The competitive vehicle routing problem is one of the important issues in transportation area. In this paper a new method for competitive VRP with time windows and stochastic demand is introduced. In the presented method a three time bounds are given and the probability of arrival time between each time bound is assumed to be uniform. The demands of each customer are different in each time wind...

This paper proposes a variation of the Multiple Ant Colony System for Vehicle Routing Problem with Time Windows (MACS-VRPTW) algorithm, which is based on an Ant Colony System approach, using two ant colonies to minimize first the number of vehicles and then the total traveled distance. As an improvement, the present work proposes to use a modified version specialized for a multiobjective contex...

−− A key issue in logistics is the efficient management of a vehicle fleet servicing a set of customers with known demands. Every vehicle route must start and finish at the assigned depot, each customer is to be visited by a single vehicle and vehicle capacities must not be exceeded. These are the constraints for the capacitated vehicle routing problem (VRP) whose objective is usually the minim...

The vehicle routing problem with time windows (VRPTW) is the problem of minimizing the total travel distance of a number of vehicles, under capacity and time window constraints, where every customer must be visited exactly once by a vehicle. We consider two generalizations of the VRPTW and propose local search algorithms. The first one treats traveling times as variables and introduce cost func...

The Vehicle Routing Problem with Time Windows (VRPTW) is a well-studied capacitated vehicle routing problem where the objective is to determine a set of feasible routes for a fleet of vehicles, in order to serve a set of customers with specified time windows. The ultimate optimization objective is to minimize the total travelling time of the vehicles. This paper presents a new hybrid heuristic ...

As a key factor of logistics distribution, vehicle routing problem (VRP) is a hot research topic in management and computation science. In this paper the principle and algorithm process of firefly algorithm are introduced in detail. Then the algorithm process and solving steps are designed for vehicle routing problem with time windows (VRPTW), including the coding and design of disturbance mech...

In this paper, we have conducted a literature review on the recent developments and publications involving the vehicle routing problem and its variants, namely vehicle routing problem with time windows (VRPTW) and the capacitated vehicle routing problem (CVRP) and also their variants. The VRP is classified as an NP-hard problem. Hence, the use of exact optimization methods may be difficult to s...

this paper presents a multi-criteria vehicle routing problem with soft time windows (vrpstw) to mini-mize fleet cost, routes cost, and violation of soft time windows penalty. in this case, the fleet is heterogene-ous. the vrpstw consists of a number of constraints in which vehicles are allowed to serve customers out of the desirable time window by a penalty. it is assumed that this relaxation a...

In this paper, we propose a metaheuristic based on annealing-like restarts to diversify and intensify local searches for solving the vehicle routing problem with time windows (VRPTW). Using the Solomon s benchmark instances for the problem, our method obtained seven new best results and equaled 19 other best results. Extensive comparisons indicate that our method is comparable to the best in pu...

The Vehicle Routing Problem with Time Windows (VRPTW) consists of constructing least cost routes from a depot to a set of geographically scattered service points and back to the depot, satisfying service time interval and capacity constraints. A Variable Neighbourhood Search algorithm with Compound Neighbourhoods is proposed to solve VRPTW in this paper. A number of independent neighbourhood op...