An ILP formulation to optimize flood evacuation paths by minimizing pedestrian speed, length and effort

Abstract

This document presents an Integer Linear Programming (ILP) approach to optimize pedestrian evacuation in flood-prone historic urban areas. The model aims to minimize total evacuation cost by integrating pedestrian speed, route length, and effort, while also selecting the optimal number and position of shelters. A modified minimum cost flow formulation is used to capture complex hydrodynamic and behavioral conditions within a directed street network. The evacuation problem is modeled through an extended graph representing the urban street network, where nodes and links simulate paths and shelters, including incomplete evacuations (deadly nodes), enabling accurate representation of real-world constraints and network dynamics.