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 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

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

Particle Swarm Optimization Algorithm to Solve Vehicle Routing Problem with Fuel Consumption Minimization

The Conventional Vehicle Routing Problem (VRP) has the objective function of minimizing the total vehicles’ traveling distance. Since the fuel cost is a relatively high component of transportation costs, in this study, the objective function of VRP has been extended by considering fuel consumption minimization in the situation wherein the loading weight and traveling time are restricted. Based on these assumptions, we proposed to extend the route division procedure proposed by Kuo and Wang [4] such that when one of the restrictions can not be met the routing division continues to create a new sub-route to find an acceptable solution. To solve the formulated problem, the Particle Swarm Optimization (PSO) algorithm is proposed to optimize the vehicle routing plan. The proposed methodology is validated by solving the problem by taking a particular day data from a bottled drinking water distribution company. It was revealed that the saving of at best 13% can be obtained from the actual routes applied by the company

Construction of an Optimal Solution for a Real-World Routing-Scheduling- Loading Problem Construcción de una Solución Óptima para un Problema de Asignación de Rutas, Horarios y Cargas del Mundo Real

Abstract This work presents an exact method for the Routing-Loading-Scheduling Problem (RoSLoP). The objective of RoSLoP consists of optimizing the delivery process of bottled products in a company study case. RoSLoP, formulated through the well-known Vehicle Routing Problem (VRP), has been solved as a rich VRP variant through approximate methods. The exact method uses a linear transformation function, which allows the reduction of the complexity of the problem to an integer programming problem. The optimal solution to this method establishes metrics of performance for approximate methods, which reach an efficiency of 100% in distance traveled and 75% in vehicles used, objectives of VRP. The transformation function reduces the computation time from 55 to four seconds. These results demonstrate the advantages of the modeling mathematical to reduce the dimensionality of problems NP-hard, which permits to obtain an optimal solution of RoSLoP. This modeling can be applied to get optimal solutions for real-world problems. Keywords: Optimization, Routing-Scheduling-Loading Problem (RoSLoP), Vehicle Routing Problem (VRP), rich VRP. Resumen Éste trabajo presenta un método exacto para el problema de Asignación de Rutas, Horarios y Cargas (RoSLoP). El objetivo de RoSLoP consiste en optimizar el proceso de entrega de productos embotellados en una compañía caso de estudio. El problema RoSLoP, formulado a través del conocido Problema de Enrutado de Vehículos (VRP), ha sido resuelto como una variable VRP enriquecida a través de métodos aproximados. El método exacto usa una función de transformación lineal, la cual permite la reducción de la complejidad del problema a un problema de programación entera. La solución óptima para éste método establece las métricas del desempeño para los métodos aproximados, los cuales alcanzan una eficiencia del 100% en distancia recorrida y 75% en vehículos utilizados, objetivos del VRP. La función de transformación reduce el tiempo del cálculo de 55 a cuatro segundos. Éstos resultados demuestran las ventajas del modelado matemático para reducir la dimensionalidad de problemas NPDuros, lo cual permite la obtención de una solución óptima del problema RoSLoP. Éste modelado puede ser aplicado para obtener las soluciones óptimas para problemas del mundo real. Palabras Clave: Optimización, Problema de Asignación de Rutas, Horarios y Cargas (RoSLoP), Problema de Enrutado de Vehículos (VRP), Problema VRP Enriquecido

Solving Capacitated Vehicle Routing Problem Using Football Game Algorithm

The Capacitated Vehicle Routing Problem (CVRP) plays an important role in the logistics transportation sector. Determining the proper route will reduce the company's operational costs. In CVRP, a number of vehicles have a capacity limit that can serve all customers. This research completes a real case study on a bottled drinking water company where the company still uses the subjective method of the driver to determine the transportation route. Based on the conditions in the company, the selection of the best route will consider vehicle capacity and demand to determine the shortest route. The execution of this case study uses the Football Game Algorithm (FGA) which was first initiated by Fadakar Ebrahimi which proved promising and had the strongest performance in all cases. FGA is expected to be able to determine the shortest distribution route from the existing cases to reduce the distribution costs incurred. This study takes data from 4 days of delivery that served 78 customers. The average daily transportation cost savings result is 42%. This amount indicates that the FGA algorithm is effective for completing a real case study in CVRP