A Column Generation Algorithm for Evacuation Planning with Cycle-Free Paths

Abstract. Evacuation planning algorithms are critical tools for assisting authorities in orchestrating large-scale evacuations to ensure optimal utilization of resources. We introduce a column generation algorithm that produces zone-based evacuation plans that consist of non-preemptive evacuation schedules with evacuation paths that are guaranteed to be cycle-free. The algorithm builds upon a similar, previously introduced algorithm that was discovered to contain a critical shortcoming; it may produce paths containing cycles which are highly undesirable from an evacuation perspective. Instead of finding the shortest path in a timeexpanded graph in the algorithm’s pricing subproblem, we propose finding one subject to a feasibility constraint which only allows paths that will eventually be cycle-free to be considered. We also suggest a hybrid algorithm to e ciently solve this new subproblem. Through experiments comparing results of both original and new algorithms when applied to a real-word evacuation scenario, we demonstrate that the new algorithm is able to produce provably high quality evacuation plans that match the quality of those produced by the original, while guaranteeing evacuation paths that are cycle-free only at the expense of increased CPU time consumption during its column generation phase.