Multi-Vehicle Covering Tour Problem: Building Routes for Urban Patrolling

Abstract

In this paper we study a particular aspect of the urban community policing: routine patrol route planning. We seek routes that guarantee visibility, as this has a sizable impact on the community perceived safety, allowing quick emergency responses and providing surveillance of selected sites (e.g., hospitals, schools). The planning is restricted to the availability of vehicles and strives to achieve balanced routes. We study an adaptation of the model for the multi-vehicle covering tour problem, in which a set of locations must be visited, whereas another subset must be close enough to the planned routes. It constitutes an NP-complete integer programming problem. Suboptimal solutions are obtained with several heuristics, some adapted from the literature and others developed by us. We solve some adapted instances from TSPLIB and an instance with real data, the former being compared with results from literature, and latter being compared with empirical data.

Modelagem para o Problema de Roteamento de Veículos Fretados

“…A literatura apresenta algumas propostas de modelos de roteamento considerando equilíbrio entre rotas, por exemplo em relac ¸ão a quantidade de vértices visitados (Oliveira et al [20,21], Ota [22]). Neste artigo, tratamos do equilíbrio na quantidade de passageiros entre rotas.…”

“…Ter algum tipo de equilíbrio entre rotas tem sido proposto na literatura. Oliveira et al [21] construíram rotas de cobertura equilibradas para viaturas policiais com o objetivo de distribuir as visitas (contato com a populac ¸ão) igualmente entre as viaturas para promover a sensac ¸ão de seguranc ¸a na atividade de patrulhamento preventivo. Oliveira et al [20] e Ota [22] estudaram modelos e métodos de resoluc ¸ão para o problema de rotas de cobertura multiveículos, em que a diferenc ¸a entre o número de visitas entre rotas é limitada.…”

Models and algorithms for last mile delivery problems with multiple shipping options

“…Another application arises in bi-level transportation networks, for example the postbox location problem (Labbé & Laporte, 1986). Last, in the routine patrol routing planning (Oliveira et al, 2015), routes need to guarantee visibility which has an influence on the community safety, providing surveillance and allowing quick emergency responses. Vehicles available for the patrol are limited and strive to achieve balanced routes.…”

Time constrained maximal covering salesman problem with weighted demands and partial coverage

“…A covering tour perspective is adopted in [14] to tackle the problem of locating satellite distribution centers to supply humanitarian aid over a disaster area. The problem of planning routes for routine patrol cars is also modeled as the m-CTP in [15].…”