ORIGINAL RESEARCH Performance evaluation of distance metrics on Firefly Algorithm for VRP with time windows Divya Aggarwal 1 • Vijay Kumar 2 Received: 20 June 2017 / Accepted: 7 November 2019 Ó Bharati Vidyapeeth’s Institute of Computer Applications and Management 2019 Abstract In this paper, a modification in randomness factor is proposed for enhancing the exploitation capability of firefly algorithm. The proposed approach is applied on Vehicle Routing Problem with Time Windows (VRPTW). There is no single distance measure that fits for all type of VRPTW. An attempt has been made to evaluate on three different distance measures on the proposed approach. The performance of proposed approach on different distance measures has been evaluated on two well-known instances of Solomon’s benchmark test. The experimental results show that the performance of Brute–Curtis distance mea- sure outperforms the other measures. Keywords Vehicle Routing Problem with Time Windows  Firefly algorithm  Optimization  Intensity 1 Introduction Vehicle Routing Problem (VRP) is a popular optimization problem where a set of customers is considered as the nodes of a graph between geographically dispersed loca- tions and a set of routes between the locations have to be determined while visiting all the customers once. Routes should have the same originating, terminating point called depot, and travel distances among nodes are to be prior known. The main aim of VRP is to minimize the total transportation cost associated with the distance traveled and simultaneously establishing the routes, which can satisfy the demand characteristics. VRP plays a key role in distribution and logistics [1]. Nowadays, a viable logistics network have a great impact for the industries and firms that have transportation activities. Vehicle Routing Problem with time windows (VRPTW) is the specialization of the classical VRP, which is appli- cable in real world problems [2]. It comprises of a fleet of vehicles that are used to serve a number of diversely located customer with predefined demand requests and specific service time intervals. Due to the applicability of VRPTW, the research has paid more attraction in this area. VRPTW is also known as NP-hard problem. The meta- heuristic algorithms have been proposed to solve the VRPTW problem. The well-known metaheuristic algo- rithms are Tabu Search (TS) [3], Genetic Algorithm (GA) [4], Ant Colony Optimization (ACO) [5], Particle Swarm Optimization (PSO) [5], and Firefly Algorithm [5]. Among them, firefly algorithm easy to implement and understand. In this paper, firefly algorithm has been used to solve VRPTW. The performance of firefly algorithm depends upon distance measure. The distance measure plays an important role in obtaining the accurate results. The selection of right distance measure affects the performance of firefly algo- rithm. They may affect the results obtained as some points may be close to one another according to one distance measure and far way according to another distance [6]. This fact motivates us to analyse the effect of various distance measures on firefly algorithm. & Divya Aggarwal aggarwaldivya2593@gmail.com Vijay Kumar vijaykumarchahar@gmail.com 1 Computer Science and Engineering Department, Thapar Institute of Engineering and Technology, Patiala, Punjab 147001, India 2 Computer Science and Engineering Department, National Institute of Technology, Hamirpur, Himachal Pradesh 177005, India 123 Int. j. inf. tecnol. https://doi.org/10.1007/s41870-019-00387-7