Contributions to Dynamic Analysis of Differential Evolution Algorithms.

The Differential Evolution (DE) algorithm is one of the most successful evolutionary computation techniques. However, its structure is not trivially translatable in terms of mathematical transformations that describe its population dynamics. In this work, analytical expressions are developed for the probability of enhancement of individuals after each application of a mutation operator followed by a crossover operation, assuming a population distributed radially around the optimum for the sphere objective function, considering the DE/rand/1/bin and the DE/rand/1/exp algorithm versions. These expressions are validated by numerical experiments. Considering quadratic functions given by f(x)=xTDTDx and populations distributed according to the linear transformation D-1 of a radially distributed population, it is also shown that the expressions still hold in the cases when f(x) is separable (D is diagonal) and when D is any nonsingular matrix and the crossover rate is Cr=1.0. The expressions are employed for the analysis of DE population dynamics. The analysis is extended to more complex situations, reaching rather precise predictions of the effect of problem dimension and of the choice of algorithm parameters.

Application of Optimal Control of Infectious Diseases in a Model-Free Scenario.

Optimal control for infectious diseases has received increasing attention over the past few decades. In general, a combination of cost state variables and control effort have been applied as cost indices. Many important results have been reported. Nevertheless, it seems that the interpretation of the optimal control law for an epidemic system has received less attention. In this paper, we have applied Pontryagin's maximum principle to develop an optimal control law to minimize the number of infected individuals and the vaccination rate. We have adopted the compartmental model SIR to test our technique. We have shown that the proposed control law can give some insights to develop a control strategy in a model-free scenario. Numerical examples show a reduction of 50% in the number of infected individuals when compared with constant vaccination. There is not always a prior knowledge of the number of susceptible, infected, and recovered individuals required to formulate and solve the optimal control problem. In a model-free scenario, a strategy based on the analytic function is proposed, where prior knowledge of the scenario is not necessary. This insight can also be useful after the development of a vaccine to COVID-19, since it shows that a fast and general cover of vaccine worldwide can minimize the number of infected, and consequently the number of deaths. The considered approach is capable of eradicating the disease faster than a constant vaccination control method.

Adjusting the Cut-Off and Maximum Pool Size in RT-qPCR Pool Testing for SARS-CoV-2.

Reverse transcription quantitative real-time polymerase chain reaction (RT-qPCR) to detect SARS-CoV-2 RNA is an essential test to monitor the occurrence of COVID-19. A methodology is proposed for the determination of maximum pool size and adjustments of cut-off values of cycle threshold (Ct in RT-qPCR pool testing, to compensate for the dilution caused by pooling. The trade-off between pool size and test sensitivity is stated explicitly. The procedure was designed to ensure that samples that would be detectable in individual testing remain detectable in pool testing. The proposed relaxation in cut-off is dependent on the pool size, allowing a relatively tight correction to avoid loss of detection of positive samples. The methodology was evaluated in a study of pool testing of adults attending a public emergency care unit, reference for COVID-19 in Belo Horizonte, Brazil, and presenting flu-like symptoms. Even samples on the edge of detectability in individual testing were detected correctly. The proposed procedure enhances the consistency of RT-qPCR pool testing by enforcing that the scales of detectability in pool processing and in individual sample processing are compatible. This may enhance the contribution of pool testing to large-scale testing for COVID-19.

Comparing community mobility reduction between first and second COVID-19 waves.

Background: In this paper, we conduct a mobility reduction rate comparison between the first and second COVID-19 waves in several localities from America and Europe using Google community mobility reports (CMR) data. Through multi-dimensional visualization, we are able to compare the reduction in mobility from the different lockdown periods for each locality selected, simultaneously considering multiple place categories provided in CMR. In addition, our analysis comprises a 56-day lockdown period for each locality and COVID-19 wave, which we analyze both as 56-day periods and as 14-day consecutive windows. Methods: We use locality-wise calibrated CMR data, which we process through seasonal-trend decomposition by LOESS (STL) to isolate trend from seasonal and noise effects. We scale trend data to draw Pareto-compliant conclusions using radar charts. For each temporal granularity considered, data for a given place category is aggregated using the area under the curve (AUC) approach. Results: In general, reduction rates observed during the first wave were much higher than during the second. Alarmingly, December holiday season mobility in some of the localities reached pre-pandemic levels for some of the place categories reported. Manaus was the only locality where second wave mobility was nearly as reduced as during the first wave, likely due to the P1 variant outbreak and oxygen supply crisis.

Data-driven inference for the spatial scan statistic.

BACKGROUND: Kulldorff's spatial scan statistic for aggregated area maps searches for clusters of cases without specifying their size (number of areas) or geographic location in advance. Their statistical significance is tested while adjusting for the multiple testing inherent in such a procedure. However, as is shown in this work, this adjustment is not done in an even manner for all possible cluster sizes. RESULTS: A modification is proposed to the usual inference test of the spatial scan statistic, incorporating additional information about the size of the most likely cluster found. A new interpretation of the results of the spatial scan statistic is done, posing a modified inference question: what is the probability that the null hypothesis is rejected for the original observed cases map with a most likely cluster of size k, taking into account only those most likely clusters of size k found under null hypothesis for comparison? This question is especially important when the p-value computed by the usual inference process is near the alpha significance level, regarding the correctness of the decision based in this inference. CONCLUSIONS: A practical procedure is provided to make more accurate inferences about the most likely cluster found by the spatial scan statistic.

Multi-objective evolutionary optimization of biological pest control with impulsive dynamics in soybean crops.

The biological pest control in agriculture, an environment-friendly practice, maintains the density of pests below an economic injury level by releasing a suitable quantity of their natural enemies. This work proposes a multi-objective numerical solution to biological pest control for soybean crops, considering both the cost of application of the control action and the cost of economic damages. The system model is nonlinear with impulsive control dynamics, in order to cope more effectively with the actual control action to be applied, which should be performed in a finite number of discrete time instants. The dynamic optimization problem is solved using the NSGA-II, a fast and trustworthy multi-objective genetic algorithm. The results suggest a dual pest control policy, in which the relative price of control action versus the associated additional harvest yield determines the usage of either a low control action strategy or a higher one.

The Q-norm complexity measure and the minimum gradient method: a novel approach to the machine learning structural risk minimization problem.

This paper presents a novel approach for dealing with the structural risk minimization (SRM) applied to a general setting of the machine learning problem. The formulation is based on the fundamental concept that supervised learning is a bi-objective optimization problem in which two conflicting objectives should be minimized. The objectives are related to the empirical training error and the machine complexity. In this paper, one general Q-norm method to compute the machine complexity is presented, and, as a particular practical case, the minimum gradient method (MGM) is derived relying on the definition of the fat-shattering dimension. A practical mechanism for parallel layer perceptron (PLP) network training, involving only quasi-convex functions, is generated using the aforementioned definitions. Experimental results on 15 different benchmarks are presented, which show the potential of the proposed ideas.

Local search with quadratic approximations into memetic algorithms for optimization with multiple criteria.

This paper proposes a local search optimizer that, employed as an additional operator in multiobjective evolutionary techniques, can help to find more precise estimates of the Pareto-optimal surface with a smaller cost of function evaluation. The new operator employs quadratic approximations of the objective functions and constraints, which are built using only the function samples already produced by the usual evolutionary algorithm function evaluations. The local search phase consists of solving the auxiliary multiobjective quadratic optimization problem defined from the quadratic approximations, scalarized via a goal attainment formulation using an LMI solver. As the determination of the new approximated solutions is performed without the need of any additional function evaluation, the proposed methodology is suitable for costly black-box optimization problems.