Comparative analysis of selected path-planning approaches in large-scale multi-agent-based environments

Highlights

• Experimental performance analysis of path-planning approaches is presented.

• Standard pathfinding, matrix-based, and pathfinding with learning are compared.

• Local and remote Open Street Map server approaches are analysed for performance.

• Experiments show statistically significant differences between the runtimes.

Abstract

Large-scale models are currently used for the simulation, analysis and control of real systems, whether technical, biological, social or economic. In multi-agent simulations of virtual economies, it is important to schedule a large number of agents across the cities involved, in order to establish a functional supply chain network for industrial production. This study describes an experimental evaluation of path-planning approaches in the field of multi-agent modelling and simulation, applied to a large-scale setting. The experimental comparison is based on a model in which agents represent economic entities and can participate in mutual interactions. For the purposes of experiment, the model is scaled to various degrees of complexity in terms of the numbers of agents and transportation nodes. Various numbers of agents are used to explore the way in which the model's complexity influences the runtime of the path-planning task. The results indicate that there are significant differences between the runtime performances associated with single approaches, for differing levels of system complexity and model sizes. The study reveals that the appropriate sharing of shortest path information can significantly improve path-planning activities. Hence, this work extends current research in the field of path-planning for multi-agent simulations by conducting an experimental performance analysis of five distinct path-planning approaches and a statistical evaluation of the results. This statistical evaluation contrasts with performance analyses conducted on the basis of ‘Big O’ notation for algorithmic complexity, which describes the limiting behaviour of the algorithm and gives only a rough performance estimate.

Introduction

The use of pathfinding algorithms represents a key task in many domains, and these algorithms are widely employed in areas such as robotics and artificial intelligence (Atallah & Blanton, 2009), video games (Algfoor, Sunar, & Kolivand, 2015), medicine (Algfoor, Sunar, Abdullah, & Kolivand, 2017), and traffic control (Bleiweiss, 2008). At a fundamental level, pathfinding algorithms deal with two problems: firstly, they are constructed to find a path between two points, or two nodes if the problem is represented as a graph; and secondly, the aim is to identify the optimal shortest path. This is a fundamental and well-known problem in operations research, and is related to finding a path between two nodes (vertices) of a graph such that the sum of the weights (in terms of cost, distance, time etc.) of its connecting edges are minimised. A plethora of algorithms has already been developed, elaborated and modified to solve pathfinding issues. In general, the main evaluation metrics associated with these algorithms are the speed of search, the quality of the resulting paths and the cost of pre-processing; however, the primary issue is that these metrics cannot be optimised simultaneously. Typical speed enhancements for pathfinding usually involve trading away optimality, either for speed or for offline pre-processing; the former makes it difficult to guarantee the quality of results, while the latter requires extra memory and pre-computing time (Zhang, Li, & Bi, 2016). The problem is even more pronounced in large-scale settings with many autonomous agents moving across numerous locations under certain restrictions. The application of pathfinding algorithms in large-scale scenarios is motivated by the need for resource-efficient and sustainable transportation planning (Pel, Agatz, Macharis, & Veelenturf, 2018) and is enabled by developments in computer science that are associated with hardware technologies (cloud computing, parallel computing, or high performance computing) and software methodologies (e.g. big data methods), which have gradually allowed the creation of more complex computational models with a growing number of participating entities. Transportation is an integral part of most socioeconomic systems, representing a family of complex adaptive systems (CAS), i.e. systems made up of large numbers of components that interact and adapt or learn (Axelrod & Cohen, 2000). Agent-based modelling (ABM) is a suitable instrument for the exploration and planning of CAS (Klügl, 2013, Railsback et al., 2006).

Most studies that deal with transportation planning problems focus on the application or performance of a particular pathfinding algorithm. For instance, Sajid, Luna, and Bekris (2012) propose the proprietary parallel ‘Push and Swap’ algorithm for multi-agent pathfinding, which utilises single-agent primitives but allows all agents to move in parallel. Alderton, Noble, Schaten, Welburn, and Atkinson (2015) have developed an agent-based model to generate routes for human movement between homes and water resources in a rural setting, and have implemented the A* algorithm to identify human movement patterns. Other studies have compared single algorithms with the intention of determining which algorithm is more efficient or less costly in terms of time, either at a general level or when comparing specific pragmatic or research problems. For example, Hudziak, Pozniak-Koszalka, Koszalka, and Kasprzak (2015) recommend a more suitable algorithm to plan the best paths for the simultaneous movement of agents operating in a large, crowded environment; in their study, they compare the Dijkstra and A* algorithms. Zarembo and Kodors (2015) collect information about the A*, BFS, Dijkstra, HPA* and LPA* pathfinding algorithms, and compare these using various criteria such as the execution time and memory requirements. Khantanapoka and Chinnasarn (2009) compare the depth-first search, iterative deepening, the breadth-first search, Dijkstra's algorithm, the best-first search, the A* algorithm, and iterative deepening A*. Considerably less attention is devoted, however, to research into approaches in which agents can share information about the shortest path, which can improve the performance of the CAS as a whole. Several implementation approaches have addressed this issue. Firstly, the shortest path between any two points can be pre-computed and made available to the agents as they travel. Secondly, the shortest path can be computed on demand and stored for reuse by other agents. Thirdly, the use of dedicated cloud-based solutions can offer information about the shortest path. The performance of any of the above strategies is encumbered with certain overheads, and the feasibility of practical implementation is questionable. To the best of our knowledge, no recent studies include an experimental performance analysis of these approaches.

The main objective of the present study is to identify an effective path-planning control method, and to provide an experimental performance analysis of approaches to the sharing of shortest path information in a large-scale transportation scenario. This scenario involves the movement of several thousand agents across up to tens of locations, and is motivated by industrial transportation needs in a specific region. The scenario is simulated in a multi-agent environment, and the time required to schedule the paths of all agents across a given number of cities is used as the main performance metric. The actual performance analysis is accomplished using selected state-of-the-art pathfinding algorithms; however, these algorithms are interchangeable with similar alternatives (for example the substitution of A* for Dijkstra) and a shift in performance is expected according to comparative studies of these algorithms (for example, Sathyaraj et al., 2008, Uditi and Arun, 2017).

The remainder of the manuscript is structured as follows. After a brief introduction, a theoretical background is presented and the selected pathfinding algorithms introduced. The third section describes the applied methodology and experimental design; then, the main findings are presented. The fifth section describes an application focused on the selected domain, and the final section summarises and concludes the paper.