The open capacitated arc routing problem

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

GRASP with evolutionary path-relinking for the capacitated arc routing problem

The Capacitated Arc Routing Problem (CARP) is a well-known NP-hard combinatorial optimization problem where, given an undirected graph, the objective is to find a minimum cost set of tours servicing a subset of required edges under vehicle capacity constraints. There are numerous applications for the CARP, such as street sweeping, garbage collection, mail delivery, school bus routing, and meter reading. A Greedy Randomized Adaptive Search Procedure (GRASP) with Path-Relinking (PR) is proposed and compared with other successful CARP metaheuristics. Some features of this GRASP with PR are (i) reactive parameter tuning, where the parameter value is stochastically selected biased in favor of those values which historically produced the best solutions in average; (ii) a statistical filter, which discard initial solutions if they are unlikely to improve the incumbent best solution; (iii) infeasible local search, where high-quality solutions, though infeasible, are used to explore the feasible/infeasible boundaries of the solution space; (iv) evolutionary PR, a recent trend where the pool of elite solutions is progressively improved by successive relinking of pairs of elite solutions. Computational tests were conducted using a set of 81 instances, and results reveal that the GRASP is very competitive, achieving the best overall deviation from lower bounds and the highest number of best solutions found. © 2011 Elsevier Ltd. All rights reserved.

Cut-first branch-and-price-second for the capacitated arc-routing problem

This paper presents the first full-fledged branch-and-price (bap) algorithm for the capacitated arc-routing problem (CARP). Prior exact solution techniques either rely on cutting planes or the transformation of the CARP into a node-routing problem. The drawbacks are either models with inherent symmetry, dense underlying networks, or a formulation where edge flows in a potential solution do not allow the reconstruction of unique CARP tours. The proposed algorithm circumvents all these drawbacks by taking the beneficial ingredients from existing CARP methods and combining them in a new way. The first step is the solution of the one-index formulation of the CARP in order to produce strong cuts and an excellent lower bound. It is known that this bound is typically stronger than relaxations of a pure set-partitioning CARP model.rnSuch a set-partitioning master program results from a Dantzig-Wolfe decomposition. In the second phase, the master program is initialized with the strong cuts, CARP tours are iteratively generated by a pricing procedure, and branching is required to produce integer solutions. This is a cut-first bap-second algorithm and its main function is, in fact, the splitting of edge flows into unique CARP tours.

On arc-routing problems

Das Basisproblem von Arc-Routing Problemen mit mehreren Fahrzeugen ist das Capacitated Arc-Routing Problem (CARP). Praktische Anwendungen des CARP sind z.B. in den Bereichen Müllabfuhr und Briefzustellung zu finden. Das Ziel ist es, einen kostenminimalen Tourenplan zu berechnen, bei dem alle erforderlichen Kanten bedient werden und gleichzeitig die Fahrzeugkapazität eingehalten wird. In der vorliegenden Arbeit wird ein Cut-First Branch-and-Price Second Verfahren entwickelt. In der ersten Phase werden Schnittebenen generiert, die dem Master Problem in der zweiten Phase hinzugefügt werden. Das Subproblem ist ein kürzeste Wege Problem mit Ressourcen und wird gelöst um neue Spalten für das Master Problem zu liefern. Ganzzahlige CARP Lösungen werden durch ein neues hierarchisches Branching-Schema garantiert. Umfassende Rechenstudien zeigen die Effektivität dieses Algorithmus. Kombinierte Standort- und Arc-Routing Probleme ermöglichen eine realistischere Modellierung von Zustellvarianten bei der Briefzustellung. In dieser Arbeit werden jeweils zwei mathematische Modelle für Park and Loop und Park and Loop with Curbline vorgestellt. Die Modelle für das jeweilige Problem unterscheiden sich darin, wie zulässige Transfer Routen modelliert werden. Während der erste Modelltyp Subtour-Eliminationsbedingungen verwendet, werden bei dem zweiten Modelltyp Flussvariablen und Flusserhaltungsbedingungen eingesetzt. Die Rechenstudie zeigt, dass ein MIP-Solver den zweiten Modelltyp oft in kürzerer Rechenzeit lösen kann oder bei Erreichen des Zeitlimits bessere Zielfunktionswerte liefert.

Waste collection routing-limited multiple landfills and heterogeneous fleet

This article deals with a real-life waste collection routing problem. To efficiently plan waste collection, large municipalities may be partitioned into convenient sectors and only then can routing problems be solved in each sector. Three diverse situations are described, resulting in three different new models. In the first situation, there is a single point of waste disposal from where the vehicles depart and to where they return. The vehicle fleet comprises three types of collection vehicles. In the second, the garage does not match any of the points of disposal. The vehicle is unique and the points of disposal (landfills or transfer stations) may have limitations in terms of the number of visits per day. In the third situation, disposal points are multiple (they do not coincide with the garage), they are limited in the number of visits, and the fleet is composed of two types of vehicles. Computational results based not only on instances adapted from the literature but also on real cases are presented and analyzed. In particular, the results also show the effectiveness of combining sectorization and routing to solve waste collection problems.

Models and Algorihtm for the Optimization of Real-World Routing and Logistics Problems

Logistics involves planning, managing, and organizing the flows of goods from the point of origin to the point of destination in order to meet some requirements. Logistics and transportation aspects are very important and represent a relevant costs for producing and shipping companies, but also for public administration and private citizens. The optimization of resources and the improvement in the organization of operations is crucial for all branches of logistics, from the operation management to the transportation. As we will have the chance to see in this work, optimization techniques, models, and algorithms represent important methods to solve the always new and more complex problems arising in different segments of logistics. Many operation management and transportation problems are related to the optimization class of problems called Vehicle Routing Problems (VRPs). In this work, we consider several real-world deterministic and stochastic problems that are included in the wide class of the VRPs, and we solve them by means of exact and heuristic methods. We treat three classes of real-world routing and logistics problems. We deal with one of the most important tactical problems that arises in the managing of the bike sharing systems, that is the Bike sharing Rebalancing Problem (BRP). We propose models and algorithms for real-world earthwork optimization problems. We describe the 3DP process and we highlight several optimization issues in 3DP. Among those, we define the problem related to the tool path definition in the 3DP process, the 3D Routing Problem (3DRP), which is a generalization of the arc routing problem. We present an ILP model and several heuristic algorithms to solve the 3DRP.

Otimização de sistema de roteirização de coleta de resíduos sólidos domiciliares urbanos utilizando ferramentas computacionais.

A operação de coleta e transporte de resíduos sólidos urbanos é indispensável dentro de quaisquer sistema de limpeza urbana. É necessário que se intensifique a pesquisa nessa área de conhecimento afim de produzir-se material de auxílio ao poder público municipal e o setor privado. Deste modo o objetivo geral deste trabalho é o estudo da utilização de ferramentas computacionais para a otimização dos roteiros dos serviços de coleta de resíduos sólidos domiciliares. Foi feito um comparativo entre os itinerários percorridos pelos caminhões de coleta quando dimensionados de forma empírica e quando dimensionados com o auxílio de ferramentas computacionais. Verificou-se as vantagens e desvantagens de cada modelo de dimensionamento e o grande potencial de redução de custos quando utilizadas ferramentas computacionais.

Electromagnetism based approach to Sector design in Waste Collection

For efficient planning of waste collection routing, large municipalities may be partitioned into convenient sectors. The real case under consideration is the municipality of Monção, in Portugal. Waste collection involves more than 1600 containers over an area of 220 km2 and a population of around 20,000 inhabitants. This is mostly a rural area where the population is distributed in small villages around the 33 boroughs centres (freguesia) that constitute the municipality. In most freguesias, waste collection is usually conducted 3 times a week. However, there are situations in which the same collection is done every day. The case reveals some general and specific characteristics which are not rare, but are not widely addressed in the literature. Furthermore, new methods and models to deal with sectorization and routing are introduced, which can be extended to other applications. Sectorization and routing are tackled following a three-phase approach. The first phase, which is the main concern of the presentation, introduces a new method for sectorization inspired by Electromagnetism and Coulomb’s Law. The matter is not only about territorial division, but also the frequency of waste collection, which is a critical issue in these types of applications. Special characteristics related to the number and type of deposition points were also a motivation for this work. The second phase addresses the routing problems in each sector: new Mixed Capacitated Arc Routing with Limited Multi-Landfills models will be presented. The last phase integrates Sectoring and Routing. Computational results confirm the effectiveness of the entire novel approach.

Étude d'un problème de tournées de véhicules sur les arcs avec contraintes de capacité et coûts de service dépendants du temps

Thèse numérisée par la Division de la gestion de documents et des archives de l'Université de Montréal

Análise do uso de SIG no roteamento dos veículos de coleta de resíduos sólidos domiciliares

Relata-se neste trabalho, a análise do uso de um Sistema de Informação Geográfica - SIG como ferramenta para roteirização de veículos de coleta de resíduos sólidos domiciliares. O software utilizado foi o TransCAD, versão 3.2, que permite desenvolver rotas utilizando algoritmos que incluem o procedimento de roteirização em arco. O objetivo é minimizar a extensão total a ser percorrida pelos veículos coletores. O estudo de caso foi realizado na cidade de Ilha Solteira - SP. Os dados coletados e os resultados obtidos pelo TransCAD foram processados no software Microsoft Excel. Os resultados obtidos demonstraram reduções percentuais de até 41% na distância total percorrida e de 68% no tempo total de percurso em relação ao serviço atual.

Análise de uso de SIG no sistema de coleta de resíduos sólidos domiciliares em uma cidade de pequeno porte

Pós-graduação em Engenharia Civil - FEIS

An integrated approach for earthwork allocation, sequencing and routing

Planning techniques for large scale earthworks have been considered in this article. To improve these activities a “block theoretic” approach was developed that provides an integrated solution consisting of an allocation of cuts to fills and a sequence of cuts and fills over time. It considers the constantly changing terrain by computing haulage routes dynamically. Consequently more realistic haulage costs are used in the decision making process. A digraph is utilised to describe the terrain surface which has been partitioned into uniform grids. It reflects the true state of the terrain, and is altered after each cut and fill. A shortest path algorithm is successively applied to calculate the cost of each haul, and these costs are summed over the entire sequence, to provide a total cost of haulage. To solve this integrated optimisation problem a variety of solution techniques were applied, including constructive algorithms, meta-heuristics and parallel programming. The extensive numerical investigations have successfully shown the applicability of our approach to real sized earthwork problems.