A reactive GRASP for a commercial territory design problem with multiple balancing requirements

Ríos‐Mercado, Roger Z.; Fernández, Elena

doi:10.1016/j.cor.2007.10.024

Cited by 121 publications

(80 citation statements)

References 19 publications

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“…In the last one, only the partitioning problem is solved. In some cases, the partitioning is solved keeping in mind that the application is an arc routing problem (Muyldermans et al, 2002(Muyldermans et al, , 2003Perrier et al, 2008;Assis et al, 2014) and in others that the application is on a node routing problem (Mourgaya and Vanderbeck, 2007;Lin and Kao, 2008;Ríos-Mercado and Fernández, 2009;Gonzalez-Ramírez et al, 2011;Jarrah and Bard, 2012;Lei et al, 2012;Salazar-Aguilar et al, 2012).…”

Section: Literature Reviewmentioning

confidence: 99%

“…Furthermore, the meaning of compactness slightly differs from author to author, being, for instance, associated with: i) zones shapes as close as possible to circles, squares or rectangles (Lin and Kao, 2008;Gonzalez-Ramírez et al, 2011;Jarrah and Bard, 2012); ii) geographically or visually compact zones (Perrier et al, 2008;Lei et al, 2012); or iii) the proximity between the demand entities in the same zone (Poot et al, 2002;Muyldermans et al, 2003;Kim et al, 2006;Tang and Miller-Hooks, 2006;Ríos-Mercado and Fernández, 2009;Salazar-Aguilar et al, 2012;Assis et al, 2014).…”

Section: Literature Reviewmentioning

confidence: 99%

“…We may find measures based on maximum travel times (Mourão et al, 2009;Gonzalez-Ramírez et al, 2011); on maximum Euclidean distances (Ríos-Mercado and Fernández, 2009;Assis et al, 2014); on the sum of the Euclidean distances (Kim et al, 2006;Mourgaya and Vanderbeck, 2007;Salazar-Aguilar et al, 2012); on the averages and standard deviations of distances, or travel times between customers, or to a reference point in a zone (Poot et al, 2002;Tang and Miller-Hooks, 2006;Mourão et al, 2009); on the perimeters of the zones (Lei et al, 2012); or even perimeters and areas of the zones (Lin and Kao, 2008). Jarrah and Bard (2012) define clusters of clients in the plane in such a way that the ratio of the difference between the maximum and the minimum x coordinate and the difference of the maximum and the minimum y coordinate lies within a given interval.…”

Section: Literature Reviewmentioning

confidence: 99%

“…In some cases, these evaluation compactness measures are also embedded in the heuristic processes (Kim et al, 2006;Tang and Miller-Hooks, 2006;Ríos-Mercado and Fernández, 2009;Gonzalez-Ramírez et al, 2011;Lei et al, 2012;Salazar-Aguilar et al, 2012;Assis et al, 2014). In other cases, authors devise compactness indicators only embedded in the solution methods (Mourgaya and Vanderbeck, 2007;Lin and Kao, 2008).…”

Section: Literature Reviewmentioning

confidence: 99%

“…Zones contiguity is generally related to the connectivity between all of its demand entities (Muyldermans et al, 2003;Perrier et al, 2008;Assis et al, 2014) or the possibility to reach all of them within the zone (Ríos-Mercado and Fernández, 2009;Salazar-Aguilar et al, 2012).…”

Section: Literature Reviewmentioning

confidence: 99%

See 4 more Smart Citations

The mixed capacitated arc routing problem with non-overlapping routes

Constantino

Gouveia

Mourão

et al. 2015

European Journal of Operational Research

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Real world applications for vehicle collection or delivery along streets usually lead to arc routing problems, with additional and complicating constraints. In this paper we focus on arc routing with an additional constraint to identify vehicle service routes with a limited number of shared nodes, i.e. vehicle service routes with a limited number of intersections. This constraint leads to solutions that are better shaped for real application purposes. We propose a new problem, the bounded overlapping MCARP (BCARP), which is defined as the mixed capacitated arc routing problem (MCARP) with an additional constraint imposing an upper bound on the number of nodes that are common to different routes. The best feasible upper bound is obtained from a modified MCARP in which the minimization criteria is given by the overlapping of the routes. We show how to compute this bound by solving a simpler problem. To obtain feasible solutions for the bigger instances of the BCARP heuristics are also proposed. Computational results taken from two well known instance sets show that, with only a small increase in total time traveled, the model BCARP produces solutions that are more attractive to implement in practice than those produced by the MCARP model.

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Section: Literature Reviewmentioning

confidence: 99%

Section: Literature Reviewmentioning

confidence: 99%

Section: Literature Reviewmentioning

confidence: 99%

Section: Literature Reviewmentioning

confidence: 99%

Section: Literature Reviewmentioning

confidence: 99%

See 3 more Smart Citations

The mixed capacitated arc routing problem with non-overlapping routes

Constantino

Gouveia

Mourão

et al. 2015

European Journal of Operational Research

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Connected graph partitioning with aggregated and non‐aggregated gap objective functions

et al. 2023

Self Cite

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This article deals with the problem of partitioning a graph into connected components by optimizing some balancing objective functions related to the vertex weights. Objective functions based on the gap or range of the partition's components, that is, the difference between the maximum and minimum weight of a vertex in the component, have been already introduced in the literature. Here we introduce the notion of aggregated gap, defined as the sum of the differences between the weights of the vertices and the minimum weight of a vertex in the component. We study new connected ‐partitioning problems whose objective is a function of the components' aggregated gap, and give NP‐hardness results for these problems on general graphs. Mathematical programming formulations are proposed for these problems adopting flow‐based constraints for modeling connectivity in a partition. Even if they are introduced for the new aggregated gap problems, such formulations are rather general and apply also to the classical non‐aggregated gap problems. Extensive computational tests, both for aggregated and non‐aggregated gap problems, are performed on a set of squared grids and randomly generated graphs with up to 120 vertices, and a number of components ranging from 2 to 9. In our experiments, we test several alternative formulations for our problems providing a comparative analysis of their performance.

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Extended construction heuristics

Resende

Ribeiro

2016

Optimization by GRASP

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A reactive GRASP for a commercial territory design problem with multiple balancing requirements

Cited by 121 publications

References 19 publications

The mixed capacitated arc routing problem with non-overlapping routes

The mixed capacitated arc routing problem with non-overlapping routes

Connected graph partitioning with aggregated and non‐aggregated gap objective functions

Extended construction heuristics

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