Design a Robust Logistics Network with an Artificial Physarum Swarm Algorithm

Abstract

The robust optimization of logistics networks can improve the ability to provide sustainable service and business sustainability after uncertain disruptions. The existing works on the robust design of logistics networks insisted that it is very difficult to build a robust network topology, and this kind of optimization problem is an NP-hard problem that cannot be easily solved. In nature, Physarum often needs to build a robust and efficient topological network to complete the foraging process. Recently, some researchers used Physarum to build a robust transportation network in professional biological laboratories and received a good performance. Inspired by the foraging behavior of natural Physarum, we proposed a novel artificial Physarum swarm system to optimize the logistics network robustness just on a personal computer. In our study, first, the robustness optimization problem of a logistics network is described as a topology optimization model based on graph theory, and four robustness indicators are proposed to build a multi-objective robustness function of logistics network topology, including the relative robustness, the betweenness robustness, the edge robustness and the closeness robustness. Second, an artificial Physarum swarm system is developed to simulate the foraging behavior of a natural Physarum swarm to solve this kind of complex robust optimization problem. The proposed artificial Physarum swarm system can search for optimal solutions by expansion and contraction operations and the exchange of information with each other through a self-learning experience and neighbor-learning experiences. The plasmodium of Physarum forms the edges, and the external food sources simulate the logistics nodes. Third, an experimental example is designed on the basis of Mexico City to verify the proposed method, and the results reveal that the artificial Physarum swarm system can help us effectively improve the logistics network robustness under disruptions and receive a better performance than natural Physarum. The article may be helpful for both theory and practice to explore the robust optimization in logistics operation and provide engineers with an opportunity to resist logistics disruptions and risk loss by a novel artificial intelligence tool.

An Artificial Physarum polycephalum Colony for the Electric Location-Routing Problem

“…The ability or behavior rules of each individual in a heuristic algorithm are very simple, so the realization of heuristic intelligence is relatively convenient and has the characteristics of simplicity. Examples include the genetic algorithm (GA) [5,36], artificial fish swarm algorithm (AFSA) [8], fuzzy logic (FL) [9,32], simulated annealing (SA) [12], particle swarm optimization (PSO) [18,37], deep reinforcement learning (DRL) [19,20,38], ant colony optimization (ACO) [21,39], machine learning (ML) and artificial neural networks (ANNs) [22,38,40], artificial bee colony (ABC) [23,41], grey wolf optimization (GWO) [24], artificial plant community (APC) [42], whale optimization algorithm(WOA) [43], and artificial slime mold (ASM) [13,44,45]. The heuristic algorithms can help us obtain a satisfactory feasible solution in a short time, but the deviation degree between the feasible solution and the optimal solution cannot be predicted.…”

“…Constraint 4 in Equation (13) indicates that the transportation volume Q vki of electric vehicle v k on all nodes should not surpass the maximum transportation volume Q vk of electric vehicle v k . Therefore, the maximum amount of cargo carried by an electric vehicle during each mission cannot exceed the vehicle's own carrying capacity limit.…”

“…Recently, researchers generally believe that the ELRP problem is a more complex task than a traditional location-routing problem (LRP). And the application of the ELRP will become increasingly widespread with the popularity of electric vehicles, such as charging station locations [2,11], battery swapping stations [12], smart cities [6], urban logistics [9,13], home health care [12], waste collection [14], electric trucks [7], electric aircraft [15], and electric buses [16].…”

Using an Artificial Physarum polycephalum Colony for Threshold Image Segmentation

“…Although swarm intelligence algorithms have been proven effective, they have also been complained of being prone to premature local optima. The Physarum polycephalum in nature can stretch out tens of thousands of filamentous hyphae to search for surrounding food [17,18,47]. This inspires us as to whether the swarm intelligence of Physarum polycephalum can be utilized to provide us with a more efficient algorithm for solving image segmentation problems.…”

“…Inspired by the intelligent behavior of a natural Physarum polycephalum, which can produce a large number of hyphae to search for food [17,18], a novel artificial Physarum polycephalum colony algorithm (APPCA) is proposed to help us solve the threshold image segmentation. The main contributions of this article are as follows:…”