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.

Modelos de sobrevivência com fração de cura e omissão nas covariáveis

In this work we study the survival cure rate model proposed by Yakovlev (1993) that are considered in a competing risk setting. Covariates are introduced for modeling the cure rate and we allow some covariates to have missing values. We consider only the cases by which the missing covariates are categorical and implement the EM algorithm via the method of weights for maximum likelihood estimation. We present a Monte Carlo simulation experiment to compare the properties of the estimators based on this method with those estimators under the complete case scenario. We also evaluate, in this experiment, the impact in the parameter estimates when we increase the proportion of immune and censored individuals among the not immune one. We demonstrate the proposed methodology with a real data set involving the time until the graduation for the undergraduate course of Statistics of the Universidade Federal do Rio Grande do Norte

Estimação clássica e Bayesiana em modelos de sobrevida com fração de cura

In Survival Analysis, long duration models allow for the estimation of the healing fraction, which represents a portion of the population immune to the event of interest. Here we address classical and Bayesian estimation based on mixture models and promotion time models, using different distributions (exponential, Weibull and Pareto) to model failure time. The database used to illustrate the implementations is described in Kersey et al. (1987) and it consists of a group of leukemia patients who underwent a certain type of transplant. The specific implementations used were numeric optimization by BFGS as implemented in R (base::optim), Laplace approximation (own implementation) and Gibbs sampling as implemented in Winbugs. We describe the main features of the models used, the estimation methods and the computational aspects. We also discuss how different prior information can affect the Bayesian estimates

Estimação de parâmetros genéticos para resistência à infecção por IMNV em camarões Litopenaeus vannamei por meio de análise de sobrevivência

The main specie of marine shrimp raised at Brazil and in the world is Litopenaeus vannamei, which had arrived in Brazil in the `80s. However, the entry of infectious myonecrosis virus (IMNV), causing the infectious myonecrosis disease in marine shrimps, brought economic losses to the national shrimp farming, with up to 70% of mortality in the shrimp production. In this way, the objective was to evaluate the survival of shrimps Litopenaeus vannamei infected with IMNV using the non parametric estimator of Kaplan-Meier and a model of frailty for grouped data. It were conducted three tests of viral challenges lasting 20 days each, at different periods of the year, keeping the parameters of pH, temperature, oxygen and ammonia monitored daily. It was evaluated 60 full-sib families of L. vannamei infected by IMNV in each viral challenge. The confirmation of the infection by IMNV was performed using the technique of PCR in real time through Sybr Green dye. Using the Kaplan-Meier estimator it was possible to detect significant differences (p <0.0001) between the survival curves of families and tanks and also in the joint analysis between viral challenges. It were estimated in each challenge, genetic parameters such as genetic value of family, it`s respective rate risk (frailty), and heritability in the logarithmic scale through the frailty model for grouped data. The heritability estimates were respectively 0.59; 0.36; and 0.59 in the viral challenges 1; 2; and 3, and it was also possible to identify families that have lower and higher rates of risk for the disease. These results can be used for selecting families more resistant to the IMNV infection and to include characteristic of disease resistance in L. vannamei into the genetic improvement programs

Avaliação genética da eficiência reprodutiva em vacas pardo-suíças por meio da análise de sobrevivência

Among the traits of economic importance to dairy cattle livestock those related to sexual precocity and longevity of the herd are essential to the success of the activity, because the stayability time of a cow in a herd is determined by their productive and reproductive lives. In Brazil, there are few studies about the reproductive efficiency of Swiss-Brown cows and no study was found using the methodology of survival analysis applied to this breed. Thus, in the first chapter of this study, the age at first calving from Swiss-Brown heifers was analyzed as the time until the event by the nonparametric method of Kaplan-Meier and the gamma shared frailty model, under the survival analysis methodology. Survival and hazard rate curves associated with this event were estimated and identified the influence of covariates on such time. The mean and median times at the first calving were 987.77 and 1,003 days, respectively, and significant covariates by the Log-Rank test, through Kaplan-Meier analysis, were birth season, calving year, sire (cow s father) and calving season. In the analysis by frailty model, the breeding values and the frailties of the sires (fathers) for the calving were predicted modeling the risk function of each cow as a function of the birth season as fixed covariate and sire as random covariate. The frailty followed the gamma distribution. Sires with high and positive breeding values possess high frailties, what means shorter survival time of their daughters to the event, i.e., reduction in the age at first calving of them. The second chapter aimed to evaluate the longevity of dairy cows using the nonparametric Kaplan-Meier and the Cox and Weibull proportional hazards models. It were simulated 10,000 records of the longevity trait from Brown-Swiss cows involving their respective times until the occurrence of five consecutive calvings (event), considered here as typical of a long-lived cow. The covariates considered in the database were age at first calving, herd and sire (cow s father). All covariates had influence on the longevity of cows by Log-Rank and Wilcoxon tests. The mean and median times to the occurrence of the event were 2,436.285 and 2,437 days, respectively. Sires that have higher breeding values also have a greater risk of that their daughters reach the five consecutive calvings until 84 months

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

Controle adaptativo por modelo de referencia e estrutura variável discreto no tempo

With the technology progess, embedded systems using adaptive techniques are being used frequently. One of these techniques is the Variable Structure Model- Reference Adaptive Control (VS-MRAC). The implementation of this technique in embedded systems, requires consideration of a sampling period which if not taken into consideration, can adversely affect system performance and even takes the system to instability. This work proposes a stability analysis of a discrete-time VS-MRAC accomplished for SISO linear time-invariant plants with relative degree one. The aim is to analyse the in uence of the sampling period in the system performance and the relation of this period with the chattering and system instability

Testes em modelos weibull na forma estendida de Marshall-Olkin

In survival analysis, the response is usually the time until the occurrence of an event of interest, called failure time. The main characteristic of survival data is the presence of censoring which is a partial observation of response. Associated with this information, some models occupy an important position by properly fit several practical situations, among which we can mention the Weibull model. Marshall-Olkin extended form distributions other a basic generalization that enables greater exibility in adjusting lifetime data. This paper presents a simulation study that compares the gradient test and the likelihood ratio test using the Marshall-Olkin extended form Weibull distribution. As a result, there is only a small advantage for the likelihood ratio test

Modelo de tempo de falha acelerado com fração de cura : uma abordagem unificada

In this work we study the accelerated failure-time generalized Gamma regression models with a unified approach. The models attempt to estimate simultaneously the effects of covariates on the acceleration/deceleration of the timing of a given event and the surviving fraction. The method is implemented in the free statistical software R. Finally the model is applied to a real dataset referring to the time until the return of the disease in patients diagnosed with breast cancer

Testes de hipóteses em modelos de sobrevivência com Fração de cura

Survival models deals with the modeling of time to event data. However in some situations part of the population may be no longer subject to the event. Models that take this fact into account are called cure rate models. There are few studies about hypothesis tests in cure rate models. Recently a new test statistic, the gradient statistic, has been proposed. It shares the same asymptotic properties with the classic large sample tests, the likelihood ratio, score and Wald tests. Some simulation studies have been carried out to explore the behavior of the gradient statistic in fi nite samples and compare it with the classic statistics in diff erent models. The main objective of this work is to study and compare the performance of gradient test and likelihood ratio test in cure rate models. We first describe the models and present the main asymptotic properties of the tests. We perform a simulation study based on the promotion time model with Weibull distribution to assess the performance of the tests in finite samples. An application is presented to illustrate the studied concepts