"title":"Interval pairwise comparisons in the presence of infeasibilities: Numerical experiments","authors":"Jiaqi Wang , Bruce Golden , Jiří Mazurek","doi":"10.1016/j.cor.2024.106856","DOIUrl":"10.1016/j.cor.2024.106856","url":null,"abstract":"<div><div>Pairwise comparisons constitute a fundamental part of many multiple-criteria decision-making methods designed to solve complex real-world problems. One of the pervasive features associated with the complexity of any problem is uncertainty. Experts are rarely able to consistently and accurately evaluate a set of alternatives under consideration due to time pressure, cognitive bias, the intricacy or intangible essence of the problem, a lack of requisite knowledge or experience, or other reasons. Interval pairwise comparisons (IPCs) allow for this uncertainty in a natural way; however, the problem of inconsistency (or infeasibility) may arise. That is, a set of interval comparisons may not allow experts to find a solution in the form of a priority vector. The aim of this paper is to provide a comparison of existing priority deriving methods for inconsistent (infeasible) IPCs via numerical examples and simulations. Our results indicate that the Interval Stretching Method is the best with respect to preserving original preferences. In addition, the question of the uniqueness of the solution is investigated for selected methods, with the Fuzzy Preference Programming method being the best in providing a unique solution. Since the majority of examined methods provide mostly non-unique solutions, modifying these methods in order to provide unique solutions might be a research direction worth considering in the future.</div></div>","PeriodicalId":10542,"journal":{"name":"Computers & Operations Research","volume":"173 ","pages":"Article 106856"},"PeriodicalIF":4.1,"publicationDate":"2024-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142356815","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 : 2024-09-25DOI: 10.1016/j.cor.2024.106848
Juliette Gerbaux , Guy Desaulniers , Quentin Cappart
Bus scheduling in public transit consists in determining a set of bus schedules to cover a set of timetabled trips at minimum cost. This planning process has evolved recently with the advent of electric buses that introduce constraints related to vehicle autonomy and battery charging process. In particular, column-generation algorithms have regained popularity for solving problems similar to the one considered in this paper, namely, the multi-depot electric vehicle scheduling problem (MDEVSP) with a piecewise linear charging function and capacitated charging stations. To tackle large-scale MDEVSP instances, we design a column generation (CG) heuristic that relies on reduced-sized networks to generate the bus schedules. The reduction is achieved by selecting a priori a subset of the arcs. Multiple selection techniques are studied: some are based on a greedy heuristic and others exploit a supervised learning algorithm relying on a graph neural network. It turns out that combining both selection types yields the best computational results. On 405 artificial instances involving between 568 and 1474 trips and generated from real bus lines in Montreal, the network reduction technique produced an average computational time reduction of 71.6% (compared to the same CG heuristic but without network reduction), while deteriorating solution cost by an average of 2.2%. On 8 larger instances containing more than 2500 trips on average, the proposed solution method also provided an average time saving of 52.5% with an average gap of 4.2% thanks to a transfer learning approach.
{"title":"A machine-learning-based column generation heuristic for electric bus scheduling","authors":"Juliette Gerbaux , Guy Desaulniers , Quentin Cappart","doi":"10.1016/j.cor.2024.106848","DOIUrl":"10.1016/j.cor.2024.106848","url":null,"abstract":"<div><div>Bus scheduling in public transit consists in determining a set of bus schedules to cover a set of timetabled trips at minimum cost. This planning process has evolved recently with the advent of electric buses that introduce constraints related to vehicle autonomy and battery charging process. In particular, column-generation algorithms have regained popularity for solving problems similar to the one considered in this paper, namely, the multi-depot electric vehicle scheduling problem (MDEVSP) with a piecewise linear charging function and capacitated charging stations. To tackle large-scale MDEVSP instances, we design a column generation (CG) heuristic that relies on reduced-sized networks to generate the bus schedules. The reduction is achieved by selecting a priori a subset of the arcs. Multiple selection techniques are studied: some are based on a greedy heuristic and others exploit a supervised learning algorithm relying on a graph neural network. It turns out that combining both selection types yields the best computational results. On 405 artificial instances involving between 568 and 1474 trips and generated from real bus lines in Montreal, the network reduction technique produced an average computational time reduction of 71.6% (compared to the same CG heuristic but without network reduction), while deteriorating solution cost by an average of 2.2%. On 8 larger instances containing more than 2500 trips on average, the proposed solution method also provided an average time saving of 52.5% with an average gap of 4.2% thanks to a transfer learning approach.</div></div>","PeriodicalId":10542,"journal":{"name":"Computers & Operations Research","volume":"173 ","pages":"Article 106848"},"PeriodicalIF":4.1,"publicationDate":"2024-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142326590","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-24DOI: 10.1016/j.cor.2024.106855
Chuangfeng Zeng, Jianjun Liu, Qinsong Li
Production and distribution are both crucial components of supply chains. Integrated production and distribution scheduling (IPDS) in the context of flexible assembly flow shop scheduling and batch delivery problems is often overlooked. A realistic problem inspired by the production and distribution processes of a dishwasher factory can be modeled as a resource-constrained flexible assembly flow shop scheduling problem with batch direct delivery (RCFAFSP-BDD). In this problem, order requirements are decomposed into several production tasks processed at different stages of the workshop, and are then delivered in batches via a third-party logistics provider to regional distributors at various locations. Auxiliary resource restrictions, hierarchical coupling constraints, machine eligibility restrictions and sequence-dependent setup times, are incorporated into the problem as operational constraints. To the best of our knowledge, this is the first attempt to solve this problem. This work formulates a mixed-integer linear programming (MIP) model to minimize total costs, including tardiness, inventory, and delivery costs. Given the problem’s strong NP-hard nature, the focus is on developing an efficient solution approach using constraint programming (CP). A CP model is proposed and enhanced with multiple redundant constraints. To reduce runtime, two branching strategies are designed for the CP model. Numerical experiments with varying instance scales reveal that the proposed CP model outperforms the MIP model in accuracy and efficiency within the given time limit. The redundant constraints and search strategy can reduce CP model runtime by up to 263.83%. Compared to manual scheduling at the studied factory, the CP model can cut costs by up to 26.59% for real data, offering viable alternatives for factory planners.
{"title":"A constraint programming approach for resource-constrained flexible assembly flow shop scheduling problem with batch direct delivery","authors":"Chuangfeng Zeng, Jianjun Liu, Qinsong Li","doi":"10.1016/j.cor.2024.106855","DOIUrl":"10.1016/j.cor.2024.106855","url":null,"abstract":"<div><div>Production and distribution are both crucial components of supply chains. Integrated production and distribution scheduling (IPDS) in the context of flexible assembly flow shop scheduling and batch delivery problems is often overlooked. A realistic problem inspired by the production and distribution processes of a dishwasher factory can be modeled as a resource-constrained flexible assembly flow shop scheduling problem with batch direct delivery (RCFAFSP-BDD). In this problem, order requirements are decomposed into several production tasks processed at different stages of the workshop, and are then delivered in batches via a third-party logistics provider to regional distributors at various locations. Auxiliary resource restrictions, hierarchical coupling constraints, machine eligibility restrictions and sequence-dependent setup times, are incorporated into the problem as operational constraints. To the best of our knowledge, this is the first attempt to solve this problem. This work formulates a mixed-integer linear programming (MIP) model to minimize total costs, including tardiness, inventory, and delivery costs. Given the problem’s strong NP-hard nature, the focus is on developing an efficient solution approach using constraint programming (CP). A CP model is proposed and enhanced with multiple redundant constraints. To reduce runtime, two branching strategies are designed for the CP model. Numerical experiments with varying instance scales reveal that the proposed CP model outperforms the MIP model in accuracy and efficiency within the given time limit. The redundant constraints and search strategy can reduce CP model runtime by up to 263.83%. Compared to manual scheduling at the studied factory, the CP model can cut costs by up to 26.59% for real data, offering viable alternatives for factory planners.</div></div>","PeriodicalId":10542,"journal":{"name":"Computers & Operations Research","volume":"173 ","pages":"Article 106855"},"PeriodicalIF":4.1,"publicationDate":"2024-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142319875","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 : 2024-09-21DOI: 10.1016/j.cor.2024.106853
Hongtao Wang , Fulgencia Villa , Eva Vallada , Rubén Ruiz
This paper introduces an automatic yard crane scheduling problem with additional assignments of input/output (I/O) points at the block. I/O points are the buffer between the block and the rest of the terminal and containers are relocated from the block to the I/O points or vice-versa. The crane schedule therefore not only considers movements, storage and retrieval of containers, but must also be coordinated with the release and due times of containers at the I/O points, which are also limited and need to be assigned during the scheduling process. This results in a complex, but at the same time, more realistic problem. Two GRASP (Greedy Randomized Adaptive Search Procedure) heuristic approaches are proposed along with improvements to the solution construction and local search phases that are specifically tailored for this problem. The proposed algorithms are statistically calibrated and comprehensive experiments are designed to assess the performance of the method, including validation across small, medium, and large size instances. The experimental results show that the proposed methods are effective and competitive when compared to existing approaches. The GRASP manages to obtain an optimality average rate of 71.25% for small instances and finds 461 new best solutions in the 480 medium and large instances, with up to 200 containers, when compared to existing approaches for this problem.
{"title":"Solving the yard crane scheduling problem with dynamic assignment of input/output points","authors":"Hongtao Wang , Fulgencia Villa , Eva Vallada , Rubén Ruiz","doi":"10.1016/j.cor.2024.106853","DOIUrl":"10.1016/j.cor.2024.106853","url":null,"abstract":"<div><div>This paper introduces an automatic yard crane scheduling problem with additional assignments of input/output (I/O) points at the block. I/O points are the buffer between the block and the rest of the terminal and containers are relocated from the block to the I/O points or vice-versa. The crane schedule therefore not only considers movements, storage and retrieval of containers, but must also be coordinated with the release and due times of containers at the I/O points, which are also limited and need to be assigned during the scheduling process. This results in a complex, but at the same time, more realistic problem. Two GRASP (Greedy Randomized Adaptive Search Procedure) heuristic approaches are proposed along with improvements to the solution construction and local search phases that are specifically tailored for this problem. The proposed algorithms are statistically calibrated and comprehensive experiments are designed to assess the performance of the method, including validation across small, medium, and large size instances. The experimental results show that the proposed methods are effective and competitive when compared to existing approaches. The GRASP manages to obtain an optimality average rate of 71.25% for small instances and finds 461 new best solutions in the 480 medium and large instances, with up to 200 containers, when compared to existing approaches for this problem.</div></div>","PeriodicalId":10542,"journal":{"name":"Computers & Operations Research","volume":"173 ","pages":"Article 106853"},"PeriodicalIF":4.1,"publicationDate":"2024-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142326592","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-21DOI: 10.1016/j.cor.2024.106852
Pedro Maristany de las Casas , Antonio Sedeño-Noda , Ralf Borndörfer
The Multiobjective Minimum Spanning Tree (MO-MST) problem generalizes the Minimum Spanning Tree problem by weighting the edges of the input graph using vectors instead of scalars. In this paper, we design a new Dynamic Programming MO-MST algorithm. Dynamic Programming for a MO-MST instance requests solving a One-to-One Multiobjective Shortest Path (MOSP) instance and both instances have equivalent solution sets. The MOSP instance is defined on a so called transition graph. We study the original size of this graph in detail and reduce its size using cost-dependent arc pruning criteria. To solve the MOSP instance on the reduced transition graph, we design the Implicit Graph Multiobjective Dijkstra Algorithm (IG-MDA), exploiting recent improvements on MOSP algorithms from the literature. All in all, the new IG-MDA outperforms the current state of the art on a big set of instances from the literature. Our code and results are publicly available.
{"title":"New Dynamic Programming algorithm for the Multiobjective Minimum Spanning Tree problem","authors":"Pedro Maristany de las Casas , Antonio Sedeño-Noda , Ralf Borndörfer","doi":"10.1016/j.cor.2024.106852","DOIUrl":"10.1016/j.cor.2024.106852","url":null,"abstract":"<div><div>The <em>Multiobjective Minimum Spanning Tree</em> (MO-MST) problem generalizes the Minimum Spanning Tree problem by weighting the edges of the input graph using vectors instead of scalars. In this paper, we design a new Dynamic Programming MO-MST algorithm. Dynamic Programming for a MO-MST instance requests solving a One-to-One Multiobjective Shortest Path (MOSP) instance and both instances have equivalent solution sets. The MOSP instance is defined on a so called transition graph. We study the original size of this graph in detail and reduce its size using cost-dependent arc pruning criteria. To solve the MOSP instance on the reduced <em>transition graph</em>, we design the Implicit Graph Multiobjective Dijkstra Algorithm (IG-MDA), exploiting recent improvements on MOSP algorithms from the literature. All in all, the new IG-MDA outperforms the current state of the art on a big set of instances from the literature. Our code and results are publicly available.</div></div>","PeriodicalId":10542,"journal":{"name":"Computers & Operations Research","volume":"173 ","pages":"Article 106852"},"PeriodicalIF":4.1,"publicationDate":"2024-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142319873","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 : 2024-09-19DOI: 10.1016/j.cor.2024.106851
Rafael A. Campos , Guilherme O. Chagas , Leandro C. Coelho , Pedro Munari
The capacitated -median problem (CPMP) involves placing identical facilities in a network and assigning customer nodes to these facilities to satisfy all customer demands with minimal transportation costs. In practical applications, demand and distance parameters are often uncertain during the planning process, leading to infeasible or excessively costly solutions if these uncertainties are disregarded. This paper addresses the robust CPMP (RCPMP), which incorporates demand uncertainty into the problem using the robust optimization paradigm. We propose a general framework to model and solve the RCPMP, considering different polyhedral uncertainty sets, namely the cardinality-constrained and the knapsack sets. We develop exact approaches encompassing compact models, different families of valid inequalities, and branch-and-cut and branch-and-price algorithms, exploring both implemented uncertainty sets and problem structure. Furthermore, we implement an efficient Variable Neighborhood Search (VNS) heuristic to solve these robust variants, which incorporates state-of-the-art algorithms, parallelization techniques, and optimized data structures. Computational experiments using adapted benchmark instances with up to 400 nodes indicate the effectiveness of the proposed approaches. The results show that using parallelization and hash tables within the VNS heuristic promotes significant performance improvements and yields near-optimal solutions for most instances, as well as outperforming the exact approaches in several instances where the optimal solution was not found. Moreover, these results highlight the benefits of using robust solutions in practical settings, especially when considering different uncertainty sets to generate solutions with advantageous trade-offs between cost and risk.
容纳 p 中值问题（CPMP）涉及在网络中放置 p 个相同的设施，并将客户节点分配给这些设施，从而以最小的运输成本满足所有客户的需求。在实际应用中，规划过程中的需求和距离参数往往是不确定的，如果忽略这些不确定性，就会导致解决方案不可行或成本过高。本文探讨了鲁棒 CPMP（RCPMP），它利用鲁棒优化范式将需求的不确定性纳入问题中。我们考虑到不同的多面体不确定性集，即卡方条件约束集和knapsack 集，提出了一个建模和求解 RCPMP 的通用框架。我们开发了包括紧凑模型、不同有效不等式族、分支-切割和分支-价格算法在内的精确方法，同时探索了已实施的不确定性集和问题结构。此外，我们还实施了一种高效的可变邻域搜索（VNS）启发式来求解这些稳健变体，该启发式结合了最先进的算法、并行化技术和优化的数据结构。使用多达 400 个节点的适应基准实例进行的计算实验表明，所提出的方法非常有效。结果表明，在 VNS 启发式中使用并行化和散列表可显著提高性能，并为大多数实例提供接近最优的解决方案，在未找到最优解决方案的若干实例中，其性能还优于精确方法。此外，这些结果凸显了在实际环境中使用稳健解决方案的好处，尤其是在考虑不同的不确定性集以生成成本与风险之间有利权衡的解决方案时。
{"title":"Exact methods and a variable neighborhood search for the robust capacitated p-median problem","authors":"Rafael A. Campos , Guilherme O. Chagas , Leandro C. Coelho , Pedro Munari","doi":"10.1016/j.cor.2024.106851","DOIUrl":"10.1016/j.cor.2024.106851","url":null,"abstract":"<div><div>The capacitated <span><math><mi>p</mi></math></span>-median problem (CPMP) involves placing <span><math><mi>p</mi></math></span> identical facilities in a network and assigning customer nodes to these facilities to satisfy all customer demands with minimal transportation costs. In practical applications, demand and distance parameters are often uncertain during the planning process, leading to infeasible or excessively costly solutions if these uncertainties are disregarded. This paper addresses the robust CPMP (RCPMP), which incorporates demand uncertainty into the problem using the robust optimization paradigm. We propose a general framework to model and solve the RCPMP, considering different polyhedral uncertainty sets, namely the cardinality-constrained and the knapsack sets. We develop exact approaches encompassing compact models, different families of valid inequalities, and branch-and-cut and branch-and-price algorithms, exploring both implemented uncertainty sets and problem structure. Furthermore, we implement an efficient Variable Neighborhood Search (VNS) heuristic to solve these robust variants, which incorporates state-of-the-art algorithms, parallelization techniques, and optimized data structures. Computational experiments using adapted benchmark instances with up to 400 nodes indicate the effectiveness of the proposed approaches. The results show that using parallelization and hash tables within the VNS heuristic promotes significant performance improvements and yields near-optimal solutions for most instances, as well as outperforming the exact approaches in several instances where the optimal solution was not found. Moreover, these results highlight the benefits of using robust solutions in practical settings, especially when considering different uncertainty sets to generate solutions with advantageous trade-offs between cost and risk.</div></div>","PeriodicalId":10542,"journal":{"name":"Computers & Operations Research","volume":"173 ","pages":"Article 106851"},"PeriodicalIF":4.1,"publicationDate":"2024-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S030505482400323X/pdfft?md5=aad08bcbafc8447800930d41a0e000aa&pid=1-s2.0-S030505482400323X-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142312546","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-18DOI: 10.1016/j.cor.2024.106846
Padraig Cororan , Rhyd Lewis
Modelling street network connectivity is a fundamental research problem in transportation science. Here, we argue that the connectivity of a street network cannot be defined independently from the users of that street network. That is, different users will experience different levels of connectivity depending on their corresponding travel behaviour. In this work, we propose a model of connectivity that is defined with respect to a user’s travel behaviour within a given street network. We demonstrate that many real-world problems can be posed as instances of an optimisation problem defined with respect to this model. This includes optimising a user’s home location with respect to their connectivity and optimising the location of a facility with respect to the connectivity of its users. We prove the above optimisation problem is NP-hard and present an integer programming solution that scales to large problem instances.
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