Two phased hybrid local search for the periodic capacitated arc routing problem

The periodic capacitated arc routing problem (PCARP) is a challenging general model with important applications. The PCARP has two hierarchical optimization objectives: a primary objective of minimizing the number of vehicles (Fv) and a secondary objective of minimizing the total cost (Fc). In this paper, we propose an effective two phased hybrid local search (HLS) algorithm for the PCARP. The first phase makes a particular effort to optimize the primary objective while the second phase seeks to further optimize both objectives by using the resulting number of vehicles of the first phase as an upper bound to prune the search space. For both phases, combined local search heuristics are devised to ensure an effective exploration of the search space. Experimental results on 63 benchmark instances demonstrate that HLS performs remarkably well both in terms of computational efficiency and solution quality. In particular, HLS discovers 44 improved best known values (new upper bounds) for the total cost objective Fc while attaining all the known optimal values regarding the objective of the number of vehicles Fv. To our knowledge, this is the first PCARP algorithm reaching such a performance. Key components of HLS are analyzed to better understand their contributions to the overall performance

A Hybrid Approach to the Optimization of Multiechelon Systems

In freight transportation there are two main distribution strategies: direct shipping and multiechelon distribution. In the direct shipping, vehicles, starting from a depot, bring their freight directly to the destination, while in the multiechelon systems, freight is delivered from the depot to the customers through an intermediate points. Multiechelon systems are particularly useful for logistic issues in a competitive environment. The paper presents a concept and application of a hybrid approach to modeling and optimization of the Multi-Echelon Capacitated Vehicle Routing Problem. Two ways of mathematical programming (MP) and constraint logic programming (CLP) are integrated in one environment. The strengths of MP and CLP in which constraints are treated in a different way and different methods are implemented and combined to use the strengths of both. The proposed approach is particularly important for the discrete decision models with an objective function and many discrete decision variables added up in multiple constraints. An implementation of hybrid approach in the ECLiPSe system using Eplex library is presented. The Two-Echelon Capacitated Vehicle Routing Problem (2E-CVRP) and its variants are shown as an illustrative example of the hybrid approach. The presented hybrid approach will be compared with classical mathematical programming on the same benchmark data sets

On the periodic hierarchical Chinese postman problem

This paper presents a mathematical formulation and a heuristic approach for a new variant of the Hierarchical Chinese Postman Problem (HCPP). Indeed, we introduce the concept of periodicity, and we define and solve, for the first time, the Periodic-HCPP, denoted as P-HCPP. Given that the resulting integer programming model makes use of a big number of binary variables and given the extended time horizon considered, 30 days in our case, the problem is characterized by a high level of complexity. However, our developed heuristic is able to solve instances having up to 40 nodes, 520 arcs and hierarchies, whereas a general-purpose solver like Gurobi was not able to provide solutions for instances having more than 10 nodes. While the collected results are very encouraging, we provide at the end of this paper a set of possible future extensions of this work

Meta-RaPS Hybridization with Machine Learning Algorithms

This dissertation focuses on advancing the Metaheuristic for Randomized Priority Search algorithm, known as Meta-RaPS, by integrating it with machine learning algorithms. Introducing a new metaheuristic algorithm starts with demonstrating its performance. This is accomplished by using the new algorithm to solve various combinatorial optimization problems in their basic form. The next stage focuses on advancing the new algorithm by strengthening its relatively weaker characteristics. In the third traditional stage, the algorithms are exercised in solving more complex optimization problems. In the case of effective algorithms, the second and third stages can occur in parallel as researchers are eager to employ good algorithms to solve complex problems. The third stage can inadvertently strengthen the original algorithm. The simplicity and effectiveness Meta-RaPS enjoys places it in both second and third research stages concurrently. This dissertation explores strengthening Meta-RaPS by incorporating memory and learning features. The major conceptual frameworks that guided this work are the Adaptive Memory Programming framework (or AMP) and the metaheuristic hybridization taxonomy. The concepts from both frameworks are followed when identifying useful information that Meta-RaPS can collect during execution. Hybridizing Meta-RaPS with machine learning algorithms helped in transforming the collected information into knowledge. The learning concepts selected are supervised and unsupervised learning. The algorithms selected to achieve both types of learning are the Inductive Decision Tree (supervised learning) and Association Rules (unsupervised learning). The objective behind hybridizing Meta-RaPS with an Inductive Decision Tree algorithm is to perform online control for Meta-RaPS\u27 parameters. This Inductive Decision Tree algorithm is used to find favorable parameter values using knowledge gained from previous Meta-RaPS iterations. The values selected are used in future Meta-RaPS iterations. The objective behind hybridizing Meta-RaPS with an Association Rules algorithm is to identify patterns associated with good solutions. These patterns are considered knowledge and are inherited as starting points for in future Meta-RaPS iteration. The performance of the hybrid Meta-RaPS algorithms is demonstrated by solving the capacitated Vehicle Routing Problem with and without time windows

Metaheuristic Approaches For Estimating In-Kind Food Donations Availability And Scheduling Food Bank Vehicles

Food banks provide services that allow households facing food insecurity to receive nutritious food items. Food banks, however, experience operational challenges as a result of constrained and uncertain supply and complex routing challenges. The goal of this research is to explore opportunities to enhance food bank operations through metaheuristic forecasting and scheduling practices. Knowledge discovery methods and supervised machine learning are used to forecast food availability at supermarkets. In particular, a quasi-greedy algorithm which selects multi-layer perceptron models to represent food availability is introduced. In addition, a new classification of the vehicle routing problem is proposed to manage the distribution and collection of food items. In particular, variants of the periodic vehicle routing problem backhauls are introduced. In addition to discussing model formulations for the routing problems, a hybrid genetic algorithm is introduced which finds good solutions for larger problem instances in a reasonable computation time

O problema de roteamento periódico e capacitado em arcos com movimentos contínuos

Orientador: Prof. Dr. Cassius Tadeu ScarpinCoorientador: Prof. Dr. José Eduardo Pécora JuniorTese (doutorado) - Universidade Federal do Paraná, Setor de Tecnologia, Programa de Pós-Graduação em Métodos Numéricos em Engenharia. Defesa : Curitiba, 22/10/2018Inclui referências: p.128-134Área de concentração: Programação MatemáticaResumo: Esse trabalho aborda o Problema de Roteamento Periódico e Capacitado em Arcos, Periodic Capacitated Arc Routing Problem (PCARP), que pode ser definido como um problema de roteamento em arcos envolvendo um horizonte de tempo composto por mais de um período, os quais podem ser formados por qualquer fração temporal desde que discretas. Um ou mais veículos, ao fazerem suas rotas, devem executar da melhor maneira possível as tarefas que estão associadas a cada arco sem exceder sua capacidade e respeitando as frequências exigidas. Esse trabalho visa classificar as pesquisas acerca do PCARP por meio de uma proposta taxonômica que considera características físicas, foco aplicável ou teórico e abordagem resolutiva. Outra contribuição é um estudo aplicado à inspeção de ferrovias, o qual é classificado como PCARP com Movimentos Contínuos. Rotas com movimentos contínuos são caracterizadas por não terem a obrigatoriedade de serem iniciadas e terminadas em um depósito. O problema tem sua formulação matemática apresentada e sua a resolução é feita utilizando métodos exato, heurístico e híbridos. O método exato consiste na utilização de um solver comercial e a heurística utilizada é um novo algoritmo de Otimização de Colônia de Formigas, Ant Colony Optimization (ACO). Ambos têm seus pontos fortes que se complementam, sendo assim foram propostas três abordagens híbridas. A primeira consiste na utilização da colônia de formigas como solução inicial para o modelo exato, e as outras duas abordagens são variações do algoritmo Busca Iterativa em Espaço Restrito, Iterative Restricted Space Search (IRSS). A IRSS é baseada na exploração estratégica do espaço de soluções de um dado problema que, nesse trabalho, será auxiliada pelo algoritmo ACO. Os resultados alcançados mostram que as estratégias de resolução propostas são capazes de superar os resultados alcançados pelo solver comercial. Palavras-chave: Problema de Roteamento Periódico e Capacitado em Arcos 1. Movimentos Contínuos 2. Otimização da Colônia de Formigas 3. Busca Iterativa em Espaço Restrito 4. Manutenção e Inspeção de Ferrovias 5.Abstract: The Periodic Capacitated Arc Routing Problem (PCARP) can be defined as an arc routing problem that involves a time horizon, which is greater than one period that can be composed by any fraction of time. One or many vehicles, while into routes, must perform, in the best way possible, all tasks in the arcs without exceeding their capacities and attending the required frequencies. This work classifies researches about PCARP using a taxonomy that considers physical features, applied or academic focus and resolution approach. An additional contribution is a study based on inspection of railroads; this one is classified as PCARP with Continuous Moves. Routes with continuous moves do not need a depot as a starting or finishing point. This work presents the mathematical formulation for the problem and tackles it with exact, heuristic and hybrid methods. The exact approach consists of the use of a commercial solver, and the heuristic is a new Ant Colony Optimization (ACO) algorithm. Both have strengths that may be combined to compose hybrid approaches, three of them are explored. The first one uses the ACO to form an initial solution to the solver, and the two others are variants of the Iterative Restricted Space Search (IRSS) framework. The IRSS strategically exploits the solution space of one problem assisted by an algorithm, in this case, the ACO. The results achieved showed that the strategies proposed are able to overcome the ones from the commercial solver. Keywords: Periodic Capacitated Arc Routing Problem 1. Continuous Moves 2. Ant Colony Optimization 3. Iterative Restricted Space Search 4. Inspection and Maintenance in Railways 5

LOCATION-ALLOCATION-ROUTING APPROACH TO SOLID WASTE COLLECTION AND DISPOSAL

Various studies have indicated that the collection phase of solid wastes, which comprises of the initial col- lection at the source of generation and the transportation to the disposal sites, is by far the most expensive. Two fundamental issues of concern in solid waste collection are the locations of initial collection and the period of collection by the dedicated vehicles. However, considering the prevailing conditions of adhoc lo- cation of waste containers and the faulty roads in many developing countries, this research was conducted to develop two e�ective models for solid waste collection and disposal such that new parameters measuring the capacity of waste ow from each source unit and road accessibility were introduced and incorporated in the mathematical formulations of the models. To formulate the problems, two classes of integer pro- gramming problems namely, Facility Location Problem (FLP) and the Vehicle Routing Problem (VRP), were used for the collection and disposal respectively. The clustering process involved in the model for the collection phase was based on the Euclidean distance relationship among the various entities within the study area. In this model, the study area was considered as a universal set and simply partitioned with each element representing a cluster. At this stage, a threshold distance was de�ned as the maximum allowable distance between a cluster and the potential collection sites. In the VRP formulation of the disposal model, two new parameters, called the accessibility ratio and road attribute, were introduced and included in the formulation. The inclusion of these parameters ensure that a waste collection vehicle uses only roads with high attributes. The solution to the model on the collection phase was based on the Lagrangian re- laxation of the set of constraints where decision variables are linked, while in the model on waste vehicle routing, the assignment constraints were relaxed. Both resulting Lagrangian dual problems were solved using sub-gradient optimization algorithm. It was shown that the resulting Lagrangian dual functions were non-di�erentiable concave functions and thus the application of the sub-gradient optimization method was justi�ed. By applying these techniques, strong lower bounds on the optimal values of the decision variables were obtained. All model implementations were based on randomly generated data that mimic real-life experience of the study area (Eti-Osa Local Government Area of Lagos State, Nigeria), as well as large-scale standard benchmark data instances in literature. These computational experiments were carried out using the CPLEX and MINOS optimization solvers on AIMMS and AMPL modeling environments. Results from the computational experiments revealed that the models are capable of addressing the challenge of solid waste collection and disposal. For instance, more than 60% reductions were obtained for the number of collection points to be activated and the container allocations for the different wastes considered. Numerical results from the disposal model showed that there is a general reduction in the total distance covered by a vehicle and a slight improvement in the number of customers visited. Result comparison with those found in literature suggested that our models are very efficient