From Genetic Algorithms to Efficient Organization

The work described in this thesis began as an inquiry into the nature and use of optimization programs based on "genetic algorithms." That inquiry led, eventually, to three powerful heuristics that are broadly applicable in gradient-ascent programs: First, remember the locations of local maxima and restart the optimization program at a place distant from previously located local maxima. Second, adjust the size of probing steps to suit the local nature of the terrain, shrinking when probes do poorly and growing when probes do well. And third, keep track of the directions of recent successes, so as to probe preferentially in the direction of most rapid ascent. These algorithms lie at the core of a novel optimization program that illustrates the power to be had from deploying them together. The efficacy of this program is demonstrated on several test problems selected from a variety of fields, including De Jong's famous test-problem suite, the traveling salesman problem, the problem of coordinate registration for image guided surgery, the energy minimization problem for determining the shape of organic molecules, and the problem of assessing the structure of sedimentary deposits using seismic data.

Optimización del sistema de transporte en el colegio The English School

La optimización de sistemas y modelos se ha convertido en uno de los factores más importantes a la hora de buscar la mayor eficiencia de un proceso. Este concepto no es ajeno al transporte escolar, ambiente que cambia constantemente al ritmo de las necesidades de sus clientes, y que responde ante una fuerte responsabilidad frente a sus usuarios, los niños que hacen uso del servicio, en cuanto al cumplimiento de tiempos y seguridad, mientras busca constantemente la reducción de costos. Este proyecto expone las problemáticas presentadas en The English School en esta área y propone un modelo de optimización simple que permitirá notables mejoras en términos de tiempos y costos, de tal forma que genere beneficios para la institución en términos financieros y de satisfacción al cliente. Por medio de la implementación de este modelo será posible identificar errores comunes del proceso, se identificarán soluciones prácticas de fácil aplicación en el manejo del transporte y se presentarán los resultados obtenidos en la muestra utilizada para desarrollar el proyecto.

Ant colony for TSP

The aim of this work is to investigate Ant Colony Algorithm for the traveling salesman problem (TSP). Ants of the artificial colony are able to generate successively shorter feasible tours by using information accumulated in the form of a pheromone trail deposited on the edges of the TSP graph. This paper is based on the ideas of ant colony algorithm and analysis the main parameters of the ant colony algorithm. Experimental results for solving TSP problems with ant colony algorithm show great effectiveness.

Estratégias de aplicações sequenciais e paralelas da metaheurística otimização por enxame de partículas ao problema do caixeiro viajante

Particle Swarm Optimization is a metaheuristic that arose in order to simulate the behavior of a number of birds in flight, with its random movement locally, but globally determined. This technique has been widely used to address non-liner continuous problems and yet little explored in discrete problems. This paper presents the operation of this metaheuristic, and propose strategies for implementation of optimization discret problems as form of execution parallel as sequential. The computational experiments were performed to instances of the TSP, selected in the library TSPLIB contenct to 3038 nodes, showing the improvement of performance of parallel methods for their sequential versions, in executation time and results

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 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

Metodologia estatística na solução do problema do caixeiro viajante e na avaliação de algoritmos : um estudo aplicado à transgenética computacional

The problems of combinatory optimization have involved a large number of researchers in search of approximative solutions for them, since it is generally accepted that they are unsolvable in polynomial time. Initially, these solutions were focused on heuristics. Currently, metaheuristics are used more for this task, especially those based on evolutionary algorithms. The two main contributions of this work are: the creation of what is called an -Operon- heuristic, for the construction of the information chains necessary for the implementation of transgenetic (evolutionary) algorithms, mainly using statistical methodology - the Cluster Analysis and the Principal Component Analysis; and the utilization of statistical analyses that are adequate for the evaluation of the performance of the algorithms that are developed to solve these problems. The aim of the Operon is to construct good quality dynamic information chains to promote an -intelligent- search in the space of solutions. The Traveling Salesman Problem (TSP) is intended for applications based on a transgenetic algorithmic known as ProtoG. A strategy is also proposed for the renovation of part of the chromosome population indicated by adopting a minimum limit in the coefficient of variation of the adequation function of the individuals, with calculations based on the population. Statistical methodology is used for the evaluation of the performance of four algorithms, as follows: the proposed ProtoG, two memetic algorithms and a Simulated Annealing algorithm. Three performance analyses of these algorithms are proposed. The first is accomplished through the Logistic Regression, based on the probability of finding an optimal solution for a TSP instance by the algorithm being tested. The second is accomplished through Survival Analysis, based on a probability of the time observed for its execution until an optimal solution is achieved. The third is accomplished by means of a non-parametric Analysis of Variance, considering the Percent Error of the Solution (PES) obtained by the percentage in which the solution found exceeds the best solution available in the literature. Six experiments have been conducted applied to sixty-one instances of Euclidean TSP with sizes of up to 1,655 cities. The first two experiments deal with the adjustments of four parameters used in the ProtoG algorithm in an attempt to improve its performance. The last four have been undertaken to evaluate the performance of the ProtoG in comparison to the three algorithms adopted. For these sixty-one instances, it has been concluded on the grounds of statistical tests that there is evidence that the ProtoG performs better than these three algorithms in fifty instances. In addition, for the thirty-six instances considered in the last three trials in which the performance of the algorithms was evaluated through PES, it was observed that the PES average obtained with the ProtoG was less than 1% in almost half of these instances, having reached the greatest average for one instance of 1,173 cities, with an PES average equal to 3.52%. Therefore, the ProtoG can be considered a competitive algorithm for solving the TSP, since it is not rare in the literature find PESs averages greater than 10% to be reported for instances of this size.

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

O problema do caixeiro viajante alugador : um estudo algorítmico

The Car Rental Salesman Problem (CaRS) is a variant of the classical Traveling Salesman Problem which was not described in the literature where a tour of visits can be decomposed into contiguous paths that may be performed in different rental cars. The aim is to determine the Hamiltonian cycle that results in a final minimum cost, considering the cost of the route added to the cost of an expected penalty paid for each exchange of vehicles on the route. This penalty is due to the return of the car dropped to the base. This paper introduces the general problem and illustrates some examples, also featuring some of its associated variants. An overview of the complexity of this combinatorial problem is also outlined, to justify their classification in the NPhard class. A database of instances for the problem is presented, describing the methodology of its constitution. The presented problem is also the subject of a study based on experimental algorithmic implementation of six metaheuristic solutions, representing adaptations of the best of state-of-the-art heuristic programming. New neighborhoods, construction procedures, search operators, evolutionary agents, cooperation by multi-pheromone are created for this problem. Furtermore, computational experiments and comparative performance tests are conducted on a sample of 60 instances of the created database, aiming to offer a algorithm with an efficient solution for this problem. These results will illustrate the best performance reached by the transgenetic algorithm in all instances of the dataset

Arquitetura multiagente baseada em nuvem de partículas para hibridização de metaheurísticas

This thesis proposes an architecture of a new multiagent system framework for hybridization of metaheuristics inspired on the general Particle Swarm Optimization framework (PSO). The main contribution is to propose an effective approach to solve hard combinatory optimization problems. The choice of PSO as inspiration was given because it is inherently multiagent, allowing explore the features of multiagent systems, such as learning and cooperation techniques. In the proposed architecture, particles are autonomous agents with memory and methods for learning and making decisions, using search strategies to move in the solution space. The concepts of position and velocity originally defined in PSO are redefined for this approach. The proposed architecture was applied to the Traveling Salesman Problem and to the Quadratic Assignment Problem, and computational experiments were performed for testing its effectiveness. The experimental results were promising, with satisfactory performance, whereas the potential of the proposed architecture has not been fully explored. For further researches, the proposed approach will be also applied to multiobjective combinatorial optimization problems, which are closer to real-world problems. In the context of applied research, we intend to work with both students at the undergraduate level and a technical level in the implementation of the proposed architecture in real-world problems

Uma análise experimental de abordagens heurísticas aplicadas ao problema do caixeiro viajante

Due to great difficulty of accurate solution of Combinatorial Optimization Problems, some heuristic methods have been developed and during many years, the analysis of performance of these approaches was not carried through in a systematic way. The proposal of this work is to make a statistical analysis of heuristic approaches to the Traveling Salesman Problem (TSP). The focus of the analysis is to evaluate the performance of each approach in relation to the necessary computational time until the attainment of the optimal solution for one determined instance of the TSP. Survival Analysis, assisted by methods for the hypothesis test of the equality between survival functions was used. The evaluated approaches were divided in three classes: Lin-Kernighan Algorithms, Evolutionary Algorithms and Particle Swarm Optimization. Beyond those approaches, it was enclosed in the analysis, a memetic algorithm (for symmetric and asymmetric TSP instances) that utilizes the Lin-Kernighan heuristics as its local search procedure

Uma abordagem por nuvem de partículas para problemas de otimização combinatória

Combinatorial optimization problems have the goal of maximize or minimize functions defined over a finite domain. Metaheuristics are methods designed to find good solutions in this finite domain, sometimes the optimum solution, using a subordinated heuristic, which is modeled for each particular problem. This work presents algorithms based on particle swarm optimization (metaheuristic) applied to combinatorial optimization problems: the Traveling Salesman Problem and the Multicriteria Degree Constrained Minimum Spanning Tree Problem. The first problem optimizes only one objective, while the other problem deals with many objectives. In order to evaluate the performance of the algorithms proposed, they are compared, in terms of the quality of the solutions found, to other approaches

Algoritmos científicos

The Scientific Algorithms are a new metaheuristics inspired in the scientific research process. The new method introduces the idea of theme to search the solution space of hard problems. The inspiration for this class of algorithms comes from the act of researching that comprises thinking, knowledge sharing and disclosing new ideas. The ideas of the new method are illustrated in the Traveling Salesman Problem. A computational experiment applies the proposed approach to a new variant of the Traveling Salesman Problem named Car Renter Salesman Problem. The results are compared to state-of-the-art algorithms for the latter problem

Algoritmo treansgenético na solução do problema do Caixeiro Viajante

The Traveling Purchaser Problem is a variant of the Traveling Salesman Problem, where there is a set of markets and a set of products. Each product is available on a subset of markets and its unit cost depends on the market where it is available. The objective is to buy all the products, departing and returning to a domicile, at the least possible cost defined as the summation of the weights of the edges in the tour and the cost paid to acquire the products. A Transgenetic Algorithm, an evolutionary algorithm with basis on endosymbiosis, is applied to the Capacited and Uncapacited versions of this problem. Evolution in Transgenetic Algorithms is simulated with the interaction and information sharing between populations of individuals from distinct species. The computational results show that this is a very effective approach for the TPP regarding solution quality and runtime. Seventeen and nine new best results are presented for instances of the capacited and uncapacited versions, respectively

Strategies to model scheduling decisions to plan the soft drink production process

In this paper we present a mixed integer model that integrates lot sizing and lot scheduling decisions for the production planning of a soft drink company. The main contribution of the paper is to present a model that differ from others in the literature for the constraints related to the scheduling decisions. The proposed strategy is compared to other strategies presented in the literature.