Enhanced exact solution methods for the Team Orienteering Problem

Keshtkaran, Morteza; Ziarati, Koorush; Bettinelli, Andrea; Vigo, Daniele

doi:10.1080/00207543.2015.1058982

Cited by 67 publications

(44 citation statements)

References 18 publications

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“…() tested their branch‐and‐cut method on an AMD Opteron 2.60 GHz using CPLEX 12.4 as an MIP solver, Keshtkaran et al. () conducted their experiments on a single core of an Intel Core i7 3.6 GHz, and finally El‐Hajj et al. () run tests on an AMD Opteron 2.60 GHz using CPLEX 12.5 as an MIP solver.…”

Section: Resultsmentioning

confidence: 99%

“…The formulation we propose for the TOP was reinforced by the introduction of connectivity constraints (CCs) and solved by means of a branch-and-cut algorithm. We compared it with the methods of Boussier et al (2007), Dang et al (2013), Keshtkaran et al (2016), andEl-Hajj et al (2016) on the 387 benchmark instances of Chao et al (1996). The total number of instances solved to optimality is 311, when tested on a single thread, and 327 when multiple threads are allowed, 10 and 26 more than any previous method, respectively.…”

Section: Introductionmentioning

confidence: 99%

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

Bianchessi

Mansini

Speranza

2017

Int Trans Operational Res

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The Team Orienteering Problem aims at maximizing the total amount of profit collected by a fleet of vehicles while not exceeding a predefined travel time limit on each vehicle. In the last years, several exact methods based on different mathematical formulations were proposed. In this paper, we present a new two‐index formulation with a polynomial number of variables and constraints. This compact formulation, reinforced by connectivity constraints, was solved by means of a branch‐and‐cut algorithm. The total number of instances solved to optimality is 327 of 387 benchmark instances, 26 more than any previous method. Moreover, 24 not previously solved instances were closed to optimality.

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Bianchessi

Mansini

Speranza

2017

Int Trans Operational Res

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“…In particular, Dang, El-Hajj, and Moukrim [33] defined a BC approach based on model TOP1 which uses Generalized Subtour Elimination and Clique cuts to strengthen the linear relaxation and is able to close some open instances that were hard for BP. The subset-row inequalities are instead used by the BCP of Keshtkaran et al [70] which, although on average is inferior with respect to the pure BP, is capable of solving some instances that were not solvable by BP.…”

Section: The Team Orienteering Problemmentioning

confidence: 99%

“…In the first four lines of the table we make a direct comparison of the algorithms by providing, for each ordered pair, the number of instances that the first algorithm is able to solve and the other is not. For example, the BC by [33] can solve 13 test instances the BP by [70] cannot solve, whereas this latter solves 36 instances unsolved by the BC. By observing the table we note that even though BCP approaches are not currently the best available ones, it is likely that a more effective integration of cuts within the BP may be the path to follow for future research, as happened for other variants of the VRP.…”

Section: The Team Orienteering Problemmentioning

confidence: 99%

“…Using various acceleration procedures in the column generation step, the algorithm is able to solve 270 instances with up to 100 potential customers from the set of 387 CGW benchmark instances. An effective bi-directional dynamic programming procedure and relaxation-based dominance procedures are the base of an enhanced BP approach by Keshtkaran et al [70] which solves 10% more instances than the previous approaches (i.e., 301 out of the 387 instances of the benchmark).…”

Section: The Team Orienteering Problemmentioning

confidence: 99%

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Chapter 10: Vehicle Routing Problems with Profits

Archetti¹,

Speranza²,

Vigo³

2014

Vehicle Routing

Self Cite

117

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The key characteristic of the class of Vehicle Routing Problems with Profits (VRPPs) is that, contrary to what happens for the most classical vehicle routing problems, the set of customers to serve is not given. Therefore, two different decisions have to be taken: (i) which customers to serve, and (ii) how to cluster the customers to be served in different routes (if more than one) and order the visits in each route. In general, a profit is associated with each customer that makes such a customer more or less attractive. Thus, any route or set of routes, starting and ending at a given depot, can be measured both in terms of cost and in terms of profit. The difference between route profit and cost may be maximized, or the profit or the cost optimized with the other measure bounded in a constraint.There are several types of applications that can be modeled by means of a problem of this class:• scheduling of the daily operations of a steel rolling mill (see, e.g., Balas [13, 16]);• design of tourist trips to maximize the value of the visited attractions in a limited period (see, e.g., Vansteenwegen and Van Oudheusden [109]);• identification of suppliers to visit to maximize the recovered claims with a limited number of auditors (see Ilhan, Iravani, and Daskin [61]);• recruiting of athletes from high schools for a college team (see Butt and Cavalier [24]);• planning of the visits of a salesperson (see, e.g., Ramesh and Brown [89]);• routing of oil tankers to serve ships at different locations (see Golden, Levy, and Vohra [57]);

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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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Enhanced exact solution methods for the Team Orienteering Problem

Cited by 67 publications

References 18 publications

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

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

Chapter 10: Vehicle Routing Problems with Profits

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

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