A Multistage Very Large-Scale Neighborhood Search for the Vehicle Routing Problem with Soft Time Windows

Abstract

This paper considers the Vehicle Routing Problem with Soft Time Windows, a challenging routing problem, where customer's time windows may be violated at a certain cost. The Vehicle Routing Problem with Soft Time Windows has a lexicographic objective function, aiming at minimizing first the number of routes, then the number of violated time windows and finally the total routing distance. We present a multi-stage Very Large-Scale Neighborhood search for this problem. Each stage corresponds to a Variable Neighborhood Descent over a parametrizable Very Large-Scale Neighborhood. These neighborhoods contain an exponential number of neighbors, as opposed to classical local search neighborhoods. Often, searching Very Large-Scale Neighborhoods can produce local optima of a higher quality than polynomial-sized neighborhoods. Furthermore we use a sophisticated heuristic to determine service start times allowing to minimize the number of violated time windows. We test our approach on number of different problem types, and compare the results to the relevant state-of-the-art. The experimental results show that our algorithm improves best-known solutions on 53% of the most studied instances. Many of these improvements stem from a reduction of the number of vehicles, a critical objective in Vehicle Routing Problems.

Flexible transit routing model considering passengers’ willingness to pay

“…The heuristic algorithm generates an initial solution according to the given constraints and then improves the performance of the initial solution based on an algorithm to obtain a satisfactory solution. The algorithms that optimise the initial solution are mostly intelligent algorithms, such as tabu search [37][38][39][40], ant colony [40][41][42], simulated annealing [43][44][45][46], and genetic algorithms [46]. A tabu search is a metaheuristic that guides a local heuristic search procedure in exploring the solution space beyond local optimality.…”

Multidepot Recycling Vehicle Routing Problem with Resource Sharing and Time Window Assignment

“…Constraint ( 16) is used to avoid subtours for vehicles. Constraint (17) represents that each vehicle has enough capacity to satisfy the total demand of assigned customers. Constraint (18) ensures that the total demand of customers served by a logistics facility should be beyond its capacity.…”

“…In real life, the time windows for most customers are viewed as soft time windows, that is, they can be violated by paying certain penalties [15,16]. Most logistics service providers try to recycle cargoes within the predetermined time windows in logistics operations to reduce the penalty cost [17]. However, the vehicles cannot provide recycling services for customers in the expected time windows due to long transportation distance and unreasonable service time windows for logistics facilities [18,19].…”

Multi‐mode resource‐constrained project scheduling using modified variable neighborhood search heuristic

“…To generate valid sequence of activities, numerous researchers have applied variable neighborhood search (VNS). Similarly, among heuristic and/or meta‐heuristic approaches, VNS is another very powerful meta‐heuristic approach for solving many combinatorial optimization problems such as the vehicle routing problem (Mouthuy et al., ; Monroy‐Licht et al., ; Polat, ), inventory routing problem (Gruler et al., ), and the traveling salesman problem (Mladenovic et al., ; Mjirda et al., ). The basic variant of VNS was first proposed in Mladenović and Hansen (), which includes an improvement phase in which a local search is applied and one of the so‐called shaking‐phase or swap‐move approaches is used to resolve local minima traps.…”