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.

Análise de escalabilidade de uma implementação paralela do simulated annealing acoplado

This paper analyzes the performance of a parallel implementation of Coupled Simulated Annealing (CSA) for the unconstrained optimization of continuous variables problems. Parallel processing is an efficient form of information processing with emphasis on exploration of simultaneous events in the execution of software. It arises primarily due to high computational performance demands, and the difficulty in increasing the speed of a single processing core. Despite multicore processors being easily found nowadays, several algorithms are not yet suitable for running on parallel architectures. The algorithm is characterized by a group of Simulated Annealing (SA) optimizers working together on refining the solution. Each SA optimizer runs on a single thread executed by different processors. In the analysis of parallel performance and scalability, these metrics were investigated: the execution time; the speedup of the algorithm with respect to increasing the number of processors; and the efficient use of processing elements with respect to the increasing size of the treated problem. Furthermore, the quality of the final solution was verified. For the study, this paper proposes a parallel version of CSA and its equivalent serial version. Both algorithms were analysed on 14 benchmark functions. For each of these functions, the CSA is evaluated using 2-24 optimizers. The results obtained are shown and discussed observing the analysis of the metrics. The conclusions of the paper characterize the CSA as a good parallel algorithm, both in the quality of the solutions and the parallel scalability and parallel efficiency