Improving air quality is an important environmental challenge of our time. Chile currently has one of the most stable and emerging economies in Latin America, where human impact on natural resources and air quality does not go unperceived. Santiago, the capital of Chile, is one of the cities in which particulate matter (PM) levels exceed national and international limits. Its location and climate cause critical conditions for human health when interaction with anthropogenic emissions is present. In this paper, we propose a predictive model based on bivariate regression to estimate PM levels, related to PM2.5 and PM10, simultaneously. Birnbaum-Saunders distributions are used in the joint modeling of real-world PM2.5 and PM10 data by considering as covariates some relevant meteorological variables employed in similar studies. The Mahalanobis distance is utilized to assess bivariate outliers and to detect suitability of the distributional assumption. In addition, we use the local influence technique for analyzing the impact of a perturbation on the overall estimation of model parameters. In the predictions, we check the categorization for the observed and predicted cases of the model according to the primary air quality regulations for PM.

The maximum diversity problem (MDP) aims to select a subset with a predetermined number of elements from a given set, maximizing the diversity among them. This NP-hard problem requires efficient algorithms that can generate high-quality solutions within reasonable computational time. In this study, we propose a novel approach that combines the biased random-key genetic algorithm (BRKGA) with local search to tackle the MDP. Our computational study utilizes a comprehensive set of MDPLib instances, and demonstrates the superior average performance of our proposed algorithm compared to existing literature results. The MDP has a wide range of practical applications, including biology, ecology, and management. We provide future research directions for improving the algorithm’s performance and exploring its applicability in real-world scenarios.

Beta regressions describe the relationship between a response that assumes values in the zero-one range and covariates. These regressions are used for modeling rates, ratios, and proportions. We study computational aspects related to parameter estimation of a class of beta regressions for the mean with fixed precision by maximizing the log-likelihood function with heuristics and other optimization methods. Through Monte Carlo simulations, we analyze the behavior of ten algorithms, where four of them present satisfactory results. These are the differential evolutionary, simulated annealing, stochastic ranking evolutionary, and controlled random search algorithms, with the latter one having the best performance. Using the four algorithms and the optim function of R, we study sets of parameters that are hard to be estimated. We detect that this function fails in most cases, but when it is successful, it is more accurate and faster than the others. The annealing algorithm obtains satisfactory estimates in viable time with few failures so that we recommend its use when the optim function fails.