Solving large-scale vehicle routing problem instances using an island-model offspring selection genetic algorithm Stefan Vonolfen * , Michael Affenzeller † , Andreas Beham ‡ , Stefan Wagner § School of Informatics, Communications and Media Upper Austria University of Applied Sciences Softwarepark 11 4232 Hagenberg Austria * stefan.vonolfen@heuristiclab.com † michael.affenzeller@heuristiclab.com ‡ andreas.beham@heuristiclab.com § stefan.wagner@heuristiclab.com Abstract—The vehicle routing problem is a class of problems that frequently occurs in the field of transportation logistics. In this work, we tackle very-large scale problem instances with time windows. Among other techniques, metaheuristics are frequently used to solve large-scale instances close to optimality. We present an island-model genetic algorithm variant and apply several techniques such as offspring selection and adaptive constraint relaxation. To validate our approach, we perform test runs on benchmark instances with 1000 customers and compare the results to the currently best-known solutions. Index Terms—Vehicle routing problem, island-model genetic algorithm, offspring selection I. I NTRODUCTION The vehicle routing problem (VRP) is an important problem class in the field of transport logistics optimization. The original formulation of the problem has been defined over 50 years ago by [1] and consists of a fleet of vehicles serving a set of customers with a certain demand from a single depot and the vehicles have a certain capacity. This formulation is referred to as the capacitated vehicle problem (CVRP). In practice often variants with many diverse constraints oc- cur. Those extended problem formulations are often called rich vehicle routing problems [2]. Thus, since then many diverse variants of vehicle routing problems have been studied in the literature, for a taxonomic review see for example [3]. The classification includes different scenario characteristics such as time windows, different problem physical characteristics such as the geographical location of customers and different information and data characteristics. One important variant frequently studied in the literature is the capacitated vehicle routing problem with time windows (CVRPTW [4]). In addition to satisfying the capacity con- straints, also time window constraints have to be considered. This means, that each customer has to be served within a certain time window and late or early arrivals are not allowed. Each customer requires a certain service time. Similar to the diversity of the studied problem variants, there are also various solution methods proposed in the literature. Since the vehicle routing problem is known to be NP-hard [5], it becomes increasingly intractable in larger problem dimensions. Today, some problem instances of the CVRPTW with 100 customers are not solved to optimality because of the high complexity. Thus, metaheuristics are frequently used to generate feasible and near-optimal solutions for large scale instances. For an overview of different metaheuristics for the VRP see for example [6] or [7]. An overview of the state-of-the-art of solving large-scale VRPTW instances is given by [8] where they compare dif- ferent algorithms in terms of their performance on large- scale problem instances. In terms of the VRPTW, problem instances up to 1000 customers can be solved efficiently using heuristics. Often hybrid variants are used to efficiently solve large-scale instances. For example [9] apply a hybridization of an evolution strategy with guided local search. In [10] a two-stage hybrid local search is used which consists a combi- nation of large neighborhood search and simulated annealing. A hybridization of branch-and-price and large neighborhood search was developed by [11]. Among other metaheuristics, such as tabu search (TS) or variable neighborhood search (VNS), genetic algorithms (GA) have been used successfully to tackle large problem instances. In this work, we present a genetic algorithm variant that is capable of robustly solving different large-scale instances. The rest of the paper is organized as following: in Section II we present our algorithmic approach, in Section III we perform test runs on several benchmark instances and in Section IV we summarize our findings and show how the approach could be extended in the future.