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...

The Vehicle Routing Problem (VRP), a famous problem of operation research, holds a central place in combinatorial optimization problems. In this problem, a fleet vehicles with Q capacity start to move from depot and return after servicing to customers in which visit only ones each customer and load more than its capacity not at all. The objective is to minimize the number of used vehicles and t...

Vehicle Routing Problem with Simultaneous Pick-up and Delivery (VRP-SPD) is regarded as an NP-hard problem, which takes unacceptable time to use traditional algorithms to solve. This article presents an artificial immune systems or AIS-based algorithm to solve the problem and the results shows competitive performance. This algorithm is embedded with a sweep approach to generate random initial p...

Recently proved successful for variants of the vehicle routing problem (VRP) involving time windows, genetic algorithms have not yet shown to compete or challenge current best search techniques in solving the classical capacitated VRP. In this paper, a hybrid genetic algorithm to address the capacitated vehicle routing problem is proposed. The basic scheme consists in concurrently evolving two ...

This research applies the meta-heuristic method of ant colony optimization (ACO) to an established set of vehicle routing problems (VRP). The procedure simulates the decision-making processes of ant colonies as they forage for food and is similar to other adaptive learning and artificial intelligence techniques such as Tabu Search, Simulated Annealing and Genetic Algorithms. Modifications are m...

Ant Colony Optimisation is a metaheuristic for combinatorial optimisation problems. In this paper we show its successful application to the Vehicle Routing Problem (VRP). First, we introduce VRP and its many variants, such as VRP with Time Windows, Time Dependent VRP, Dynamic VRP, VRP with Pickup and Delivery. These variants have been formulated in order to bring the VRP as close as possible to...

Vehicle Routing problem (VRP) is the challenging and sophisticated optimization problem which can be solved by various approaches like Exact methods, metaheuristic optimization algorithm and Mathematical approaches including linear and integer programming Techniques. Exact algorithms can only solve relatively small problems of VRP. Several approximate algorithms have proven successfully to find...

The aim of this study was to evaluate the potential of polyelectrolyte complex nanoparticles (PENPs) based on hyaluronic acid/chitosan hydrochloride (HA/HCS) for co-loading mitoxantrone (MTO) and verapamil (VRP) to overcome multidrug resistance in breast tumors. PENPs co-loaded with MTO and VRP (MTO-VRP-PENPs) were affected by the method of preparation, molecular weight of HA, mass ratios and i...

A recent focal point in research on the vehicle routing problem (VRP) is the issue of robustness in which customer demand is uncertain. In this paper, we conduct a theoretical analysis of the demand distributions whose induced workloads are as undesirable as possible. We study two common variations of VRP in a continuous approximation setting: the first is the VRP with time windows, and the sec...

The Vehicle Routing Problem (VRP) is a classical problem in Operations Research. It is a generalisation of the Travelling Salesman Problem in which a set of locations must be visted by one of a number of vehicles. All vehicles start and end at a depot location. The aim of the problem is to minimise the total distance covered by the trucks. There are many different variants of the VRP. For examp...