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

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.

Uma investigação de algoritmos exatos e metaheurísticos aplicados ao nonograma

Nonogram is a logical puzzle whose associated decision problem is NP-complete. It has applications in pattern recognition problems and data compression, among others. The puzzle consists in determining an assignment of colors to pixels distributed in a N  M matrix that satisfies line and column constraints. A Nonogram is encoded by a vector whose elements specify the number of pixels in each row and column of a figure without specifying their coordinates. This work presents exact and heuristic approaches to solve Nonograms. The depth first search was one of the chosen exact approaches because it is a typical example of brute search algorithm that is easy to implement. Another implemented exact approach was based on the Las Vegas algorithm, so that we intend to investigate whether the randomness introduce by the Las Vegas-based algorithm would be an advantage over the depth first search. The Nonogram is also transformed into a Constraint Satisfaction Problem. Three heuristics approaches are proposed: a Tabu Search and two memetic algorithms. A new function to calculate the objective function is proposed. The approaches are applied on 234 instances, the size of the instances ranging from 5 x 5 to 100 x 100 size, and including logical and random Nonograms

O problema do caixeiro alugador com coleta de bonus: um estudo algoritmico

This paper introduces a new variant of the Traveling Car Renter Problem, named Prizecollecting Traveling Car Renter Problem. In this problem, a set of vertices, each associated with a bonus, and a set of vehicles are given. The objective is to determine a cycle that visits some vertices collecting, at least, a pre-defined bonus, and minimizing the cost of the tour that can be traveled with different vehicles. A mathematical formulation is presented and implemented in a solver to produce results for sixty-two instances. The proposed problem is also subject of an experimental study based on the algorithmic application of four metaheuristics representing the best adaptations of the state of the art of the heuristic programming.We also provide new local search operators which exploit the neighborhoods of the problem, construction procedures and adjustments, created specifically for the addressed problem. Comparative computational experiments and performance tests are performed on a sample of 80 instances, aiming to offer a competitive algorithm to the problem. We conclude that memetic algorithms, computational transgenetic and a hybrid evolutive algorithm are competitive in tests performed

Busca heurística através de algoritmo genético e memético com construção de vocábulos para o problema de atribuição de localidades a anéis Sonet

Telecommunications play a key role in contemporary society. However, as new technologies are put into the market, it also grows the demanding for new products and services that depend on the offered infrastructure, making the problems of planning telecommunications networks, despite the advances in technology, increasingly larger and complex. However, many of these problems can be formulated as models of combinatorial optimization, and the use of heuristic algorithms can help solving these issues in the planning phase. In this project it was developed two pure metaheuristic implementations Genetic algorithm (GA) and Memetic Algorithm (MA) plus a third hybrid implementation Memetic Algorithm with Vocabulary Building (MA+VB) for a problem in telecommunications that is known in the literature as Problem SONET Ring Assignment Problem or SRAP. The SRAP arises during the planning stage of the physical network and it consists in the selection of connections between a number of locations (customers) in order to meet a series of restrictions on the lowest possible cost. This problem is NP-hard, so efficient exact algorithms (in polynomial complexity ) are not known and may, indeed, even exist

Metaheurísticas evolutivas para o problema de roteamento de unidades móveis de pistoneio

This paper presents metaheuristic strategies based on the framework of evolutionary algorithms (Genetic and Memetic) with the addition of Technical Vocabulary Building for solving the Problem of Optimizing the Use of Multiple Mobile Units Recovery of Oil (MRO units). Because it is an NP-hard problem, a mathematical model is formulated for the problem, allowing the construction of test instances that are used to validate the evolutionary metaheuristics developed

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