The capacitated dispersion problem: an optimization model and a memetic algorithm

Martı́, Rafael; Martı́nez-Gavara, Anna; Sánchez‐Oro, Jesús

doi:10.1007/s12293-020-00318-1

Cited by 16 publications

(21 citation statements)

References 25 publications

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“…Finally, constraint (4) defines the values that decision variables can take. This model can be linearized, as shown by Peiró et al [19] and Martí et al [51].…”

Section: Problem Definitionmentioning

confidence: 99%

“…Algorithm 1 shows the main procedure of the constructive heuristic, which extends the algorithm proposed by Martí et al [51]. This approach generates a feasible initial solution (S).…”

Section: A Constructive Heuristicmentioning

confidence: 99%

“…The proposed algorithms were compared with the BKS reported by Martí et al [51], who employed both Gurobi and approximate methods as solving approaches. A Geometric probability distribution with parameter β = 0.3 was used for all the performed experiments.…”

Section: Computational Environmentmentioning

confidence: 99%

“…Each instance was run 30 times with different random seeds. Three groups of instances proposed by Martí et al [51] were employed, namely:…”

Section: Computational Environmentmentioning

confidence: 99%

“…A set of benchmark instances were used to compare the results yielded by both the exact and the metaheuristic approaches. Additionally, Martí et al [51] also proposed both an exact and a heuristic approach to solve the CDP.…”

mentioning

confidence: 99%

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A Multi-Start Biased-Randomized Algorithm for the Capacitated Dispersion Problem

et al. 2022

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The capacitated dispersion problem is a variant of the maximum diversity problem in which a set of elements in a network must be determined. These elements might represent, for instance, facilities in a logistics network or transmission devices in a telecommunication network. Usually, it is considered that each element is limited in its servicing capacity. Hence, given a set of possible locations, the capacitated dispersion problem consists of selecting a subset that maximizes the minimum distance between any pair of elements while reaching an aggregated servicing capacity. Since this servicing capacity is a highly usual constraint in real-world problems, the capacitated dispersion problem is often a more realistic approach than is the traditional maximum diversity problem. Given that the capacitated dispersion problem is an NP-hard problem, whenever large-sized instances are considered, we need to use heuristic-based algorithms to obtain high-quality solutions in reasonable computational times. Accordingly, this work proposes a multi-start biased-randomized algorithm to efficiently solve the capacitated dispersion problem. A series of computational experiments is conducted employing small-, medium-, and large-sized instances. Our results are compared with the best-known solutions reported in the literature, some of which have been proven to be optimal. Our proposed approach is proven to be highly competitive, as it achieves either optimal or near-optimal solutions and outperforms the non-optimal best-known solutions in many cases. Finally, a sensitive analysis considering different levels of the minimum aggregate capacity is performed as well to complete our study.

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“…Finally, constraint (4) defines the values that decision variables can take. This model can be linearized, as shown by Peiró et al [19] and Martí et al [51].…”

Section: Problem Definitionmentioning

confidence: 99%

“…Algorithm 1 shows the main procedure of the constructive heuristic, which extends the algorithm proposed by Martí et al [51]. This approach generates a feasible initial solution (S).…”

Section: A Constructive Heuristicmentioning

confidence: 99%

Section: Computational Environmentmentioning

confidence: 99%

“…Each instance was run 30 times with different random seeds. Three groups of instances proposed by Martí et al [51] were employed, namely:…”

Section: Computational Environmentmentioning

confidence: 99%

mentioning

confidence: 99%

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A Multi-Start Biased-Randomized Algorithm for the Capacitated Dispersion Problem

et al. 2022

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Formulations and valid inequalities for the capacitated dispersion problem

2022

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This work focuses on the capacitated dispersion problem for which we study several mathematical formulations in different spaces using variables associated with nodes, edges, and costs. The relationships among the presented formulations are investigated by comparing the projections of the feasible sets of the LP relaxations onto the subspace of natural variables. These formulations are then strengthened with families of valid inequalities and variable-fixing procedures. The separation problems associated with the valid inequalities that are exponential in number are shown to be polynomially solvable by reducing them to longest path problems in acyclic graphs. The dual bounds obtained from stronger but larger formulations are used to improve the strength of weaker but smaller formulations. Several sets of computational experiments are conducted to illustrate the usefulness of the findings, as well as the aptness of the formulations for different types of instances.

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Discrete Diversity Optimization: Models and Instances

Martínez-Gavara

2023

Springer Optimization and Its Applications

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The capacitated dispersion problem: an optimization model and a memetic algorithm

Cited by 16 publications

References 25 publications

A Multi-Start Biased-Randomized Algorithm for the Capacitated Dispersion Problem

A Multi-Start Biased-Randomized Algorithm for the Capacitated Dispersion Problem

Formulations and valid inequalities for the capacitated dispersion problem

Discrete Diversity Optimization: Models and Instances

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