Applying min–max<i>k</i>postmen problems to the routing of security guards

Willemse, Elias J.; Joubert, Johan W.

doi:10.1057/jors.2011.26

Cited by 25 publications

(28 citation statements)

References 24 publications

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“…TABU-GUARD was proposed to tackle MMRPP (including MMCPP) by Willemse and Joubert (2012). This algorithm follows three stages: (1) generating multiple random initial solutions by a PI method (see Introduction), (2) IMPROVE-SOLUTION, which iteratively attempts to shorten the longest route by exchanging or reallocating edges between different routes, (3) TABU-SEARCH, which further improves the solutions.…”

Section: Tabu-guard For Mmrppmentioning

confidence: 99%

“…The length of 1-tour is w(1-tour). The tour is encoded by the scheme of Willemse and Joubert (2012), in which only required edges are explicitly represented per route and it is assumed that the shortest path is used between consecutive required edges. Thus, 1-tour is denoted as RPPT = {r 1 ,SPR(r 1 , r 2 ), r 2 , .…”

Section: Stage 1: Generating Initial Solutionsmentioning

confidence: 99%

“…The min-max RPP (MMRPP) or min-max CPP (MMCPP) has been studied by several authors (Ahr and Reinelt 2006, Benavent et al 2009, Willemse and Joubert 2012, but all of them are limited to a single depot for all postmen. So far, there is no study on the MMRPP/MMCPP in the multiple-depot case.…”

Section: Introductionmentioning

confidence: 99%

“…These methods with proper improved heuristics obtained a better solution in most instances than the Frederickson heuristic. Later, a Parallel-Insertion method (henceforth referred to as PI) was proposed to solve both MMCPP and MMRPP by Willemse and Joubert (2012). Essentially, this algorithm generates multiple routes that traverse the required edges that are farthest from the depot, and then adds each untraversed required edge to an existing route such that the resulting increase of route length is minimised.…”

Section: Introductionmentioning

confidence: 99%

“…Later, Willemse and Joubert (2012) introduced a tabu search algorithm TABU-GUARD, which can be applied to both MMCPP and MMRPP. TABU-GUARD outperformed the other strategies and achieved the best solutions for MMCPP test instances.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

A Balanced Route Design for Min-Max Multiple-Depot Rural Postman Problem (MMMDRPP): a police patrolling case

Chen

Cheng

Shawe‐Taylor

2017

International Journal of Geographical Information Science

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Providing distributed services on road networks is an essential concern for many applications, such as mail delivery, logistics and police patrolling. Designing effective and balanced routes for these applications is challenging, especially when involving multiple postmen from distinct depots. In this research, we formulate this routing problem as a MinMax Multiple-Depot Rural Postman Problem (MMMDRPP). To solve this routing problem, we develop an efficient tabu-search-based algorithm and propose three novel lower bounds to evaluate the routes. To demonstrate its practical usefulness, we show how to formulate the route design for police patrolling in London as an MMMDRPP and generate balanced routes using the proposed algorithm. Furthermore, the algorithm is tested on multiple adapted benchmark problems. The results demonstrate the efficiency of the algorithm in generating balanced routes. ARTICLE HISTORY

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Section: Tabu-guard For Mmrppmentioning

confidence: 99%

Section: Stage 1: Generating Initial Solutionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A Balanced Route Design for Min-Max Multiple-Depot Rural Postman Problem (MMMDRPP): a police patrolling case

Chen

Cheng

Shawe‐Taylor

2017

International Journal of Geographical Information Science

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Solving the large‐scale min–max K‐rural postman problem for snow plowing

et al. 2017

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International audienceThis article studies the snow plow routing problem, which is a modified version of the min–max problem with k-vehicles for arc routing on a mixed graph with hierarchy. Each arc or edge is given a priority and instead of minimizing the overall finishing time, we minimize the latest finishing time for each priority class. We consider turn restrictions, route balancing, and variable vehicle speeds in a real large-scale network. To solve the problem, we present a graph transformation from a directed rural postman problem with turn penalties to an asymmetric traveling salesman problem. We then make the following modifications to the metaheuristics to better handle the constraints: development of new neighborhood operators, several applications of the same destruction operators before repair of the solution, and a dynamic arc-grouping procedure when links are removed or inserted. We tested our methodology on three real networks with 1,626 to 2,146 street segments and 613 to 723 intersections. The results show that our approach can improve the solution, and the grouping procedure is helpful. The results also show that some operators perform better than others; the network topology seems to explain these variations. Finally, we validated our methodology by comparing to some routes planned in the past and to some routes obtained from a commercial solver

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An updated annotated bibliography on arc routing problems

Mourão

Pinto

2017

Networks

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The number of arc routing publications has increased significantly in the last decade. Such an increase justifies a second annotated bibliography, a sequel to Corberán and Prins (Networks 56 (2010), 50–69), discussing arc routing studies from 2010 onwards. These studies are grouped into three main sections: single vehicle problems, multiple vehicle problems and applications. Each main section catalogs problems according to their specifics. Section 2 is therefore composed of four subsections, namely: the Chinese Postman Problem, the Rural Postman Problem, the General Routing Problem (GRP) and Arc Routing Problems (ARPs) with profits. Section 3, devoted to the multiple vehicle case, begins with three subsections on the Capacitated Arc Routing Problem (CARP) and then delves into several variants of multiple ARPs, ending with GRPs and problems with profits. Section 4 is devoted to applications, including distribution and collection routes, outdoor activities, post‐disaster operations, road cleaning and marking. As new applications emerge and existing applications continue to be used and adapted, the future of arc routing research looks promising. © 2017 Wiley Periodicals, Inc. NETWORKS, Vol. 70(3), 144–194 2017

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Applying min–maxkpostmen problems to the routing of security guards

Cited by 25 publications

References 24 publications

A Balanced Route Design for Min-Max Multiple-Depot Rural Postman Problem (MMMDRPP): a police patrolling case

A Balanced Route Design for Min-Max Multiple-Depot Rural Postman Problem (MMMDRPP): a police patrolling case

Solving the large‐scale min–max K‐rural postman problem for snow plowing

An updated annotated bibliography on arc routing problems

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