Swarm Intelligence: Application of the Ant Colony Optimization Algorithm to Logistics-Oriented Vehicle Routing Problems

Every year at the annual conference for the Council of Supply Chain Management Professionals (CSCMP), three to five sessions are offered that focus on modeling or optimizing logistics, transportation and/or supply chain networks. Quite often these conference sessions expressly, or in passing, address the issue of vehicle routing. Commercially available products, some of which are referenced in these sessions, provide the ability to evaluate organization’s transportation problems, but often the nature of the algorithms employed goes unexplained for reasons associated with proprietary data, or simply the desire to not overwhelm the customer. Against this backdrop a new class of metaheuristics quantitative tools has emerged that is capable of providing solutions closer to optimality, and often in less time. This article focuses on one of these emergent metaheuristics, Ant Colony Optimization (ACO), that models the seemingly intelligent behavior of swarming insects, and compares it against one of the classic workhorse vehicle routing algorithms, the Clark-Wright Savings model, in a logistics focused environment. Practitioners and academicians unfamiliar with metaheuristics in general and ACO in particular are served to better understand “what’s under the hood” of the vehicle routing software, and the heuristics techniques they employ, as they may encounter them as decision-makers or researchers. The vehicle routing problem (VRP) is an important problem that has been extensively studied by logisticians, operations researchers and mathematicians for the last several decades. The traditional single depot vehicle routing problem simultaneously determines the routes for several vehicles from a central supply depot to a number of customers, including a return to the depot while staying within the limits of the capacity of each vehicle. This problem is economically important due to the costs associated with providing and operating delivery vehicles to transport products to a set of geographically dispersed customers. When an organization is able to minimize the length of its routes or decrease the number of its vehicles, it is, in theory, able to provide better service to its customers and thereby obtain a more profitable and competitive position. The classic vehicle routing problem typically involves minimizing costs of the combined routes for a number of vehicles. Quite often distance traveled by the vehicles is used as a surrogate for the objective of cost. In the past, the majority of research on the vehicle routing problem has used demand sets with randomly generated customer locations. However, it has been recognized by logistics researchers (Ballou and Agarwal 1988) that, within the logistics domain, patterns tend to exist in the spatial dispersion of customers. This research uses these spatial dispersion problems, representing five different spatial patterns believed to be more representative of logistics distribution of products in real-world markets than the classic operations research problem sets employing more uniform distributions. Because route selection for an individual vehicle allows any combination of customers, the vehicle routing problem is considered a combinatorial optimization problem and the number of feasible solutions for the problem increases exponentially with the number of customers. Additionally, the vehicle routing problem is related to the