Abstract In this article, we define a new routing problem that arises in the last‐mile delivery of parcels, in which customers can be served either directly at home by a capacitated truck, or possibly with a drone carried on the truck, or in a self‐service mode using one of the available lockers. We investigate four different formulations, and for one of them, we propose a branch‐and‐cut approach. We also discuss some possible variants of the original problem. In the computational experiments, we analyze and compare the performance of the four formulations for the problem and its variants, and we provide some useful managerial insights.
{"title":"Last‐mile delivery with drone and lockers","authors":"Marco Antonio Boschetti, Stefano Novellani","doi":"10.1002/net.22190","DOIUrl":"https://doi.org/10.1002/net.22190","url":null,"abstract":"Abstract In this article, we define a new routing problem that arises in the last‐mile delivery of parcels, in which customers can be served either directly at home by a capacitated truck, or possibly with a drone carried on the truck, or in a self‐service mode using one of the available lockers. We investigate four different formulations, and for one of them, we propose a branch‐and‐cut approach. We also discuss some possible variants of the original problem. In the computational experiments, we analyze and compare the performance of the four formulations for the problem and its variants, and we provide some useful managerial insights.","PeriodicalId":54734,"journal":{"name":"Networks","volume":"99 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135590419","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Konstantin Pavlikov, Niels Christian Petersen, Jon Lilholt Sørensen
Abstract The family of Rounded Capacity (RC) inequalities is one of the most important sets of valid inequalities for the Capacitated Vehicle Routing Problem (CVRP). This paper considers the problem of separation of violated RC inequalities and develops an exact procedure employing mixed integer linear programming. The developed routine is demonstrated to be very efficient for small and medium‐sized problem instances. For larger‐scale problem instances, an iterative approach for exact separation of RC inequalities is developed, based upon a selective variable pricing strategy. The approach combines column and row generation and allows us to introduce variables only when they are needed, which is essential when dealing with large‐scale problem instances. A computational study demonstrates scalability of the proposed separation routines and provides exact RC‐based lower bounds to some of the publicly available unsolved CVRP instances. The same computational study provides RC‐based lower bounds for very large‐scale CVRP instances with more than 3000 locations obtained within appropriate computational time limits.
{"title":"Exact separation of the rounded capacity inequalities for the capacitated vehicle routing problem","authors":"Konstantin Pavlikov, Niels Christian Petersen, Jon Lilholt Sørensen","doi":"10.1002/net.22183","DOIUrl":"https://doi.org/10.1002/net.22183","url":null,"abstract":"Abstract The family of Rounded Capacity (RC) inequalities is one of the most important sets of valid inequalities for the Capacitated Vehicle Routing Problem (CVRP). This paper considers the problem of separation of violated RC inequalities and develops an exact procedure employing mixed integer linear programming. The developed routine is demonstrated to be very efficient for small and medium‐sized problem instances. For larger‐scale problem instances, an iterative approach for exact separation of RC inequalities is developed, based upon a selective variable pricing strategy. The approach combines column and row generation and allows us to introduce variables only when they are needed, which is essential when dealing with large‐scale problem instances. A computational study demonstrates scalability of the proposed separation routines and provides exact RC‐based lower bounds to some of the publicly available unsolved CVRP instances. The same computational study provides RC‐based lower bounds for very large‐scale CVRP instances with more than 3000 locations obtained within appropriate computational time limits.","PeriodicalId":54734,"journal":{"name":"Networks","volume":"68 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135247318","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract The technician routing and scheduling problem (TRSP) optimizes routes for technicians serving tasks subject to qualifications, time constraints, and routing costs. In the literature, the TRSP is solved either to provide actual technician work schedules or to perform what‐if analyses on different TRSP scenarios. A TRSP scenario consists of a given number of tasks, technicians, skills, working hours and so forth. We present a method which builds optimal TRSP scenarios with respect to technician fleet, their skills, their working hours and digitization of task equipment. The scenarios are built such that the combined TRSP costs (OPEX) and investment costs (CAPEX) are minimized. By using a holistic approach we can generate scenarios that would not have been found by studying the investments individually. The proposed method consists of a matheuristic based on column generation. To reduce computational time, the routing costs of a technician are estimated instead of solved to optimality. The proposed method is evaluated on data from the literature and on real‐life data from a telecommunication company. The evaluation shows that the proposed method successfully suggests attractive scenarios. The method especially excels in ensuring that more tasks are serviced, but also in reducing travel time with around 16% in the real‐life instance. We believe that the proposed method could constitute an important strategic tool for routing companies. In the conclusion, we propose future research directions to extend the applicability.
{"title":"Decision support for the technician routing and scheduling problem","authors":"Mette Gamst, David Pisinger","doi":"10.1002/net.22188","DOIUrl":"https://doi.org/10.1002/net.22188","url":null,"abstract":"Abstract The technician routing and scheduling problem (TRSP) optimizes routes for technicians serving tasks subject to qualifications, time constraints, and routing costs. In the literature, the TRSP is solved either to provide actual technician work schedules or to perform what‐if analyses on different TRSP scenarios. A TRSP scenario consists of a given number of tasks, technicians, skills, working hours and so forth. We present a method which builds optimal TRSP scenarios with respect to technician fleet, their skills, their working hours and digitization of task equipment. The scenarios are built such that the combined TRSP costs (OPEX) and investment costs (CAPEX) are minimized. By using a holistic approach we can generate scenarios that would not have been found by studying the investments individually. The proposed method consists of a matheuristic based on column generation. To reduce computational time, the routing costs of a technician are estimated instead of solved to optimality. The proposed method is evaluated on data from the literature and on real‐life data from a telecommunication company. The evaluation shows that the proposed method successfully suggests attractive scenarios. The method especially excels in ensuring that more tasks are serviced, but also in reducing travel time with around 16% in the real‐life instance. We believe that the proposed method could constitute an important strategic tool for routing companies. In the conclusion, we propose future research directions to extend the applicability.","PeriodicalId":54734,"journal":{"name":"Networks","volume":"49 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135014599","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Victor Hugo Vidigal Corrêa, Hang Dong, Manuel Iori, André Gustavo dos Santos, Mutsunori Yagiura, Giorgio Zucchi
Abstract This paper addresses a real‐world multi‐period orienteering problem arising in a large Italian company that needs to patrol an area in order to provide security services to a set of customers. Each customer requires different services on a weekly basis. Some services are mandatory, while others are optional. It might be impossible to perform all optional services, and each of them is assigned a score when performed. The challenge is to determine a set of routes, one per day, that maximizes a weighted sum of the total collected score and total working time, while meeting several operational constraints, including hard time windows, maximum riding time, minimum number of services performed, and minimum time between two consecutive visits for the same service at the same customer. To solve the problem, we propose an iterated local search that invokes at each iteration an inner variable neighborhood descent procedure. Computational tests performed on a large number of real‐world instances prove that the developed algorithm is very efficient, and finds in a short time solutions that are consistently better than those produced by a mathematical model, and those in use at the company.
{"title":"An iterated local search for a multi‐period orienteering problem arising in a car patrolling application","authors":"Victor Hugo Vidigal Corrêa, Hang Dong, Manuel Iori, André Gustavo dos Santos, Mutsunori Yagiura, Giorgio Zucchi","doi":"10.1002/net.22187","DOIUrl":"https://doi.org/10.1002/net.22187","url":null,"abstract":"Abstract This paper addresses a real‐world multi‐period orienteering problem arising in a large Italian company that needs to patrol an area in order to provide security services to a set of customers. Each customer requires different services on a weekly basis. Some services are mandatory, while others are optional. It might be impossible to perform all optional services, and each of them is assigned a score when performed. The challenge is to determine a set of routes, one per day, that maximizes a weighted sum of the total collected score and total working time, while meeting several operational constraints, including hard time windows, maximum riding time, minimum number of services performed, and minimum time between two consecutive visits for the same service at the same customer. To solve the problem, we propose an iterated local search that invokes at each iteration an inner variable neighborhood descent procedure. Computational tests performed on a large number of real‐world instances prove that the developed algorithm is very efficient, and finds in a short time solutions that are consistently better than those produced by a mathematical model, and those in use at the company.","PeriodicalId":54734,"journal":{"name":"Networks","volume":"31 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135397265","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Bryan David Galarza Montenegro, Kenneth Sörensen, Pieter Vansteenwegen
Public transportation out of suburban or rural areas is crucial. Feeder transportation services offer a solution by transporting passengers to areas where more options for public transport are available. On one hand, fully flexible demand‐responsive feeder services (DRFSs) efficiently tailor their service to the needs of the passengers. On the other hand, traditional feeder services provide predictability and easier cost control. In this article, a semi‐flexible DRFS is considered, which combines positive characteristics of both traditional services as well as fully flexible services. This feeder service has two types of bus stops: mandatory bus stops and optional bus stops. Mandatory bus stops are guaranteed to be visited by a bus within a certain time interval. Optional stops are only visited when there is demand for transportation nearby. The performance of this feeder service is optimized with the use of a new type of metaheuristic framework, which we denote as parameter space search. Experimental results on small benchmark instances indicate that the heuristic performs on average 12.42% better than LocalSolver, a commercial optimization solver, with an average runtime of 2.1 s. Larger instances can also be solved, typically within 2 min.
{"title":"A demand‐responsive feeder service with a maximum headway at mandatory stops","authors":"Bryan David Galarza Montenegro, Kenneth Sörensen, Pieter Vansteenwegen","doi":"10.1002/net.22185","DOIUrl":"https://doi.org/10.1002/net.22185","url":null,"abstract":"Public transportation out of suburban or rural areas is crucial. Feeder transportation services offer a solution by transporting passengers to areas where more options for public transport are available. On one hand, fully flexible demand‐responsive feeder services (DRFSs) efficiently tailor their service to the needs of the passengers. On the other hand, traditional feeder services provide predictability and easier cost control. In this article, a semi‐flexible DRFS is considered, which combines positive characteristics of both traditional services as well as fully flexible services. This feeder service has two types of bus stops: mandatory bus stops and optional bus stops. Mandatory bus stops are guaranteed to be visited by a bus within a certain time interval. Optional stops are only visited when there is demand for transportation nearby. The performance of this feeder service is optimized with the use of a new type of metaheuristic framework, which we denote as parameter space search. Experimental results on small benchmark instances indicate that the heuristic performs on average 12.42% better than LocalSolver, a commercial optimization solver, with an average runtime of 2.1 s. Larger instances can also be solved, typically within 2 min.","PeriodicalId":54734,"journal":{"name":"Networks","volume":" ","pages":""},"PeriodicalIF":2.1,"publicationDate":"2023-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47636134","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this article, we consider a particular case of bi‐objective optimization (BOO), called bi‐objective minimization (BOM), where the two objective functions to be minimized take only positive values. As well as for BOO, most of the methods proposed in the literature for solving BOM focus on computing the Pareto‐optimal solutions representing different trade‐offs between two objectives. However, it may be difficult for a central decision‐maker to determine the preferred solutions due to the huge number of solutions in the Pareto set. We propose a novel criterion for selecting the preferred Pareto‐optimal solutions by introducing the concept of ‐Nash Fairness (‐) solutions inspired by the definition of proportional fairness. The ‐ solutions are the feasible solutions achieving some proportional nash equilibrium between the two objectives. The positive parameter is introduced to reflect the relative importance of the first objective to the second one. For this work, we will discuss existential and algorithmic questions about the ‐ solutions by first showing their existence for BOM. Furthermore, the ‐ solution set can be a strict subset of the Pareto set. As there are possibly many ‐ solutions, we focus on extreme ‐ solutions achieving the smallest values for one of the objectives. Then, we propose two Newton‐based iterative algorithms for finding extreme ‐ solutions. Finally, we present computational results on some instances of the bi‐objective travelling salesman problem (BOTSP) and the bi‐objective shortest path problem.
{"title":"Generalized nash fairness solutions for bi‐objective minimization problems","authors":"Minh Hieu Nguyen, Mourad Baiou, Viet Hung Nguyen, Thi Quynh Trang Vo","doi":"10.1002/net.22182","DOIUrl":"https://doi.org/10.1002/net.22182","url":null,"abstract":"In this article, we consider a particular case of bi‐objective optimization (BOO), called bi‐objective minimization (BOM), where the two objective functions to be minimized take only positive values. As well as for BOO, most of the methods proposed in the literature for solving BOM focus on computing the Pareto‐optimal solutions representing different trade‐offs between two objectives. However, it may be difficult for a central decision‐maker to determine the preferred solutions due to the huge number of solutions in the Pareto set. We propose a novel criterion for selecting the preferred Pareto‐optimal solutions by introducing the concept of ‐Nash Fairness\u0000(‐) solutions inspired by the definition of proportional fairness. The ‐ solutions are the feasible solutions achieving some proportional nash equilibrium between the two objectives. The positive parameter is introduced to reflect the relative importance of the first objective to the second one. For this work, we will discuss existential and algorithmic questions about the ‐ solutions by first showing their existence for BOM. Furthermore, the ‐ solution set can be a strict subset of the Pareto set. As there are possibly many ‐ solutions, we focus on extreme ‐ solutions achieving the smallest values for one of the objectives. Then, we propose two Newton‐based iterative algorithms for finding extreme ‐ solutions. Finally, we present computational results on some instances of the bi‐objective travelling salesman problem (BOTSP) and the bi‐objective shortest path problem.","PeriodicalId":54734,"journal":{"name":"Networks","volume":" ","pages":""},"PeriodicalIF":2.1,"publicationDate":"2023-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49161999","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The angular‐metric traveling salesman problem (AngleTSP) aims to find a tour visiting a given set of vertices in the Euclidean plane exactly once while minimizing the cost given by the sum of all turning angles. If the cost is obtained by combining the sum of all turning angles and the traveled distance, the problem is called angular‐distance‐metric traveling salesman problem (AngleDistanceTSP). In this work, we study the symmetric variants of these problems. Because both the AngleTSP and AngleDistanceTSP are NP‐hard, multiple heuristic approaches have been proposed in the literature. Nevertheless, a good tradeoff between solution quality and runtime is hard to find. We propose a granular tabu search (GTS) that considers the geometric features of the two problems in the design of starting solutions and sparsification methods. We further enrich the GTS with components that guarantee both intensification and diversification during the search. The computational results on benchmark instances from the literature show that (i) for the AngleTSP, our GTS lies on the Pareto frontier of the best performing‐heuristics, and (ii) for the AngleDistanceTSP, our GTS provides the best solution quality across all existing heuristics in competitive runtimes. In addition, new best‐known solutions are found for most benchmark instances for which an optimal solution is not available.
{"title":"A tabu search with geometry‐based sparsification methods for angular traveling salesman problems","authors":"Rossana Cavagnini, Michael Schneider, Alina Theiß","doi":"10.1002/net.22180","DOIUrl":"https://doi.org/10.1002/net.22180","url":null,"abstract":"The angular‐metric traveling salesman problem (AngleTSP) aims to find a tour visiting a given set of vertices in the Euclidean plane exactly once while minimizing the cost given by the sum of all turning angles. If the cost is obtained by combining the sum of all turning angles and the traveled distance, the problem is called angular‐distance‐metric traveling salesman problem (AngleDistanceTSP). In this work, we study the symmetric variants of these problems. Because both the AngleTSP and AngleDistanceTSP are NP‐hard, multiple heuristic approaches have been proposed in the literature. Nevertheless, a good tradeoff between solution quality and runtime is hard to find. We propose a granular tabu search (GTS) that considers the geometric features of the two problems in the design of starting solutions and sparsification methods. We further enrich the GTS with components that guarantee both intensification and diversification during the search. The computational results on benchmark instances from the literature show that (i) for the AngleTSP, our GTS lies on the Pareto frontier of the best performing‐heuristics, and (ii) for the AngleDistanceTSP, our GTS provides the best solution quality across all existing heuristics in competitive runtimes. In addition, new best‐known solutions are found for most benchmark instances for which an optimal solution is not available.","PeriodicalId":54734,"journal":{"name":"Networks","volume":" ","pages":""},"PeriodicalIF":2.1,"publicationDate":"2023-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48787484","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
To plan the postal deliveries of our industry partner DHL Group (DHL), the single truck and trailer routing problem with satellite depots (STTRPSD) is solved to optimize mail carriers routes. In this application context, instances feature a high number of customers and satellites, and they are based on real street networks. This motivates the study of the asymmetric STTRPSD (ASTTRPSD). The heuristic solution methods proposed in the literature for the STTRPSD can either solve only the symmetric problem variant, or it is unclear whether they can also be used to solve the ASTTRPSD. We introduce an iterated local search, called ILS‐ASTTRPSD, which generates different first‐level tours in the perturbation phase, and improves the second‐level tours in the local search phase. To speed up the search, granular neighborhoods are used. The computational results on instances from the literature prove the capability of ILS‐ASTTRPSD to return high‐quality solutions. On DHL instances, ILS‐ASTTRPSD significantly decreases total travel times of the mail carriers and returns solutions with a different structure compared to the ones provided by DHL. Based on these differences, we give recommendations on how DHL could design more efficient mail carrier practices. Dedicated computational experiments reveal that considering parking and loading times when solving the ASTTRPSD leads to lower travel times, and that ignoring parking times is more counterproductive than ignoring loading times. Moreover, we assess the robustness of our solutions under parking time fluctuations. Finally, we derive properties of instances for which optimal solutions contain multiple second‐level tours rooted at the same parking spot and for which the optimal solutions of the ASTTRPSD correspond to the ones of a pure traveling salesman problem.
{"title":"A granular iterated local search for the asymmetric single truck and trailer routing problem with satellite depots at DHL Group","authors":"Rossana Cavagnini, Michael Schneider, Alina Theiß","doi":"10.1002/net.22178","DOIUrl":"https://doi.org/10.1002/net.22178","url":null,"abstract":"To plan the postal deliveries of our industry partner DHL Group (DHL), the single truck and trailer routing problem with satellite depots (STTRPSD) is solved to optimize mail carriers routes. In this application context, instances feature a high number of customers and satellites, and they are based on real street networks. This motivates the study of the asymmetric STTRPSD (ASTTRPSD). The heuristic solution methods proposed in the literature for the STTRPSD can either solve only the symmetric problem variant, or it is unclear whether they can also be used to solve the ASTTRPSD. We introduce an iterated local search, called ILS‐ASTTRPSD, which generates different first‐level tours in the perturbation phase, and improves the second‐level tours in the local search phase. To speed up the search, granular neighborhoods are used. The computational results on instances from the literature prove the capability of ILS‐ASTTRPSD to return high‐quality solutions. On DHL instances, ILS‐ASTTRPSD significantly decreases total travel times of the mail carriers and returns solutions with a different structure compared to the ones provided by DHL. Based on these differences, we give recommendations on how DHL could design more efficient mail carrier practices. Dedicated computational experiments reveal that considering parking and loading times when solving the ASTTRPSD leads to lower travel times, and that ignoring parking times is more counterproductive than ignoring loading times. Moreover, we assess the robustness of our solutions under parking time fluctuations. Finally, we derive properties of instances for which optimal solutions contain multiple second‐level tours rooted at the same parking spot and for which the optimal solutions of the ASTTRPSD correspond to the ones of a pure traveling salesman problem.","PeriodicalId":54734,"journal":{"name":"Networks","volume":" ","pages":""},"PeriodicalIF":2.1,"publicationDate":"2023-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44569797","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
E. Fernández, I. Lari, J. Puerto, F. Ricca, A. Scozzari
This article deals with the problem of partitioning a graph into connected components by optimizing some balancing objective functions related to the vertex weights. Objective functions based on the gap or range of the partition's components, that is, the difference between the maximum and minimum weight of a vertex in the component, have been already introduced in the literature. Here we introduce the notion of aggregated gap, defined as the sum of the differences between the weights of the vertices and the minimum weight of a vertex in the component. We study new connected ‐partitioning problems whose objective is a function of the components' aggregated gap, and give NP‐hardness results for these problems on general graphs. Mathematical programming formulations are proposed for these problems adopting flow‐based constraints for modeling connectivity in a partition. Even if they are introduced for the new aggregated gap problems, such formulations are rather general and apply also to the classical non‐aggregated gap problems. Extensive computational tests, both for aggregated and non‐aggregated gap problems, are performed on a set of squared grids and randomly generated graphs with up to 120 vertices, and a number of components ranging from 2 to 9. In our experiments, we test several alternative formulations for our problems providing a comparative analysis of their performance.
{"title":"Connected graph partitioning with aggregated and non‐aggregated gap objective functions","authors":"E. Fernández, I. Lari, J. Puerto, F. Ricca, A. Scozzari","doi":"10.1002/net.22181","DOIUrl":"https://doi.org/10.1002/net.22181","url":null,"abstract":"This article deals with the problem of partitioning a graph into connected components by optimizing some balancing objective functions related to the vertex weights. Objective functions based on the gap or range of the partition's components, that is, the difference between the maximum and minimum weight of a vertex in the component, have been already introduced in the literature. Here we introduce the notion of aggregated gap, defined as the sum of the differences between the weights of the vertices and the minimum weight of a vertex in the component. We study new connected ‐partitioning problems whose objective is a function of the components' aggregated gap, and give NP‐hardness results for these problems on general graphs. Mathematical programming formulations are proposed for these problems adopting flow‐based constraints for modeling connectivity in a partition. Even if they are introduced for the new aggregated gap problems, such formulations are rather general and apply also to the classical non‐aggregated gap problems. Extensive computational tests, both for aggregated and non‐aggregated gap problems, are performed on a set of squared grids and randomly generated graphs with up to 120 vertices, and a number of components ranging from 2 to 9. In our experiments, we test several alternative formulations for our problems providing a comparative analysis of their performance.","PeriodicalId":54734,"journal":{"name":"Networks","volume":" ","pages":""},"PeriodicalIF":2.1,"publicationDate":"2023-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46134158","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This article introduces the cumulative school bus routing problem, which concerns the transport of students from a school using a fleet of identical buses. The objective of the problem is to select a drop‐off point for each student among potential locations within a certain walking distance and to generate routes such that the sum of arrival times of all students from their school to their homes is minimized. The article describes six polynomial‐size mixed integer linear programming formulations based on original and auxiliary graphs, and the formulations are numerically compared on real instances. The article reports the results of computational experiments performed to evaluate the performance of the proposed models.
{"title":"The cumulative school bus routing problem: Polynomial‐size formulations","authors":"Farnaz Farzadnia, T. Bektaş, Jens Lysgaard","doi":"10.1002/net.22179","DOIUrl":"https://doi.org/10.1002/net.22179","url":null,"abstract":"This article introduces the cumulative school bus routing problem, which concerns the transport of students from a school using a fleet of identical buses. The objective of the problem is to select a drop‐off point for each student among potential locations within a certain walking distance and to generate routes such that the sum of arrival times of all students from their school to their homes is minimized. The article describes six polynomial‐size mixed integer linear programming formulations based on original and auxiliary graphs, and the formulations are numerically compared on real instances. The article reports the results of computational experiments performed to evaluate the performance of the proposed models.","PeriodicalId":54734,"journal":{"name":"Networks","volume":" ","pages":""},"PeriodicalIF":2.1,"publicationDate":"2023-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42709479","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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