A bio-inspired approach: Firefly algorithm for Multi-Depot Vehicle Routing Problem with Time Windows

Abstract

In this research, an improved bio-inspired metaheuristic named firefly is utilized to solve the Multi-Depot Vehicle Routing Problem with Time Windows (MDVRP-TW) and it is a generalization of Vehicle Routing Problem with Time Windows. This paper discusses the use of biological intelligence in analysis and optimization on MDVRP-TW. The objective of the MDVRP-TW is to minimize the overall distance, means of transportation within a specified time gap, along with other constraints such as limitation of vehicle capacity, restrictions of route duration length to satisfy the customer’s requirements. The routes must be designed where each customer is visited only once in a particular time gap with one vehicle and all the routes must originate and end at the same depot. The overall demand should not go beyond the vehicle’s capacity on each route. Multi-objective problems have attracted the attentions of many researchers in recent years, as they are more closely related to real-world situations. However, transportation is a significant factor for the current society, exhibiting and planning a complicated transport system was a very thought-provoking task. Many research studies have shown several successful metaheuristics and heuristic methodologies to solve MDVRP-TW in which, instead of a single depot, numerous depots with varying locations. In this work considered both the earliest time and latest arrival time window (double-sided time window). It is assumed that if an arrival time is more significant than the latest time, it will lead to an infeasible solution whereas, if an arrival time is lesser than the earliest time, then it will lead to a waiting time. However, due to its challenging task and multi-objective and limitations, there is still a space to solve it. In this work, a novel technique that combines an improved firefly algorithm (IFA), which uses different mechanisms, namely, inter-depot approach in assignment phase, Clarke & wright algorithm, and local search method in routing and scheduling phase were applied. The suggested technique has been evaluated using Cordeau standard benchmark instances and proved the technique’s novelty and feasibility. In a few circumstances, the modified firefly algorithm outperforms other algorithms, and optimal benchmark solution in terms of results and competence.