On a geometric graph-covering problem related to optimal safety-landing-site location

TL;DR

This paper introduces integer programming models for optimally placing safety-landing sites in urban air-transportation networks, addressing finite point sets and convex regions, with techniques to improve computational efficiency.

Contribution

It presents novel integer programming formulations for the SLS location problem, including set-cover and second-order cone models, and introduces a strong fixing method to enhance solution efficiency.

Findings

Set-cover approach for finite candidate points

Mixed-integer second-order cone model for convex sets

Strong fixing technique reduces problem size

Abstract

We propose integer-programming formulations for an optimal safety-landing site (SLS) location problem that arises in the design of urban air-transportation networks. We first develop a set-cover based approach for the case where the candidate location set is finite and composed of points, and we link the problems to solvable cases that have been studied. We then use a mixed-integer second-order cone program to model the situation where the locations of SLSs are restricted to convex sets only. Finally, we introduce strong fixing, which we found to be very effective in reducing the size of integer programs.