Ant Colony Optimization with Heuristic Repair for the Dynamic Vehicle Routing Problem Iaˆ e S. Bonilha † , Michalis Mavrovouniotis * , Felipe M. M¨ uller ‡ , Georgios Ellinas * , Marios Polycarpou * ∗ KIOS Research and Innovation Center of Excellence, Department of Electrical and Computer Engineering, University of Cyprus, 2109 Nicosia, Cyprus. email: {mavrovouniotis.michalis,gellinas,mpolycar}@ucy.ac.cy † PPGEP, Federal University of Santa Maria, 97105-900, Santa Maria, Brazil. email: iaesb@hotmail.com ‡ Department of Applied Computing, Federal University of Santa Maria, 97105-900, Santa Maria, Brazil. email: felipe@inf.ufsm.br Abstract—Ant colony optimization (ACO) algorithms have proved to be suitable for solving dynamic optimization problems. The intrinsic characteristics of ACO algorithms enables them to transfer knowledge from past optimized environments via their pheromone trails to shorten the optimization process in the current environment. In this work, change-related information is also utilized when a dynamic change occurs. The dynamic vehicle routing problem is addressed where nodes are removed, representing customers that have already been visited, or added, representing customers that placed a new order and need to be visited. These change-related information are used to heuristically repair the solution of the previous environment, based on effective moves of the unstringing and stringing operator. Experimental results show that utilizing change-related information is beneficial in the generated dynamic test cases. Index Terms—Ant colony optimization, heuristic repair, dy- namic vehicle routing problem I. I NTRODUCTION Ant colony optimization (ACO) algorithms have proved to be powerful problem-solving tools. They are able to provide the optimal (or near optimal) solution for difficult vehicle routing problems (VRPs) [1], [2]. Traditionally, researchers have focused their attention on static optimization problems, where the environment of the problem remains fixed during the optimization process of an algorithm. However, many real-world applications are subject to dynamic environments. Dynamic optimization problems (DOPs) are challenging, since the aim of an algorithm is not only to locate the optimum of the problem quickly, but also to efficiently track the moving optimum when changes occur [3]. A dynamic change may involve factors such as the objective function, input variables, problem instance, and constraints. This work has been supported by the European Union’s Horizon 2020 research and innovation programme under grant agreement No. 739551 (KIOS CoE) and from the Government of the Republic of Cyprus through the Di- rectorate General for European Programmes, Coordination and Development. A simple way to address DOPs is to restart the optimization process of an algorithm whenever a dynamic change occurs. However, this strategy is usually used in case the dynamic changes are severe. On the contrary, when dynamic changes are small to medium, it is more efficient to adapt to the changing environment by transferring past knowledge since the new environment will be in some sense related to the previous one. ACO is a good choice in adapting to dynamic changes because it naturally implements a memory structure via the pheromone trails, allowing ACO to remember and transfer the past knowledge [4]. Furthermore, previous works on dynamic versions of the well-known traveling salesperson problem (TSP) proved that a dynamic change also contains information that could be useful in the optimization process of the newly generated environment. Guntsch and Middendorf [5] utilized the location of the dynamic changes to locally repair the pheromone trails of ACO. Later on, the same authors utilized change-related information to repair previous infeasible solutions [6]. In this work, change-related information are utilized for the dynamic VRP (DVRP) where nodes are inserted (i.e., representing orders from new customers) and removed (i.e., representing already visited customers). Suppose that new orders have arrived and need to be served causing a dynamic change to the current solution. But the vehicles have already left the depot serving the already scheduled orders. A new feasible solution that includes the new orders and omits the already served orders is required. Therefore, change-related information is used to repair the previous solution, which becomes infeasible by the insertion and/removal of nodes, when a dynamic change occurs. The Unstringing and Stringing (US) [7] moves are used to heuristically repair the solution. In particular, the unstringing moves are used to remove the affected nodes from the solution, whereas the stringing moves are used to insert the new nodes in the solution. Although the US has been designed for TSP solutions, in this work we extend it for VRP solutions which is the main contribution of this paper. 978-1-7281-2547-3/20/$31.00 ©2020 IEEE