Multi-task evolutionary optimization of multi-echelon location routing problems via a hierarchical fuzzy graph

Abstract

Multi-echelon location-routing problems (ME-LRPs) deal with determining the location of facilities and the routes of vehicles on multi-echelon routing tasks. Since the assignment relationship in multi-echelon routing tasks is uncertain and varying, ME-LRPs are very challenging to solve, especially when the number of the echelons increases. In this study, the ME-LRP is formulated as a hierarchical fuzzy graph, in which high-order fuzzy sets are constructed to represent the uncertain assignment relationship as different routing tasks and cross-task operators are used for routing task selection. Then, an evolutionary multi-tasking optimization algorithm is designed to simultaneously solve the multiple routing tasks. To alleviate negative transfer between the different routing tasks, multi-echelon assignment information is considered together with associated routing task selection in multi-tasking evolution optimization. The experimental results on multi-echelon routing benchmark problems demonstrate the competitiveness of the proposed method.