A Selector Operator-Based Adaptive Large Neighborhood Search for the Covering Tour Problem

Abstract

The Covering Tour Problem finds application in distribution network design. It includes two types of vertices: the covering ones and the ones to be covered. This problem is about identifying a lowest-cost Hamiltonian cycle over a subset of the covering vertices in such a way that every element not of this type is covered. In this case, a vertex is considered covered when it is located within a given distance from a vertex in the tour. This paper presents a solution procedure based on a Selector operator that allows to convert a giant tour into an optimal CTP solution. This operator is embedded in an adaptive large neighborhood search. The method is competitive as shown by the quality of results evaluated using the output of a state-of-the-art exact algorithm.

Last mile delivery routing problem using autonomous electric vehicles

“…Furthermore, several methods have been proposed for CTP, including reduction rules (Motta, Nogueira & Ochi, 2010;Motta, Ochi & Martinhon, 2001b), combined cooperative strategy (EA with branch-and-cut algorithm) (Jozefowiez, Semet & Talbi, 2007), ABC (Pandiri & Singh, 2019), Greedy Randomized Adaptive Search Procedure (GRASP) (Motta, Ochi & Martinhon, 2001a), A selector operator-based adaptive Large Neighborhood Search (LNS) (Leticia Vargas, Jozefowiez & Ngueveu, 2015;, dynamic programming (Vargas, Jozefowiez & Ngueveu, 2017), heuristic algorithm using local search (Murakami, 2018a). Also, according to the literature, the other variants and extensions of CTP are multiobjective CTP (Nolz, Doerner, Gutjahr & Hartl, 2010), Multi-vehicle CTP (m-CTP) (Ha, Bostel, Langevin & Rousseau, 2013;Hachicha, Hodgson, Laporte & Semet, 2000;Jozefowiez, 2014;Kammoun, Derbel, Ratli & Jarboui, 2015,1;Lopes, Souza & da Cunha, 2013;Margolis, Song & Mason, 2022;Murakami, 2014,1;Oliveira, Moretti & Reis, 2015;Ziegler, 2013) in which m routes are found to visit a part of the customers and cover the remaining ones while satisfying a maximum tour length, multi-objective m-CTP (Glize, Roberti, Jozefowiez & Ngueveu, 2020), m-CTP with split delivery (Naji-Azimi, Renaud, Ruiz & Salari, 2012), Multi-vehicle multi-CTP (mm-CTP) (Kammoun, Derbel & Jarboui, 2018,2;Pham, Hà & Nguyen, 2017) (for dataset description on mm-CTP see (Pham, Hà & Nguyen, 2018)), Multi-Vehicle Probabilistic CTP (MVPCTP) (Karaoğlan, Erdoğan & Koç, 2018), Prize-collecting CTP (PCCTP) (Clímaco, Rosseti, Silva & Guerine, 2021), stochastic CTP (Tricoire, Graf & Gutjahr, 2012;Zehetner & Gutjahr, 2018), geometric CTP (Arkin...…”

A large neighborhood search approach to the vehicle routing problem with delivery options

“…Moccia et al [2012] handle the GVRPTW, when a customer is inserted in a route, the options for the other customers of this route can be changed through dynamic programming. Vargas et al [2015] solve the CTP with an ALNS algorithm that uses dynamic programming to decompose a giant tour into routes. Drexl [2012] underlined that Hempsch and Irnich [2008] was almost the only paper considering synchronized resources.…”

The Covering Path Problem on a Grid

“…The CTP can also be treated as a generalized traveling salesman problem (GTSP) ( [18]): given several sets of nodes, the GTSP seeks to determine a shortest tour passing at least once through each set. Recent work continues on designing solution approaches for the CTP and multi-vehicle CTP; such as branch and price ( [24]), column generation ( [28]) and adaptive large neighborhood search ( [27]).…”

“…Denote d i the distance between F i and F i+1 , and L = T −1 i=1 d i the path length. Let S i be the set of integer points covered by F i and f LB−D (•) be the lower bound function defined in(27). Similar to(7) we haveN ≤ |S 1 | + T −1 i=1 |S i+1 − S i |.…”