Sequential variable neighborhood descent variants: an empirical study on the traveling salesman problem

Abstract

In a single local search algorithm, several neighborhood structures are usually explored. The simplest way is to define a single neighborhood as the union of all predefined neighborhood structures; the other possibility is to make an order (or sequence) of the predefined neighborhoods, and to use them in the first improvement or the best improvement fashion, following that order. In this work, first we classify possible variants of sequential use of neighborhoods and then, empirically analyze them in solving the classical traveling salesman problem (TSP). We explore the most commonly used TSP neighborhood structures, such as 2-opt and insertion neighborhoods. In our empirical study, we tested 76 different such heuristics on 15,200 random test instances. Several interesting observations are derived. In addition, the two best of 76 heuristics (used as local searches within a variable neighborhood search) are tested on 23 test instances taken from the TSP library (TSPLIB). It appears that the union of neighborhoods does not perform well.

A variable neighborhood search for flying sidekick traveling salesman problem

“…() and Mjirda et al. (), which corresponds to step 3 of the HGVNS framework, is defined in Algorithm . Given an initial solution (line ), the main loop iterates over parameter k until it reaches the stop condition, which is the number of neighborhoods considered .…”

Less is more approach: basic variable neighborhood search for the obnoxious p‐median problem

“…This idea comes from the following properties: (i) a local optimum relative to one neighborhood structure is not necessarily a local optimum for another neighborhood structure; (ii) a global optimum is a local optimum with respect to all neighborhood structures. The first property is usually exploited by using multiple local searches in the improvement step as in variable neighborhood descent (see, e.g., Hansen et al., ; Mjirda et al., ; Duarte et al., ). The second property suggests using several neighborhoods, if the found local optima are of poor quality.…”

VNS methods for home care routing and scheduling problem with temporal dependencies, and multiple structures and specialties

“…After this study of the literature, we decided to focus on the development of meta‐heuristics, in particular variants of VNS algorithm, motivated by the lack of such meta‐heuristics in our problem, despite the efficiency of VNS in several variants of VRP (Kammoun et al., ; Mjirda et al., ). We extended the VRPTW‐S presented in (Bredström and Rönnqvist, ) to define and study a new variant of VRP that we called VRPTW‐TD‐2MS, motivated by a real case study of the home care structures network of Roanne town in France.…”

“…The GVNS has been used to deal with VRP variants in literature, for example, Mjirda et al. () designed GVNS with different type of VND to solve the traveling salesman problem. Algorithm shows the entire GVNS that we have developed for our problem.…”