Multi-objective periodic cash transportation problem with path dissimilarity and arrival time variation

This paper introduces a multi-objective periodic routing problem in the context of cash transportation, which attempts to increase security by generating unpredictable alternative paths and spreading arrival times at each demand node. The current study covers the shortcomings of previous models on dissimilar routing and cash transportation problems from several aspects. The studied problem has three objectives, including completion times, risk of robbery, and customers’ satisfaction level considering the effects of traffic congestion as a daily phenomenon. On top of these, we extend the studied routing problem in multigraph setting, which can keep a set of efficient paths with multiple attributes (e.g., risk, time). Such representation enables us to evoke dissimilar route plans not only by reordering the sequence of nodes but also by employing alternative links even in a fix sequence of nodes. To handle the computational challenges arising from these properties, we propose a new evolutionary algorithm based on NSGA-II. The proposed method is embedded with a fuzzy logic technique to guide the applied operators and benefits from caching memory to accelerate and diversify the searching process. The results of implementing the proposed algorithm on test instances confirm the effectiveness of our method in compression to standard NSGA-II. In addition, our performed sensitivity analyses show that the multigraph setting can substantially improve the quality of solutions with respect to all studied objectives.