Songklanakarin J. Sci. Technol. 41 (1), 151-158, Jan. – Feb. 2019 Original Article An artificial bee colony algorithm for the vehicle routing problem with backhauls and time windows Tanawat Worawattawechai 1* , Boonyarit Intiyot 1 , and Chawalit Jeenanunta 2 1 Department of Mathematics and Computer Science, Faculty of Science, Chulalongkorn University, Pathum Wan, Bangkok, 10330 Thailand 2 School of Management Technology, Sirindhorn International Institute of Technology, Thammasat University, Khlong Luang, Pathum Thani, 12120 Thailand Received: 16 August 2016; Revised: 11 August 2017; Accepted: 8 October 2017 Abstract The vehicle routing problem with backhauls and time windows (VRPBTW) aims to find a feasible vehicle route that minimizes the total traveling distance while imposing capacity, backhaul, and time-window constraints. We present an enhanced artificial bee colony algorithm (EABCA), which is a meta-heuristic, to solve this problem. Three strategies - a forbidden list, the sequential search for onlookers, and the combination of 1-move intra-route exchange and λ-interchange technique - are introduced for EABCA. The proposed method was tested on a set of benchmark instances. The computational results show that the EABCA can produce better solutions than the basic ABCA, and it discovered many new best-known solutions. Keywords: meta-heuristic, artificial bee colony, backhaul, time window, vehicle routing problems 1. Introduction The vehicle routing problem with backhaul and time window (VRPBTW) is extended from the vehicle routing problem with backhaul (VRPB) by adding a specified service time window for each customer. There are three main constraint categories for VRPBTW model, namely capacity constraints, backhaul constraints and time window constraints. For the capacity constraints, the number of customers serviced by a vehicle is restricted by the capacity of the vehicle. For the backhaul constraints, the vehicles serve all demands of the linehual customers and the same vehicles also pick up demands from the backhaul customers. In addition, the backhaul customers cannot be served before linehaul customers. For the time window constraints, the vehicle arrival time at each customer must not exceed the upper bound of the customer’s time window. In general, the VRPBTW is a class of the NP-hard combinatorial optimization problems, which is too difficult to solve exactly within a reasonable time. Consequently, there are many heuristic methods proposed to get a near optimal solution for this problem. An increasing number of the publications on heuristic approaches for vehicle routing problem have been developed for the past two decades. However, only few studies have been devoted to the VRPBTW. A brief review of these studies is divided into two parts based on the types of the proposed methods, namely non-meta-heuristic methods and meta-heuristic methods. A few non-meta-heuristic methods were proposed to solve VRPBTW. Thangiah et al. (1996) presented a push forward insert heuristic (PFIH). This algorithm applied an insertion heuristic for route construction and improved solution by λ-interchange and 2-opt* exchange procedures to solve VRPBTW problems. The algorithm was tested on benchmark instances of Gélinas et al. (1995). Although the solutions of PFIH were within 2.5% of the optimum on average, PFIH almost always gave worse results than average for large-sized problems. Ropke and Pisinger (2006) trans- formed the VRPBTW into the VRPB by ordering the routes *Corresponding author Email address: i.am.t.tanawat@gmail.com