Two-stage Particle Swarm Optimization Algorithm for the Time Dependent Alternative Vehicle Routing Problem

Hsiaofan Wang Yenyi Lee

doi:10.4172/2168-9679.1000170

Abstract

This study considered a Time Dependent Alternative Vehicle Routing Problem (TDAVRP) in a multi-graph network (TDAVRP) and was formulated into a Mixed Integer Programming model. Due to its NP nature, an algorithm based on Particle Swarm Optimization (PSO) with local improvement was developed to speed up the solution procedure. By using different sets of Solomon’s benchmark problems and continuous travel time functions, the accuracy and efficiency of the two-stage PSO were evaluated. The computational results showed that the proposed algorithm is capable of deriving optimal or near optimal solutions in a short period of time when the size of the problems are small and is able to obtain feasible solutions within a reasonable time when solving the large problems which cannot be solved by ILOG CPLEX. In addition, Sensitivity Analysis was conducted to evaluate the performances of the parameters. The results indicated that the number of customers is a sensitive parameter and will influence the required number of vehicles, value of violations and percentage of alternative edges in the solution sets.

Highlights

According to a report published by the International Energy Agency in 2009, approximately 23% of global carbon dioxide emissions can be traced back to transportation [1]
Several researchers have studied the Time Dependent Vehicle Routing Problem (TDVRP) which takes the issues of time-dependent travel time into account
Different from the other VRP variants, the TDVRP is to determine a set of vehicle routes originating and terminating at a single depot when the travel time of vehicles depends on the time of day in order to minimize the total travel cost

Summary

Introduction

According to a report published by the International Energy Agency in 2009, approximately 23% of global carbon dioxide emissions can be traced back to transportation [1]. Reducing the total time spent on traveling and the number of vehicles assigned at distribution centers would be one of the methods to decrease carbon dioxide emissions caused by transportation. Traveling conditions change throughout the day, and the problems associated with congestion are most obvious during peak-hours. When this is the case of the delivery of the goods, allowing the drivers to take alternative routes will let them easier to meet the requirement of the delivery time by the customers. All customers are visited within their claimed time windows exactly once, and the total demand of customers assigned to each route does not violate the capacity of the vehicle

Methods

Results

Discussion

Conclusion