A Column-Generation Algorithm for Evacuation Planning with Elementary Paths

Abstract

Evacuation planning algorithms are critical tools for assisting authorities in orchestrating large-scale evacuations while ensuring optimal utilization of resources. To be deployed in practice, these algorithms must include a number of constraints that dramatically increase their complexity. This paper considers the zone-based non-preemptive evacuation planning problem in which each evacuation zone is assigned a unique evacuation path to safety and the flow of evacuees over time for a given zone follows one of a set of specified response curves. The starting point of the paper is the recognition that the first and only optimization algorithm previously proposed for zone-based non-preemptive evacuation planning may produce non-elementary paths, i.e., paths that visit the same node multiple times over the course of the evacuation. Since non-elementary paths are undesirable in practice, this paper proposes a column-generation algorithm where the pricing subproblem is a least-cost path under constraints. The paper investigates a variety of algorithms for solving the subproblem as well as their hybridization. Experimental results on a real-life case study show that the new algorithm produces evacuation plans with elementary paths of the same quality as the earlier algorithm in terms of the number of evacuees reaching safety and the completion time of the evacuation, at the expense of a modest increase in CPU time.