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Pickup capacitated vehicle routing problem with three-dimensional loading constraints: Model and algorithms

TRANSPORTATION RESEARCH PART E-LOGISTICS AND TRANSPORTATION REVIEW 2023年第1期176卷

作者： Chi, Jushang He, Shiwei Beijing Jiaotong Univ Key Lab Transport Ind Big Data Applicat Technol Co Beijing Peoples R China

This study addresses the pickup capacitated vehicle routing problem with three-dimensional loading constraints (3L-PCVRP), which combined the container loading problem (CLP) and the capacitated vehicle routing problem (CVRP). A mixed-integer linear programming model for 3LPCVRP is designed with the objective of minimizing the total transportation cost. The basic constraints of CLP and CVRP as well as the practical constraints imposed by the pickup operations are incorporated in 3L-PCVRP. An improved branch-and-price-based (B & P) algorithm is proposed to solve 3L-PCVRP. The 3L-PCVRP model is decomposed into the restricted master problem (RMP) for selecting routes and the subproblem (SP) for generating routes that satisfy the loading and routing constraints. A label-correcting-based algorithm (LCA) is presented to solve the SP, which employs a two-stage method and two enhanced loading algorithms to ensure the loading feasibility of the routes. The two loading algorithms (tree search and greedy heuristic algorithms) are improved by a new evaluation function and an improved space-merging method. The twostage method is designed to call the two loading algorithms at different frequencies to investigate the route feasibility accurately and efficiently. Numerical experiments are designed to test the performance of the proposed algorithms. The efficiency and effectiveness of the improved loading algorithms are demonstrated in hundreds randomly generated instances. For small-scale 3L-PCVRP instances, the B & P algorithm can generate solutions that are not worse than those of the solver within 0.14% of the solver's running time. The efficiency and effectiveness of the improved B & P algorithm are also validated in large-scale benchmark instances.

关键词： Three-dimensional loading Routing Pickup operation Loading algorithm branch-and-price algorithm

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Electric bus charging scheduling on a bus network

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TRANSPORTATION RESEARCH PART C-EMERGING TECHNOLOGIES 2024年 161卷

作者： Zhou, Yu Meng, Qiang Ong, Ghim Ping Wang, Hua Beihang Univ Sch Transportat Sci & Engn Beijing 100191 Peoples R China Beihang Univ Sch Transportat Sci & Engn Key Lab Intelligent Transportat Technol & Syst Minist Educ Beijing 100191 Peoples R China Natl Univ Singapore Dept Civil & Environm Engn Singapore 117576 Singapore Hefei Univ Technol Sch Automot & Transportat Engn Hefei 230009 Peoples R China

This study addresses the electric bus charging scheduling problem (EBCSP) within a bus network comprising multiple bus routes, depots, and a fleet of heterogeneous electric buses (EBs) operated by a public transport (PT) operator. The EBCSP aims to minimize total costs by concurrently determining the assignment of EBs to trips(i.e., EB-to-trip assignment) and their corresponding charging schedules. A partial charging policy allows for flexible charging durations, considering a published timetable consisting of trip tasks. We formulate the EBCSP as a mixed-integer linear programming model and a set-covering formulation. For small-scale EBCSPs, we propose a branch-and-price algorithm utilizing the set-covering formulation for exact solutions. As large-scale EBCSPs pose computational challenges, we develop an optimizationbased adaptive large neighborhood search ( opt -ALNS) method. The opt -ALNS method employs ALNS operators for EB-to-trip assignment and solves the remaining linear programming problem efficiently. To enhance the opt -ALNS process, we introduce a labeling method to assess solution feasibility and rebuild solutions. Moreover, we incorporate EB battery degradation effects into the proposed method. Finally, we assess the performance of the opt -ALNS method on real-life instances and compare it with the branch-and-price algorithm.

关键词： Electric bus charging scheduling Bus network Mixed-integer linear programming model Set-covering model branch-and-price algorithm Adaptive large neighborhood search method Battery degradation

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Optimization models for targeted offers in direct marketing: Exact and heuristic algorithms

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2011年第3期210卷 670-683页

作者： Nobibon, Fabrice Talla Leus, Roe Spieksma, Frits C. R. Katholieke Univ Leuven Operat Res Grp B-3000 Louvain Belgium

This paper presents an optimization model for the selection of sets of clients that will receive an offer for one or more products during a promotion campaign. We show that the problem is strongly NP-hard and that it is unlikely that a constant-factor approximation algorithm can be proposed for solving this problem. We propose an alternative set-covering formulation and develop a branch-and-price algorithm to solve it. We also describe eight heuristics to approximate an optimal solution, including a depth-first branch-and-price heuristic and a tabu-search algorithm. We perform extensive computational experiments both with the exact as well as with the heuristic algorithms. Based on our experiments, we suggest the use of optimal algorithms for small and medium-size instances, while heuristics (especially tabu search and branch-and-price-based routines) are preferable for large instances and when time is an important factor. (C) 2010 Elsevier B.V. All rights reserved.

关键词： Direct marketing campaign Integer programming branch-and-price algorithm Non-approximability Heuristics Tabu search

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The Multiple Steiner TSP with order constraints: complexity and optimization algorithms

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SOFT COMPUTING 2020年第23期24卷 17957-17968页

作者： Gabrel, Virginie Mahjoub, A. Ridha Taktak, Raouia Uchoa, Eduardo PSL Res Univ Univ Paris Dauphine CNRS LAMSADE F-75016 Paris France Univ Sfax CRNS ISIMS Sfax Tunisia Univ Sfax CRNS LT2S Sfax Tunisia Univ Fed Fluminense Dept Engn Prod Niteroi RJ Brazil

We consider a variant of the Travelling Salesman Problem (TSP), the Multiple Steiner TSP with Order constraints (MSTSPO). Consider a weighted undirected graph and a set of salesmen, and each salesman is associated with a set of compulsory vertices to visit, called terminals. The MSTSPO consists in finding a minimum-cost subgraph containing for each salesman a tour going in a specified order through its terminals. Along with its importance from a theoretical point of view, the problem is also challenging in practice since it has applications in telecommunication networks. We show that the problem is NP-hard even for a single salesman and propose integer programming formulations. We then devise both branch-and-Cut and branch-and-price algorithms to solve the problem. The extensive computational results are presented, showing the efficiency of our algorithms.

关键词： Steiner TSP Order constraints Integer linear programming branch-and-price algorithm branch-and-Cut algorithm

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algorithms for the bin packing problem with scenarios

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JOURNAL OF COMBINATORIAL OPTIMIZATION 2024年第4期48卷 1-28页

作者： Borges, Yulle G. F. de Lima, Vinicius L. Miyazawa, Flavio K. Pedrosa, Lehilton L. C. de Queiroz, Thiago A. Schouery, Rafael C. S. Univ Estadual Campinas Inst Comp Campinas SP Brazil Fed Univ Catalao Inst Math & Technol Catalao GO Brazil

This paper presents theoretical and practical results for the bin packing problem with scenarios, a generalization of the classical bin packing problem which considers the presence of uncertain scenarios, of which only one is realized. For this problem, we propose approximation algorithms whose ratios are bounded by the square root of the number of scenarios times the approximation ratio for an algorithm for the vector bin packing problem. We also show how an asymptotic polynomial-time approximation scheme is derived when the number of scenarios is constant, that is, not a part of the input. As a practical study of the problem, we present a branch-and-price algorithm to solve an exponential set-cover model and a variable neighborhood search heuristic. Experiments show the competence of the branch-and-price in obtaining optimal solutions for about 59% of the instances considered, while the combined heuristic and branch-and-price optimally solved 62% of the instances considered.

关键词： Bin packing problem Scenarios Approximation algorithm Variable neighborhood search branch-and-price algorithm

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A column generation approach for SONET ring assignment

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NETWORKS 2006年第3期47卷 157-171页

作者： Macambira, EM Maculan, N de Souza, CC Univ Estadual Campinas Inst Computacao BR-13084971 Campinas SP Brazil Univ Fed Rio de Janeiro COPPE Programa Engn Sistemas & Computacao BR-21941972 Rio De Janeiro Brazil

In this article we consider the SONET ring assignment problem (SRAP) presented in [7]. The authors pointed out the inadequacy of solving SRAP instances using their integer programming formulation and commercial linear programming solvers. Similar experiences with IP models for SRAP are reported in [1]. In this article we reformulate SRAP as a set partitioning model with an additional knapsack constraint. This new formulation has an exponential number of columns and, to solve it, we implemented a branch-and-price/column generation algorithm. Extensive computational experiments showed that the new algorithm is orders of magnitude faster than standard branch-and-bound codes running on compact IP models introduced earlier. Instances taken from [1,7], which could not be solved there in hours of computation were solved here to optimality in just a few seconds. (c) 2006 Wiley Periodicals, Inc.

关键词： telecommunication network design SONET ring integer programming column generation branch-and-price algorithm

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A novel predict-then-optimize method for sustainable bike-sharing management: a data-driven study in China

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ANNALS OF OPERATIONS RESEARCH 2022年 1-33页

作者： Zhou, Yu Li, Qin Yue, Xiaohang Nie, Jiajia Guo, Qiang Chongqing Univ Sch Econ & Business Adm Chongqing Peoples R China Chongqing Univ Chongqing Key Lab Logist Chongqing Peoples R China Univ Wisconsin Sheldon B Lubar Sch Business Milwaukee WI 53201 USA Southwest Jiaotong Univ Sch Econ & Management Chengdu Peoples R China Key Lab Serv Sci & Innovat Sichuan Prov Chengdu Peoples R China

Sustainable operations management will appeal to the post-pandemic world. As the economy recovers, the surging demand for low-carbon bike-sharing has led to exacerbated mismatch in urban transportation. It is a serious challenge to optimize the reallocation schedule of sharing bikes among multiple positions in a network. To address the problem, we develop a novel predict-then-optimize method consisting of a data-driven robust optimization model and a branch-and-price algorithm. The optimization model derives the predicted demand surplus of each position based on historical data, enabling the optimal reallocation schedule in the network at minimum operational costs. Based on the prediction, the branch-and-price algorithm can find out the best routes of assigning bikes to specific positions that further improves transportation efficiency. Finally, we deploy the predict-then-optimize method to a realistic bike-sharing network in one major city of China. The computational results demonstrate that our method can significantly save the cost of operations and reduce the waste of resources. Therefore, the novel predict-then-optimize method has a great potential to facilitate the sustainable development of bike-sharing systems in urban transportation.

关键词： Bike-sharing system Reallocation scheduling Predict-then-optimize method Data-driven models branch-and-price algorithm

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Coastal shuttle tanker inventory routing model with a discrete loaded quantity

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APPLIED ECONOMICS 2021年第53期53卷 6120-6137页

作者： Xin, Xu Wang, Xiaoli Chen, Zigen Chen, Kang Tongji Univ Sch Econ & Management Shanghai Peoples R China Dalian Maritime Univ Sch Maritime Econ & Management Dalian Liaoning Peoples R China

This paper investigates a coastal shuttle tanker inventory routing problem. We convert the problem into a vehicle routing problem with time windows by using the discrete tanker loaded quantity and formulate this problem as an integer programming model. The model aims to minimize the total operating costs of the tanker fleet during the observation period. The composition and scheduling scheme of the fleet and loaded quantity of each tanker are collaboratively optimized. Based on the branch-and-price algorithm framework, an exact algorithm that can solve the actual-scale problem is designed. The efficiency and effectiveness of the algorithm are tested, and a sensitivity analysis is conducted for the fuel cost of the tankers. The results provide managerial insights that are expected to be beneficial for oil companies.

关键词： ship scheduling maritime inventory routing problem loaded quantity branch-and-price algorithm discrete demand

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An exact method for vehicle routing problem with backhaul discounts in urban express delivery network

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CLEANER LOGISTICS AND SUPPLY CHAIN 2024年 11卷

作者： Zhao, Jinqiu Liu, Yongwu Zhang, Jinwei Zhang, Jing Huang, Yixiao Yu, Le Xie, Binglei Harbin Inst Technol Shenzhen Sch Architecture Shenzhen 518000 Guangdong Peoples R China Hong Kong Polytech Univ Dept Aeronaut & Aviat Engn Hong Kong 999077 Peoples R China Southern Power Grid Supply Chain Grp Co Ltd Guangzhou 511466 Guangdong Peoples R China Liaoning Tech Univ Sch Software Huludao 125000 Liaoning Peoples R China SF Express Grp Co Ltd Shenzhen 518000 Guangdong Peoples R China Shenzhen Technol Univ Coll Urban Transportat & Logist Shenzhen 518000 Guangdong Peoples R China

The surge in e -commerce has led to an increased demand for urban express services, requiring the strategic development of delivery networks that are both efficient and cost-effective. This study addresses a practical vehicle routing problem (VRP) in an urban express delivery network to minimize transportation costs. Specifically, it considers the implementation of backhaul discounts, a factor disregarded in the existing literature. This VRP is further complicated by various realistic constraints, including pickup and delivery, time windows, multiple trips, heterogeneous fleets, and docking capacity limitations, which make most general VRP solvers inapplicable. This study proposes a trip-based formulation to overcome this challenge and develop a tailored branchand-price algorithm. Feasible trips are classified into four types to simplify the computation of backhaul discounts, thereby enhancing solution efficiency. Validation with real-world data from SF Express substantiates the efficacy of our method and yields insights for sustainable city logistics management. Moreover, our simplified column generation algorithm exhibits competitive performance, achieving optimal solutions expeditiously for the tested instances.

关键词： Vehicle routing Backhaul discounts Pickup and delivery Multiple trips branch-and-price algorithm

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The multi-terminal vertex separator problem: Complexity, Polyhedra and algorithms

The multi-terminal vertex separator problem: Complexity, Pol...

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作者： Youcef Magnouche PSL Research University

学位级别：博士

This thesis deals with the multi-terminal vertex separator problem. Given a graph G = (V ∪T, E) with V ∪T the set of vertices, where T is a set of terminals, and a weight function w: V → Z, associated with nonterminal nodes, the multi-terminal vertex separator problem consists in partitioning V ∪ T into k + 1 subsets {S, V 1,..., V k } such that there is no edge between two different subsets V i and V j, each V i contains exactly one terminal and the weight of S is minimum. In this thesis, we consider the problem from a polyhedral point of view. We give two integer programming formulations for the problem, for one of them, we investigate the related polyhedron and discuss its polyhedral structure. We describe some valid inequalities and characterize when these inequalities define facets. We also derive separation algorithms for these inequalities. Using these results, we develop a branch-and-Cut algorithm for the problem, along with an extensive computational study is presented. We also study the multi-terminal vertex separator polytope in the graphs decompos- able by one node cutsets. If G is a graph that decomposes into G 1 and G 2, we show that the multi-terminal vertex separator polytope in G can be described from two lin- ear systems related to G 1 and G 2. This gives rise to a technique for characterizing the multi-terminal vertex separator polytope in the graphs that are recursively decompos- able. We also obtain a procedure to describe facets for this polytope and show that the multi-terminal vertex separator problem can also be decomposed. Applications of this technique are also discussed. Moreover, we propose three extended formulations for the problem and derive branch- and-price and branch-and-Cut-and-price algorithms. For each formulation we present a column generation scheme to solve the linear relaxation, the way to compute the dual bound and the branching scheme. We present computational results and discuss the performance of each algorithm. Further,

关键词： Combinatorial optimization Polytope Facet branch-and-Cut algorithm branch-and-price algorithm Composition of polyhedra

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