Ant colony optimization and its application to the vehicle routing problem with pickups and deliveries

Ant Colony Optimization (ACO) is a population-based metaheuristic that can be used to find approximate solutions to difficult optimization problems. It was first introduced for solving the Traveling Salesperson Problem. Since then many implementations of ACO have been proposed for a variety of combinatorial optimization. In this chapter, ACO is applied to the Vehicle Routing Problem with Pickup and Delivery (VRPPD). VRPPD determines a set of vehicle routes originating and ending at a single depot and visiting all customers exactly once. The vehicles are not only required to deliver goods but also to pick up some goods from the customers. The objective is to minimize the total distance traversed. The chapter first provides an overview of ACO approach and presents several implementations to various combinatorial optimization problems. Next, VRPPD is described and the related literature is reviewed, Then, an ACO approach for VRPPD is discussed. The approach proposes a new visibility function which attempts to capture the “delivery” and “pickup” nature of the problem. The performance of the approach is tested using well-known benchmark problems from the literature

An ant colony algorithm for the mixed vehicle routing problem with backhauls

The Vehicle Routing Problem with Pickup and Delivery (VRPPD) is a variant of the Vehicle Routing Problem where the vehicles are not only required to deliver goods but also to pick up some goods from the customers. The Mixed Vehicle Routing Problem with Backhauls (MVRPB) is a special case of VRPPD where each customer has either a delivery or a pickup demand to be satisfied and the customers can be visited in any order along the route. Given a fleet of vehicles and a set of customers with known pickup or delivery demands MVRPB determines a set of vehicle routes originating and ending at a single depot and visiting all customers exactly once. The objective is to minimize the total distance traversed with the least number of vehicles. For this problem, we propose an Ant Colony Optimization algorithm with a new visibility function which attempts to capture the “delivery” and “pickup” nature of the problem. Our numerical tests to compare the performance of the proposed approach with those of the well-known benchmark problems reveal that the proposed approach provides encouraging results

Ant colony optimization approach for the capacitated vehicle routing problem with simultaneous delivery and pick-up

We propose an Ant Colony Optimization (ACO) algorithm to the NPhard Vehicle Routing Problem with Simultaneous Delivery and Pick-up (VRPSDP). In VRPSDP, commodities are delivered to customers from a single depot utilizing a fleet of identical vehicles and empty packages are collected from the customers and transported back to the depot. The objective is to minimize the total distance traveled. The algorithm is tested with the well-known benchmark problems from the literature. The experimental study indicates that our approach produces comparable results to those of the benchmark problems in the literature

The Vehicle Routing Problem with Divisible Deliveries and Pickups

The vehicle routing problem with divisible deliveries and pickups is a new and interesting model within reverse logistics. Each customer may have a pickup and delivery demand that have to be served with capacitated vehicles. The pickup and the delivery quantities may be served, if beneficial, in two separate visits. The model is placed in the context of other delivery and pickup problems and formulated as a mixed-integer linear programming problem. In this paper, we study the savings that can be achieved by allowing the pickup and delivery quantities to be served separately with respect to the case where the quantities have to be served simultaneously. Both exact and heuristic results are analysed in depth for a better understanding of the problem structure and an average estimation of the savings due to the possibility of serving pickup and delivery quantities separately

A Survey On Multi Trip Vehicle Routing Problem

The vehicle routing problem (VRP) and its variants are well known and greatly explored in the transportation literature. The vehicle routing problem can be considered as the scheduling of vehicles (trucks) to a set of customers under various side constraints. In most studies, a fundamental assumption is that a vehicle dispatched for service finishes its duty in that scheduling period after it returns back to the depot. Clearly, in many cases this assumption may not hold. Thus, in the last decade some studies appeared in the literature where this basic assumption is relaxed, and it is allowed for a vehicle to make multiple trips per period. We consider this new variant of the VRP an important one with direct practical impact. In this survey, we define the vehicle routing problem with multiple trips, define the current state-of-the-art, and report existing results from the current literature

On the use of biased-randomized algorithms for solving non-smooth optimization problems

Soft constraints are quite common in real-life applications. For example, in freight transportation, the fleet size can be enlarged by outsourcing part of the distribution service and some deliveries to customers can be postponed as well; in inventory management, it is possible to consider stock-outs generated by unexpected demands; and in manufacturing processes and project management, it is frequent that some deadlines cannot be met due to delays in critical steps of the supply chain. However, capacity-, size-, and time-related limitations are included in many optimization problems as hard constraints, while it would be usually more realistic to consider them as soft ones, i.e., they can be violated to some extent by incurring a penalty cost. Most of the times, this penalty cost will be nonlinear and even noncontinuous, which might transform the objective function into a non-smooth one. Despite its many practical applications, non-smooth optimization problems are quite challenging, especially when the underlying optimization problem is NP-hard in nature. In this paper, we propose the use of biased-randomized algorithms as an effective methodology to cope with NP-hard and non-smooth optimization problems in many practical applications. Biased-randomized algorithms extend constructive heuristics by introducing a nonuniform randomization pattern into them. Hence, they can be used to explore promising areas of the solution space without the limitations of gradient-based approaches, which assume the existence of smooth objective functions. Moreover, biased-randomized algorithms can be easily parallelized, thus employing short computing times while exploring a large number of promising regions. This paper discusses these concepts in detail, reviews existing work in different application areas, and highlights current trends and open research lines

Vehicle Routing Based on Discrete Particle Swarm Optimization and Google Maps API

Transportation imposes considerable cost on goods and has a significant influence on competitive advantage of a company. How to reduce the costs and improve the profit of a company is an important issue. Vehicle routing is a critical factor in reducing transportation costs. Finding optimal vehicle routes offers great potential to efficiently manage fleets, reduce costs and improve service quality. An effective scheme to manage fleets and determine vehicle routes for delivering goods is important for carriers to survive. In the existing literature, a variety of vehicle routing problems (VRP) have been studied. However, most papers do not integrate with GIS. In this paper, we consider a variant of VRP called Vehicle Routing Problem with Arbitrary Pickup and Delivery points (VRPAPD). The goal of this paper is to develop an algorithm for VRPAPD based on Google Maps API. To achieve this goal, we propose an operation model and formulate an optimization problem. In our problem formulation, we consider a set of goods to be picked up and delivered. Each goods has a source address and a destination address. The vehicles to transport the goods have associated capacities, including the maximal weight a vehicle can be carried and the maximal distance a vehicle can travel. The problem is to minimize the routes for picking up and delivering goods. The emerging Google Maps API provides a convenient package to develop an effective vehicle routing system. In this paper, we develop a vehicle routing algorithm by combining a discrete particle swarm optimization (DPSO) method with Google Maps API. We illustrate the effectiveness of our algorithm by an example