ARTICLE IN PRESS JID: CAEE [m3Gsc;February 6, 2018;21:11] Computers and Electrical Engineering 000 (2018) 1–15 Contents lists available at ScienceDirect Computers and Electrical Engineering journal homepage: www.elsevier.com/locate/compeleceng An improved ant colony optimization for the multi-trip Capacitated Arc Routing Problem  Erfan Babaee Tirkolaee a , Mehdi Alinaghian b , Ali Asghar Rahmani Hosseinabadi c , Mani Bakhshi Sasi b , Arun Kumar Sangaiah d,* a Department of Industrial Engineering, Mazandaran University of Science and Technology, Babol, Iran b Department of Industrial and Systems Engineering, Isfahan University of Technology, Isfahan, Iran c Young Researchers and Elite Club, Ayatollah Amoli Branch, Islamic Azad University, Amol, Iran d School of Computing Science and Engineering, Vellore Institute of Technology (VIT), Vellore-632014, India a r t i c l e i n f o Article history: Received 21 September 2017 Revised 27 January 2018 Accepted 29 January 2018 Available online xxx Keywords: Urban waste collection Disposal facility Multi-trip Capacitated Arc Routing Problem Improved Max-Min Ant System Taguchi design method a b s t r a c t The urban waste collection problem and its disposal activities are among the most impor- tant municipal services involving many operational issues. In this paper, a mixed-integer linear programming (MILP) model was developed for the multi-trip Capacitated Arc Rout- ing Problem (CARP) in order to minimize total cost. In the proposed model, depots and disposal facilities were located in different places. In order to validate the proposed model, several small-sized instances were solved by the CPLEX solver of GAMS software. Then, a hybrid algorithm using the Taguchi parameter design method was developed based on an improved Max-Min Ant System (IMMAS) to solve well-known test problems and large- sized instances. Computational results show high efficiency for the proposed algorithm. © 2018 Elsevier Ltd. All rights reserved. 1. Introduction Nowadays, a variety of Municipal Solid Waste (MSW) is produced, and the outbreak of its pertaining social, economic and environmental incompatibilities has encountered municipal services management with many problems in the fields of collection, transportation, processing and disposing of such waste. Since 75 to 80 percent of solid waste management system costs concern collection and transportation of wastes [1], evaluation and optimization of this system play a significant role in reducing these costs. Waste must be collected, transferred and disposed in accordance with hygiene considerations in the fastest possible way. The most common way is to collect waste from residential houses and transport them directly to disposal facilities. Accordingly, the importance of optimizing waste management systems becomes more notable. Therefore, choosing the optimal policy of waste collection has an important effect on reduction in costs. In the routing problems defined for urban waste collection, two categories of problems are defined [2]. In the first category which is called Vehicle Routing Problem (VRP), a series of predetermined nodes are defined, the objective of which is to find the optimal routes that traverse all the nodes. In the second category which is called Arc Routing Problem (ARP), a number of edges are defined in the network, and the objective is to find the optimal routes that traverse all those edges. The urban waste collection is  Reviews processed and recommended for publication to the Editor-in-Chief by Associate Editor Dr. G. Ramirez Gonzalez. * Corresponding author. E-mail addresses: E.Babaee@in.iut.ac.ir (E.B. Tirkolaee), Alinaghian@in.iut.ac.ir (M. Alinaghian), A.R.Hosseinabadi@iaubeh.ac.ir (A.A.R. Hosseinabadi), M.Bakhshi@in.iut.ac.ir (M.B. Sasi), sarunkumar@vit.ac.in, arunkumarsangaiah@gmail.com (A.K. Sangaiah). https://doi.org/10.1016/j.compeleceng.2018.01.040 0045-7906/© 2018 Elsevier Ltd. All rights reserved. Please cite this article as: E.B. Tirkolaee et al., An improved ant colony optimization for the multi-trip Capacitated Arc Routing Problem, Computers and Electrical Engineering (2018), https://doi.org/10.1016/j.compeleceng.2018.01.040