A multi-depot travelling salesman problem and its iterative and integrated approaches

This paper formulates a logistics distribution problem as the multi-depot travelling salesman problem (MDTSP). The decision makers not only have to determine the travelling sequence of the salesman for delivering finished products from a warehouse or depot to a customer, but also need to determine which depot stores which type of products so that the total travelling distance is minimised. The MDTSP is similar to the combination of the travelling salesman and quadratic assignment problems. In this paper, the two individual hard problems or models are formulated first. Then, the problems are integrated together, that is, the MDTSP. The MDTSP is constructed as both integer nonlinear and linear programming models. After formulating the models, we verify the integrated models using commercial packages, and most importantly, investigate whether an iterative approach, that is, solving the individual models repeatedly, can generate an optimal solution to the MDTSP. Copyright © 2006 Inderscience Enterprises Ltd.

Solving Travelling Salesman Problem in a Simulation of Genetic Algorithms with DNA

In this paper it is explained how to solve a fully connected N-City travelling salesman problem (TSP) using a genetic algorithm. A crossover operator to use in the simulation of a genetic algorithm (GA) with DNA is presented. The aim of the paper is to follow the path of creating a new computational model based on DNA molecules and genetic operations. This paper solves the problem of exponentially size algorithms in DNA computing by using biological methods and techniques. After individual encoding and fitness evaluation, a protocol of the next step in a GA, crossover, is needed. This paper also shows how to make the GA faster via different populations of possible solutions.

An Effective Exact Algorithm for One Particular Case of the Travelling-Salesman Problem

The article presents the exact algorithm for solving one case of the job-scheduling problem for the case when the source matrix is ordered by rows.

A multilevel approach to the travelling salesman problem

Abstract not available

Integración de Google Maps y TSP Solvers para la definición y resolución del TSP

Este trabajo final de carrera presenta la arquitectura e implementación de un entorno web para la descripción y visualización de instancias reales del TSP (Travelling Salesman Problem), a través de Google Maps, y su posterior resoluación mediante tècnicas de optimización combinatoria.

A Study of Ordered Gene Problems Featuring DNA Error Correction and DNA Fragment Assembly with a Variety of Heuristics, Genetic Algorithm Variations, and Dynamic Representations

Ordered gene problems are a very common classification of optimization problems. Because of their popularity countless algorithms have been developed in an attempt to find high quality solutions to the problems. It is also common to see many different types of problems reduced to ordered gene style problems as there are many popular heuristics and metaheuristics for them due to their popularity. Multiple ordered gene problems are studied, namely, the travelling salesman problem, bin packing problem, and graph colouring problem. In addition, two bioinformatics problems not traditionally seen as ordered gene problems are studied: DNA error correction and DNA fragment assembly. These problems are studied with multiple variations and combinations of heuristics and metaheuristics with two distinct types or representations. The majority of the algorithms are built around the Recentering- Restarting Genetic Algorithm. The algorithm variations were successful on all problems studied, and particularly for the two bioinformatics problems. For DNA Error Correction multiple cases were found with 100% of the codes being corrected. The algorithm variations were also able to beat all other state-of-the-art DNA Fragment Assemblers on 13 out of 16 benchmark problem instances.

Optimal Path Searching through Specified Routes using different Algorithms

To connect different electrical, network and data devices with the minimum cost and shortest path, is a complex job. In huge buildings, where the devices are placed at different locations on different floors and only some specific routes are available to pass the cables and buses, the shortest path search becomes more complex. The aim of this thesis project is, to develop an application which indentifies the best path to connect all objects or devices by following the specific routes.To address the above issue we adopted three algorithms Greedy Algorithm, Simulated Annealing and Exhaustive search and analyzed their results. The given problem is similar to Travelling Salesman Problem. Exhaustive search is a best algorithm to solve this problem as it checks each and every possibility and give the accurate result but it is an impractical solution because of huge time consumption. If no. of objects increased from 12 it takes hours to search the shortest path. Simulated annealing is emerged with some promising results with lower time cost. As of probabilistic nature, Simulated annealing could be non optimal but it gives a near optimal solution in a reasonable duration. Greedy algorithm is not a good choice for this problem. So, simulated annealing is proved best algorithm for this problem. The project has been implemented in C-language which takes input and store output in an Excel Workbook

Melhoria da segurança pública: uma proposta para alocação de unidades policiais utilizando o modelo das p-medianas e do caixeiro viajante

The decrease in crime is one of the core issues that cause concern in society today. This study aims to propose improvements to public safety from the choice of points to the location of police units, ie the points which support the car and the police. For this, three models were developed in order to assist decision making regarding the best placement of these bases. The Model of Police Units Routing has the intention to analyze the current configuration of a given region and develop optimal routes for round preventative. The Model of Allocation and Routing for New Police Units (MARNUP) used the model of facility location called p-median weighted and traveling salesman problem (TSP) combined aiming an ideal setting for regions that do not yet have support points or to assess how far the distribution is present in relation to that found in solution. The Model Redefinition and Routing Unit Police (MRRUP) seek to change the current positioning taking into account the budgetary constraints of the decision maker. To verify the applicability of these models we used data from 602 points to instances of police command that is responsible for the capital city of Natal. The city currently has 31 police units for 36 of these 19 districts and police have some assistance. This reality can lead to higher costs and higher response times for answering emergency calls. The results of the models showed that in an ideal situation it is possible to define a distance of 500 km/round, whereas in this 900 km are covered by approximately round. However, a change from three-point lead reduced to 700 km / round which represents a decrease of 22% in the route. This reduction should help improve response time to emergency care, improving the level of service provided by the increase of solved cases, reducing police shifts and routing preventive patrols

Algoritmo memético com infecção viral: uma aplicação ao problema do caixeiro viajante assimétrico

The Combinatorial Optimization is a basic area to companies who look for competitive advantages in the diverse productive sectors and the Assimetric Travelling Salesman Problem, which one classifies as one of the most important problems of this area, for being a problem of the NP-hard class and for possessing diverse practical applications, has increased interest of researchers in the development of metaheuristics each more efficient to assist in its resolution, as it is the case of Memetic Algorithms, which is a evolutionary algorithms that it is used of the genetic operation in combination with a local search procedure. This work explores the technique of Viral Infection in one Memetic Algorithms where the infection substitutes the mutation operator for obtaining a fast evolution or extinguishing of species (KANOH et al, 1996) providing a form of acceleration and improvement of the solution . For this it developed four variants of Viral Infection applied in the Memetic Algorithms for resolution of the Assimetric Travelling Salesman Problem where the agent and the virus pass for a symbiosis process which favored the attainment of a hybrid evolutionary algorithms and computational viable

Algoritmo Q-learning como estratégia de exploração e/ou explotação para metaheurísticas GRASP e algoritmo genético

Techniques of optimization known as metaheuristics have achieved success in the resolution of many problems classified as NP-Hard. These methods use non deterministic approaches that reach very good solutions which, however, don t guarantee the determination of the global optimum. Beyond the inherent difficulties related to the complexity that characterizes the optimization problems, the metaheuristics still face the dilemma of xploration/exploitation, which consists of choosing between a greedy search and a wider exploration of the solution space. A way to guide such algorithms during the searching of better solutions is supplying them with more knowledge of the problem through the use of a intelligent agent, able to recognize promising regions and also identify when they should diversify the direction of the search. This way, this work proposes the use of Reinforcement Learning technique - Q-learning Algorithm - as exploration/exploitation strategy for the metaheuristics GRASP (Greedy Randomized Adaptive Search Procedure) and Genetic Algorithm. The GRASP metaheuristic uses Q-learning instead of the traditional greedy-random algorithm in the construction phase. This replacement has the purpose of improving the quality of the initial solutions that are used in the local search phase of the GRASP, and also provides for the metaheuristic an adaptive memory mechanism that allows the reuse of good previous decisions and also avoids the repetition of bad decisions. In the Genetic Algorithm, the Q-learning algorithm was used to generate an initial population of high fitness, and after a determined number of generations, where the rate of diversity of the population is less than a certain limit L, it also was applied to supply one of the parents to be used in the genetic crossover operator. Another significant change in the hybrid genetic algorithm is the proposal of a mutually interactive cooperation process between the genetic operators and the Q-learning algorithm. In this interactive/cooperative process, the Q-learning algorithm receives an additional update in the matrix of Q-values based on the current best solution of the Genetic Algorithm. The computational experiments presented in this thesis compares the results obtained with the implementation of traditional versions of GRASP metaheuristic and Genetic Algorithm, with those obtained using the proposed hybrid methods. Both algorithms had been applied successfully to the symmetrical Traveling Salesman Problem, which was modeled as a Markov decision process

Aplicaçaõ das técnicas Path-relinking e Vocabulary buiding na melhoria de performance do algoritmo memético para o problema do caixeiro viajante assimétrico

The present essay shows strategies of improvement in a well succeded evolutionary metaheuristic to solve the Asymmetric Traveling Salesman Problem. Such steps consist in a Memetic Algorithm projected mainly to this problem. Basically this improvement applied optimizing techniques known as Path-Relinking and Vocabulary Building. Furthermore, this last one has being used in two different ways, in order to evaluate the effects of the improvement on the evolutionary metaheuristic. These methods were implemented in C++ code and the experiments were done under instances at TSPLIB library, being possible to observe that the procedures purposed reached success on the tests done

Teoria dos grafos e suas aplicações

Pós-graduação em Matemática Universitária - IGCE

A Study of Different Subsequence Elimination Strategies for the Soft Drink Production Planning

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Reformulações para o problema integrado de dimensionamento e sequenciamento da produção

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)