GRASP with path relinking for the orienteering problem

Campos, Vicente; Martı́, Rafael; Sánchez‐Oro, Jesús; Duarte, Abraham

doi:10.1057/jors.2013.156

Cited by 63 publications

(47 citation statements)

References 17 publications

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“…The nodes in the route form a cycle in the permutation and a node which is not in the route is codified as a fixed point, i.e, π(i) = i. Figure 1 shows a solution of an OP whose associated codification is the following permutation, π = (6,2,3,4,8,7,5,1). Note that the nodes in the solution route {1, 6, 7, 5, 8, 1} form a cycle in the permutation π, while those nodes off the route {2, 3, 4} are fixed points in the permutation.…”

Section: Individual Codificationmentioning

confidence: 99%

“…A common heuristic that appears in the literature in order to calculate the addcost value is to evaluate the cost of each possible insertion in the route and to take the minimum value [6,20]. If m represents the number of visited nodes, then the computational cost of selecting the candidate to insert at each step of this approach is O((n − m) · m) ≤ O(n 2 ).…”

Section: Add Operatormentioning

confidence: 99%

“…The proposed approach has been compared with the exact branch-and-cut algorithm (B&C) [10] and three state-of-the-art heuristics: GRASP with Path Relinking (GRASP-PR) [6], tabu search (TS) [12] and the two-parameter interactive algorithm (2-P IA) [20]. Results for TS are not reported because they were not competitive compared with the rest of the approaches, but they are available upon request from the authors.…”

Section: Computational Experimentsmentioning

confidence: 99%

“…For comparison purposes, the following algorithms have been tested: the exact B&C algorithm from [10] and two heuristics: GRASP-PR [6] and 2-P IA [20]. For each heuristic, 10 runs have been performed at each instance, while the exact algorithm has been run once.…”

Section: Comparison With State-of-the-art Algorithmsmentioning

confidence: 99%

“…A classification of the exact algorithms is presented in [8], where the branch-and-cut [10] should be highlighted. Plenty of heuristic approaches have also been proposed, such as tabu search [12], artificial neural networks [29], ant colony optimisation [16], variable neighbourhood search [3], two-parameter iterative algorithm [20] or a greedy randomised adaptive search procedure with and without path relinking [6].…”

Section: Introductionmentioning

confidence: 99%

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An efficient evolutionary algorithm for the orienteering problem

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Section: Individual Codificationmentioning

confidence: 99%

Section: Add Operatormentioning

confidence: 99%

Section: Computational Experimentsmentioning

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Section: Comparison With State-of-the-art Algorithmsmentioning

confidence: 99%

Section: Introductionmentioning

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An efficient evolutionary algorithm for the orienteering problem

Kobeaga

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

Chakraborty

Agarwal

2021

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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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Hybrid genetic algorithm for undirected traveling salesman problems with profits

Hao

2023

Networks

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The orienteering problem (OP) and prize‐collecting traveling salesman problem (PCTSP) are two typical TSPs with profits, in which each vertex has a profit and the goal is to visit several vertices to optimize the collected profit and travel costs. The OP aims to collect the maximum profit without exceeding the given travel cost. The PCTSP seeks to minimize the travel costs while ensuring a minimum profit threshold. This study introduces a hybrid genetic algorithm that addresses both the OP and PCTSP under a unified framework. The algorithm combines an extended edge‐assembly crossover operator to produce promising offspring solutions, and an effective local search to ameliorate each offspring solution. The algorithm is further enforced by diversification‐oriented mutation and population‐diversity management. Extensive experiments demonstrate that the method competes favorably with the best existing methods in terms of both the solution quality and computational efficiency. Additional experiments provide insights into the roles of the key components of the proposed method.

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GRASP with path relinking for the orienteering problem

Cited by 63 publications

References 17 publications

An efficient evolutionary algorithm for the orienteering problem

An efficient evolutionary algorithm for the orienteering problem

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

Hybrid genetic algorithm for undirected traveling salesman problems with profits

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