A Criteria-Based Approach to the Traveling Salesman Problem (TSP)

The “traveling salesman problem (TSP)” is a classic minimum cost network flow problem in mathematical programming and graph theory that can be formulated in multiple configurations. The fundamental question, however, is: “what is a cost”? The original “traveling salesman problem (TSP)” defines distance as the cost and the objective is to minimize distance traveled. This paper proposes other “cost” criteria to the original problem and also proposes a maximum revenue network flow as a variant to improve managerial decision-making. The proposed decision table methodology can be applied to problems that involve multiple locations or multiple tasks to complete

A new genetic algorithm for the asymmetric traveling salesman problem

The asymmetric traveling salesman problem (ATSP) is one of the most important combinatorial optimization problems. It allows us to solve, either directly or through a transformation, many real-world problems. We present in this paper a new competitive genetic algorithm to solve this problem. This algorithm has been checked on a set of 153 benchmark instances with known optimal solution and it outperforms the results obtained with previous ATSP heuristic methods. © 2012 Elsevier Ltd. All rights reserved.This work has been partially supported by the Ministerio de Educacion y Ciencia of Spain (Project No. TIN2008-06441-C02-01).Yuichi Nagata; Soler Fernández, D. (2012). A new genetic algorithm for the asymmetric traveling salesman problem. Expert Systems with Applications. 39(10):8947-8953. https://doi.org/10.1016/j.eswa.2012.02.029S89478953391

APLIKASI ALGORITMA BACKTRACKING UNTUK MENENTUKAN RUTE OPTIMAL DISTRIBUSI AIR ISI ULANG GONZALO DI KOTA AMBON

Distribution is a delivery of goods from an original area to the destination area, wherein the distribution, the problem of travel routes is very important because it can affect the time and cost of doing the distribution. The optimal route itself is a route that minimizes the distance and travel time. This research using the Backtracking Algorithm as part of the Traveling salesman problem method in finding the shortest route or minimum distance. In this research, the Backtracking algorithm is applied to search the minimum route for Gonzalo refill water distribution. The results obtained are the path with the shortest route in Ambon City, such as: Gonzalo - Jln. Karang Panjang - Jln. Pitu ina - Jln. Dr. Kayadoe - Terminal mardika - Jln. Wr. Supratman - Jln. A.Y. Patty - Jln. Said Commands - Jln. Pattimura - Jln A. Yani - Gonzalo, with a long of travel route is 15,301 Km

State transition algorithm for traveling salesman problem

Discrete version of state transition algorithm is proposed in order to solve the traveling salesman problem. Three special operators for discrete optimization problem named swap, shift and symmetry transformations are presented. Convergence analysis and time complexity of the algorithm are also considered. To make the algorithm simple and efficient, no parameter adjusting is suggested in current version. Experiments are carried out to test the performance of the strategy, and comparisons with simulated annealing and ant colony optimization have demonstrated the effectiveness of the proposed algorithm. The results also show that the discrete state transition algorithm consumes much less time and has better search ability than its counterparts, which indicates that state transition algorithm is with strong adaptability. © 2012 Chinese Assoc of Automati

Routing Optimization Under Uncertainty

We consider a class of routing optimization problems under uncertainty in which all decisions are made before the uncertainty is realized. The objective is to obtain optimal routing solutions that would, as much as possible, adhere to a set of specified requirements after the uncertainty is realized. These problems include finding an optimal routing solution to meet the soft time window requirements at a subset of nodes when the travel time is uncertain, and sending multiple capacitated vehicles to different nodes to meet the customers’ uncertain demands. We introduce a precise mathematical framework for defining and solving such routing problems. In particular, we propose a new decision criterion, called the Requirements Violation (RV) Index, which quantifies the risk associated with the violation of requirements taking into account both the frequency of violations and their magnitudes whenever they occur. The criterion can handle instances when probability distributions are known, and ambiguity when distributions are partially characterized through descriptive statistics such as moments. We develop practically efficient algorithms involving Benders decomposition to find the exact optimal routing solution in which the RV Index criterion is minimized, and we give numerical results from several computational studies that show the attractive performance of the solutions

Heuristic and exact algorithms for the dominating cycle problem

Orientadores: Fábio Luiz Usberti, Celso CavellucciDissertação (mestrado) - Universidade Estadual de Campinas, Instituto de ComputaçãoResumo: Esta dissertação dedicou-se ao estudo de uma generalização do Problema do Caixeiro Viajante (TSP), denominada Problema do Ciclo Dominante (DCP). Essa generalização consiste na composição de dois problemas NP-difíceis: o TSP e o Problema do Conjunto k-Dominante em Grafos (k-DSP). O objetivo do DCP consiste em encontrar um ciclo de custo mínimo em um grafo não-direcionado, partindo de um vértice origem, tal que cada vértice do grafo ou pertence ao ciclo ou está a uma distância de até k de um vértice do ciclo. A motivação de estudo do DCP consiste em sua aplicação para um problema de roteamento, onde empresas que atuam como fornecedores de energia, gás ou água, possuem empregados responsáveis por registrar o consumo de clientes dispersos geograficamente. Considera-se que esses empregados, denominados leituristas, possuem aparelhos de medição remota, com raio de alcance pré-definido. Com esses aparelhos, os leituristas não precisam visitar cada cliente; basta que em suas rotas de leitura todos os clientes estejam no raio de alcance do aparelho. Esta dissertação apresentou um método heurístico e um método exato para solução do DCP. O método heurístico é baseado na metaheurística GRASP (Greedy Randomized Adaptive Search Procedure). Um algoritmo Branch-and-Cut é proposto como método exato para o DCP. Os métodos, heurístico e exato, são testados com um conjunto representativo de instâncias e os resultados obtidos são comparados, avaliando a eficiência de cada método no que diz respeito aos desvios de otimalidadeAbstract: This dissertation studies a generalization of the Travelling Salesman Problem (TSP), called the Dominating Cycle Problem (DCP). This generalization is a composition of two NP-hard problems: the TSP and the k-Dominating Set Problem in Graphs (k-DSP). The aim of the DCP is to find a minimum cost cycle in an undirected graph, from a source vertex, such that each vertex in the graph either belongs to the cycle, or is at a distance of up to k of some vertex in the cycle. The DCP is motivated by its application to a routing problem, where utilities that act as energy, gas or water suppliers, have employees responsible for recording the consumption of geographically dispersed customers. It is considered that these employees, called meter readers, have remote measurement devices, with pre-defined range. With these devices, meter readers do not need to visit each client; it suffices that all clients are within the device range from the reading routes. This dissertation presented a heuristic method and an exact method for the solution of the DCP. The heuristic method is based on GRASP (Greedy Randomized Adaptive Search Procedure). A Branch-and-Cut algorithm is proposed as the exact method for the DCP. The methods, heuristic and exact, are tested with a representative set of instances and the obtained results are compared, evaluating the efficiency of each method with respect to deviations from optimalityMestradoCiência da ComputaçãoMestre em Ciência da Computação13641421406901CAPESFuncam

Design methodologies and architectures of hardware-based evolutionary algorithms for aerospace optimisation applications on FPGAS

This thesis is a study of new design methods for allowing evolutionary algorithms to be more effectively utilised in aerospace optimisation applications where computation needs are high and computation platform space may be restrictive. It examines the applicability of special hardware computational platforms known as field programmable gate arrays and shows that with the right implementation methods they can offer significant benefits. This research is a step forward towards the advancement of efficient and highly automated aircraft systems for meeting compact physical constraints in aerospace platforms and providing effective performance speedups over traditional methods

Propuesta de mejora en el área del tren de laminación de acero mediante la reducción del tiempo de cambio de formato a través del uso de herramientas de optimización matemática y herramientas de manufactura esbelta

El sector siderúrgico dedicado a la construcción es cada vez más competitivo. La competencia mundial y la reducción de barreras arancelarias entre países de distintos continentes han originado que las empresas de este rubro busquen mejorar la eficiencia de sus procesos para mantener costos bajos y ofrecer precios competitivos. Por este motivo muchas fábricas a nivel mundial están optimizando sus procesos para conseguir reducir sus costos. Un campo muy importante dentro del sector siderúrgico es el de la fabricación de aceros laminados en caliente. El proceso de laminación de Acero consiste en la reducción de medidas de una barra (palanquilla) caliente haciéndola pasar través de una serie de casetas o stands hasta conseguir la forma y las medidas requeridas del producto final. Cada caseta está conformada por dos rodillos motorizados que tienen canales tallados con un perfil necesario para cada producto. Dependiendo del proceso y de la ubicación de la caseta, los canales tallados en los cilindros pueden ser exclusivos para un producto o pueden servir para varios productos. El tren de laminación donde se enfoca esta tesis tiene una cartera de 300 productos aproximadamente, de los cuales puede laminar hasta 40 productos distintos en un mismo mes, por lo que es imprescindible realizar los cambios de formato empleando el menor tiempo posible, con el fin de mejorar la utilización de la planta y obtener costos competitivos de producción. Para reducir el tiempo de cambios de formato se debe considerar dos aspectos: Primero la secuenciación de los productos, pues hay productos más compatibles entre sí, ya sea por utilizar los mismos diseños de canal en ciertas casetas, o por utilizar los mismos accesorios. En segundo lugar, se debe optimizar los recursos y las tareas durante la ejecución del cambio de formato para reducir el tiempo. La presente tesis se enfoca en desarrollar estrategias para reducir los tiempos de cambio de formato en un tren de laminación, para lo cual se desarrollan dos metodologías: Primero se propone el uso de modelos de optimización mediante un algoritmo de ruteo llamado TSP (Traveling Salesman Problem), el cual utilizaremos para optimizar la secuencia de productos del programa mensual, de tal manera que la secuencia sea la que demande el menor cambio de accesorios (utillaje y casetas) en el mes. La segunda estrategia es proponer el uso de la metodología SMED para reducir los tiempos de ejecución de cada cambio.Tesi

Dynamic routing on stochastic time-dependent networks using real-time information

In just-in-time (JIT) manufacturing environments, on-time delivery is one of the key performance measures for dispatching and routing of freight vehicles. Both the travel time delay and its variability impact the efficiency of JIT logistics operations, that are becoming more and more common in many industries, and in particular, the automotive industry. In this dissertation, we first propose a framework for dynamic routing of a single vehicle on a stochastic time dependent transportation network using real-time information from Intelligent Transportation Systems (ITS). Then, we consider milk-run deliveries with several pickup and delivery destinations subject to time windows under same network settings. Finally, we extend our dynamic routing models to account for arc traffic condition dependencies on the network. Recurrent and non-recurrent congestion are the two primary reasons for travel time delay and variability, and their impact on urban transportation networks is growing in recent decades. Hence, our routing methods explicitly account for both recurrent and non-recurrent congestion in the network. In our modeling framework, we develop alternative delay models for both congestion types based on historical data (e.g., velocity, volume, and parameters for incident events) and then integrate these models with the forward-looking routing models. The dynamic nature of our routing decisions exploits the real-time information available from various ITS sources, such as loop sensors. The forward-looking traffic dynamic models for individual arcs are based on congestion states and state transitions driven by time-dependent Markov chains. We propose effective methods for estimation of the parameters of these Markov chains. Based on vehicle location, time of day, and current and projected network congestion states, we generate dynamic routing policies using stochastic dynamic programming formulations. All algorithms are tested in simulated networks of Southeast-Michigan and Los Angeles, CA freeways and highways using historical traffic data from the Michigan ITS Center, Traffic.com, and Caltrans PEMS