A Balanced Route Design for Min-Max Multiple-Depot Rural Postman Problem (MMMDRPP): a police patrolling case

Providing distributed services on road networks is an essential concern for many applications, such as mail delivery, logistics and police patrolling. Designing effective and balanced routes for these applications is challenging, especially when involving multiple postmen from distinct depots. In this research, we formulate this routing problem as a Min-Max Multiple-Depot Rural Postman Problem (MMMDRPP). To solve this routing problem, we develop an efficient tabu-search-based algorithm and propose three novel lower bounds to evaluate the routes. To demonstrate its practical usefulness, we show how to formulate the route design for police patrolling in London as an MMMDRPP and generate balanced routes using the proposed algorithm. Furthermore, the algorithm is tested on multiple adapted benchmark problems. The results demonstrate the efficiency of the algorithm in generating balanced routes

New Heuristic Algorithms for the Windy Rural Postman Problem

[EN] In this paper we deal with the windy rural postman problem. This problem generalizes several important arc routing problems and has interesting real-life applications. Here, we present several heuristics whose study has lead to the design of a scatter search algorithm for the windy rural postman problem. Extensive computational experiments over different sets of instances, with sizes up to 988 nodes and 3952 edges, are also presented. (c) 2004 Elsevier Ltd. All rights reserved.Benavent, E.; Corberán, A.; Piñana, E.; Plana. I.; Sanchís Llopis, JM. (2005). New Heuristic Algorithms for the Windy Rural Postman Problem. Computers & Operations Research. 32(12):3111-3128. doi:10.1016/j.cor.2004.04.007S31113128321

B-splines in EMD and Graph Theory in Pattern Recognition

With the development of science and technology, a large amount of data is waiting for further scientific exploration. We can always build up some good mathematical models based on the given data to analyze and solve the real life problems. In this work, we propose three types of mathematical models for different applications.;In chapter 1, we use Bspline based EMD to analysis nonlinear and no-stationary signal data. A new idea about the boundary extension is introduced and applied to the Empirical Mode Decomposition(EMD) algorithm. Instead of the traditional mirror extension on the boundary, we propose a ratio extension on the boundary.;In chapter 2 we propose a weighted directed multigraph for text pattern recognition. We set up a weighted directed multigraph model using the distances between the keywords as the weights of arcs. We then developed a keyword-frequency-distance-based algorithm which not only utilizes the frequency information of keywords but also their ordering information.;In chapter 3, we propose a centrality guided clustering method. Different from traditional methods which choose a center of a cluster randomly, we start clustering from a LEADER - a vertex with highest centrality score, and a new member is added into an existing community if the new vertex meet some criteria and the new community with the new vertex maintain a certain density.;In chapter 4, we define a new graph optimization problem which is called postman tour with minimum route-pair cost. And we model the DNA sequence assembly problem as the postman tour with minimum route-pair cost problem

An updated annotated bibliography on arc routing problems

The number of arc routing publications has increased significantly in the last decade. Such an increase justifies a second annotated bibliography, a sequel to Corberán and Prins (Networks 56 (2010), 50–69), discussing arc routing studies from 2010 onwards. These studies are grouped into three main sections: single vehicle problems, multiple vehicle problems and applications. Each main section catalogs problems according to their specifics. Section 2 is therefore composed of four subsections, namely: the Chinese Postman Problem, the Rural Postman Problem, the General Routing Problem (GRP) and Arc Routing Problems (ARPs) with profits. Section 3, devoted to the multiple vehicle case, begins with three subsections on the Capacitated Arc Routing Problem (CARP) and then delves into several variants of multiple ARPs, ending with GRPs and problems with profits. Section 4 is devoted to applications, including distribution and collection routes, outdoor activities, post-disaster operations, road cleaning and marking. As new applications emerge and existing applications continue to be used and adapted, the future of arc routing research looks promising.info:eu-repo/semantics/publishedVersio

Approximation algorithms for general cluster routing problem

Graph routing problems have been investigated extensively in operations research, computer science and engineering due to their ubiquity and vast applications. In this paper, we study constant approximation algorithms for some variations of the general cluster routing problem. In this problem, we are given an edge-weighted complete undirected graph $G=(V,E,c),$ whose vertex set is partitioned into clusters $C_{1},\dots ,C_{k}.$ We are also given a subset $V'$ of $V$ and a subset $E'$ of $E.$ The weight function $c$ satisfies the triangle inequality. The goal is to find a minimum cost walk $T$ that visits each vertex in $V'$ only once, traverses every edge in $E'$ at least once and for every $i\in [k]$ all vertices of $C_i$ are traversed consecutively.Comment: In COCOON 202

Algoritmos e formulações matemáticas para problemas de roteamento em arcos

Orientador: Fábio Luiz UsbertiTese (doutorado) - Universidade Estadual de Campinas, Instituto de ComputaçãoResumo: Problemas de roteamento em arcos têm por objetivo determinar rotas de custo mínimo que visitam um subconjunto de arcos de um grafo, com uma ou mais restrições adicionais. Esta tese estuda três problemas NP-difíceis de roteamento em arcos: (1) o problema de roteamento em arcos capacitado (CARP); (2) o problema de roteamento em arcos capacitado e aberto (OCARP); e (3) o problema do carteiro chinês com cobertura (CCPP). Apresentamos formulações matemáticas e métodos exatos e heurísticos para tratar computacionalmente esses problemas: (i) uma heurística construtiva gulosa e randomizada é proposta para o CARP; (ii) uma metaheurística de algoritmos genéticos híbrido e dois métodos de limitantes inferiores por programação linear inteira, um branch-and-cut e um baseado em redes de fluxos, são propostos para o OCARP; e (iii) um método exato branch-and-cut com desigualdades válidas e uma heurística construtiva são propostos para o CCPP. Extensivos experimentos computacionais utilizando instâncias de benchmark foram executados para demonstrar o desempenho dos métodos propostos em relação aos métodos da literatura, considerando tanto a qualidade das soluções obtidas quanto o tempo de processamento. Nossos resultados mostram que os métodos propostos são estado da arte. Os problemas estudados apresentam aplicações práticas relevantes: o CARP tem aplicações em coleta de lixo urbano e remoção de neve de estradas; o OCARP tem aplicações em roteamento de leituristas e na definição de caminhos de corte em chapas metálicas; e o CCPP tem aplicações em roteamento de leituristas com o uso de tecnologia wireless. A solução desses problemas remete à diminuição de custos logísticos, melhorando a competitividade das empresasAbstract: Arc routing problems aim to find minimum cost routes that visit a subset of arcs of a graph, with one or more side constraints. This thesis studies three NP-hard arc routing problems: (1) the capacitated arc routing problem (CARP); (2) the open capacitated arc routing problem (OCARP); and (3) the covering Chinese postman problem (CCPP). We present mathematical formulations and heuristic and exact methods to computationally solve these problems: (i) a greedy and randomized constructive heuristic is proposed for the CARP; (ii) a hybrid genetic algorithm metaheuristic and two linear integer programming lower bound methods, one based on branch-and-cut and one based on flow networks, are proposed for the OCARP; and (iii) an exact branch-and-cut method with valid inequalities and a constructive heuristic are proposed for the CCPP. Extensive computational experiments using benchmark instances were performed to demonstrate the performance of the proposed methods in comparison to the previous methods, regarding both quality of solutions and processing time. Our results show that the proposed methods are state-of-the-art. The studied problems have many relevant practical applications: the CARP has applications on urban waste collection and snow removal; the OCARP has applications on the routing of meter readers and the cutting of metal sheets; and last, the CCPP has applications on automated meter readers routing. The solution of these problems leads to the reduction of logistics costs, improving businesses competitivenessDoutoradoCiência da ComputaçãoDoutor em Ciência da Computação2016/00315-0FAPES