A branch‐and‐cut algorithm for the Team Orienteering Problem

Bianchessi, Nicola; Mansini, Renata; Speranza, Maria

doi:10.1111/itor.12422

Cited by 52 publications

(44 citation statements)

References 11 publications

(34 reference statements)

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“…We remark that, although (15) is redundant for F 1 (see, again, Corollary 1), this inequality was preserved in our experiments as a way to properly reproduce the original algorithm of Bianchessi et al [24]. In fact, we conjecture that CPLEX does benefit from this inequality when the separation of built-in cuts is enabled.…”

Section: Baseline Branch-and-cut Algorithmsupporting

confidence: 53%

“…In any case, the results clearly indicate the superiority of our algorithm (CPA) in solving the original benchmark of TOP instances, even when compared to the original report of B-B&C. Precisely, our algorithm was able to solve to optimality 31 and 14 more instances than B-B&C when considering our implementation and the original report in [24], respectively. In addition, the average gaps of the solutions (regarding the unsolved instances) provided by CPA are comparable to those of B-B&C (both in our implementation and in the original report) for all instance sets.…”

Section: Configuration Of Inequalitiesmentioning

confidence: 68%

“…In this section, we present two compact Mixed Integer Linear Programming (MILP) formulations for STOP. The first one, denoted by F 1 , directly extends the TOP formulation of Bianchessi et al [24] through the addition of constraints that impose the selection of mandatory vertices.…”

Section: Mathematical Formulationsmentioning

confidence: 99%

“…Here, the Baseline Branchand-Cut and the Cutting-Plane Algorithm are referred to as B-B&C and CPA, respectively. Both of them were set to run for up to 7200s, the same time limit established in previous works concerning TOP [5,20,21,22,23,24]. 35…”

Section: Computational Experimentsmentioning

confidence: 99%

“…Results for the original benchmark of TOP instances. In a second experiment, we evaluated the performance of CPA by comparing the results obtained by the algorithm with the ones of B-B&C reported in [24]. To make a fair comparison, we also report the results of our implementation of B-B&C running within our experimental environment.…”

Section: Inequalitiesmentioning

confidence: 99%

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A cutting-plane algorithm for the Steiner team orienteering problem

Assunção

Mateus

2019

Computers & Industrial Engineering

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The Team Orienteering Problem (TOP) is an NP-hard routing problem in which a fleet of identical vehicles aims at collecting rewards (prizes) available at given locations, while satisfying restrictions on the travel times. In TOP, each location can be visited by at most one vehicle, and the goal is to maximize the total sum of rewards collected by the vehicles within a given time limit. In this paper, we propose a generalization of TOP, namely the Steiner Team Orienteering Problem (STOP). In STOP, we provide, additionally, a subset of mandatory locations. In this sense, STOP also aims at maximizing the total sum of rewards collected within the time limit, but, now, every mandatory location must be visited. In this work, we propose a new commoditybased formulation for STOP and use it within a cutting-plane scheme. The algorithm benefits from the compactness and strength of the proposed formulation and works by separating three families of valid inequalities, which consist of some general connectivity constraints, classical lifted cover inequalities based on dual bounds and a class of conflict cuts. To our knowledge, the last class of inequalities is also introduced in this work. A state-of-the-art branch-and-cut algorithm from the literature of TOP is adapted to STOP and used as baseline to evaluate the performance of the cutting-plane. Extensive computational experiments show the competitiveness of the new algorithm while solving several STOP and TOP instances. In particular, it is able to solve, in total, 14 more TOP instances than any other previous exact algorithm and finds eight new optimality certificates. With respect to the new STOP instances introduced in this work, our algorithm solves 30 more instances than the baseline.

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Section: Baseline Branch-and-cut Algorithmsupporting

confidence: 53%

Section: Configuration Of Inequalitiesmentioning

confidence: 68%

Section: Mathematical Formulationsmentioning

confidence: 99%

Section: Computational Experimentsmentioning

confidence: 99%

Section: Inequalitiesmentioning

confidence: 99%

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A cutting-plane algorithm for the Steiner team orienteering problem

Assunção

Mateus

2019

Computers & Industrial Engineering

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Solving the team orienteering problem with nonidentical agents: A Lagrangian approach

Chakraborty

Agarwal

2021

Networks

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The team orienteering problem (TOP) requires a team of time-constrained agents to maximize the total collected profit by serving a subset of given customers. The exact solution approaches for TOP in the literature have considered only the case of identical agents, even though the heterogeneity of the agents is of essence in many applications. The heuristic approaches, on the other hand, although providing good feasible solutions, do not offer any measure of solution quality, such as an optimality gap. In this study, we consider an extension of the conventional TOP in which the agents are allowed to be identical as well as completely nonidentical. We explore a Lagrangian relaxation based approach that simultaneously obtains tight upper and lower bounds on the optimal solution of the problem and, therefore, provides a measure of solution quality by way of duality gap. Our algorithm achieves an average gap of less than 2% within an average time of around 120 s across 135 randomly generated instances with up to 100 customers and five nonidentical agents. We also introduce a new set of valid symmetry breaking constraints that significantly improves the effectiveness of our formulation and Lagrangian implementation for the case of identical agents. For the three most difficult sets of benchmark instances for TOP with identical agents, our approach achieves upper bounds that are, on average, 1.08% above the best-known solutions, and feasible solutions that are 0.35% below the best-known solutions. The average time taken to solve these problems was about 115 s.

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A Generic Exact Solver for Vehicle Routing and Related Problems

Pessoa

Sadykov

Uchôa

et al. 2019

Lecture Notes in Computer Science

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Major advances were recently obtained in the exact solution of Vehicle Routing Problems (VRPs). Sophisticated Branch-Cutand-Price (BCP) algorithms for some of the most classical VRP variants now solve many instances with up to a few hundreds of customers. However, adapting and reimplementing those successful algorithms for other variants can be a very demanding task. This work proposes a BCP solver for a generic model that encompasses a wide class of VRPs. It incorporates the key elements found in the best recent VRP algorithms: ng-path relaxation, rank-1 cuts with limited memory, and route enumeration; all generalized through the new concept of "packing set". This concept is also used to derive a new branch rule based on accumulated resource consumption and to generalize the Ryan and Foster branch rule. Extensive experiments on several variants show that the generic solver has an excellent overall performance, in many problems being better than the best existing specific algorithms. Even some non-VRPs, like bin packing, vector packing and generalized assignment, can be modeled and effectively solved.

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A branch‐and‐cut algorithm for the Team Orienteering Problem

Cited by 52 publications

References 11 publications

A cutting-plane algorithm for the Steiner team orienteering problem

A cutting-plane algorithm for the Steiner team orienteering problem

Solving the team orienteering problem with nonidentical agents: A Lagrangian approach

A Generic Exact Solver for Vehicle Routing and Related Problems

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