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...

We can reformulate a vehicle routing problem (VRP) as an open shop scheduling problem (SSP) by representing visits as activities, vehicles as resources on the factory floor, and travel as set up costs between activities. In this paper we present two reformulations: from VRP to open shop, and the inverse, from SSP to VRP. Not surprisingly, VRP technology performs poorly on reformulated SSP’s, as...

We propose an abstraction of emerging vehicle routing problems, the VRP with Black Box Feasibility. In this problem the routes of a basic VRP need to satisfy an unknown set of constraints. A black box function to test the feasibility of a route is provided. Practical examples of such problems are combinations of VRP with Loading or VRP with Scheduling. We propose a heuristic column generation-b...

We analyze a model of conflict with endogenous choice of effort, where subsets of the contenders may force the resolution to be sequential: First the alliance fights it out with the rest and – in case they win – later they fight it out among themselves. For three-player games, we find that it will not be in the interest of any two of them to form an alliance. We obtain this result under two dif...

the problem of designing a set of routes with minimum cost to serve a collection of customers with a fleet of vehicles is a fundamental challenge when the number of customers to be dropped or picked up is not known during the planning horizon. the purpose of this paper is to develop a vehicle routing problem (vrp) model that addresses stochastic simultaneous pickup and delivery in the urban pub...

One of the motivations of hyper-heuristic research is to investigate the development of adaptive decision support systems that can be applied to a range of different problems and different problem instances [5]. One possible approach is to dynamically adjust the preferences of a set of simple lowlevel heuristics (or neighbourhood operators) during the search. Hyper-heuristics have been used to ...