This paper proposes a combined feedback and feed-forward control system to support the frequency regulation of multi-area interconnected hybrid microgrids considering renewable energy sources (RESs). The proposed control system is based on a fractional-order proportional-integral-derivative-accelerated (FOPIDA) controller in the feed-forward direction and a fractional-order integral-derivative with a low-pass filter compensator (FOIDN) controller in the feedback direction, referred to as a FOPIDA-FOIDN controller. Moreover, the parameters of the proposed FOPIDA-FOIDN controller (i.e., twelve parameters in each area) are optimally tuned using a proposed hybrid of two metaheuristic optimization algorithms, i.e., hybrid artificial gorilla troops optimizer (AGTO) and equilibrium optimizer (EO), and this hybrid is referred to as HGTOEO. The robustness and reliability of the proposed control system are validated by evaluating its performance in comparison to that of other counterparts’ controllers utilized in the literature, such as PID, FOPID, and tilt integral derivative (TID) controller, under the different operating conditions of the studied system. Furthermore, the proficiency of the proposed HGTOEO algorithm is checked against other powerful optimizers, such as the genetic algorithm, Jaya algorithm, improved Jaya algorithm, multi-verse optimizer, and cost-effective multi-verse optimizer, to optimally design the PID controller for the load frequency control of the studied two-area interconnected microgrid. The MATLAB simulation results demonstrate the viability and dependability of the proposed FOPIDA-FOIDN controller based on the HGTOEO algorithm under a variety of load perturbations and random production of RESs.

In this paper, we introduce the inverse exponentiated Lomax power series (IELoPS) class of distributions, obtained by compounding the inverse exponentiated Lomax and power series distributions. The IELoPS class contains some significant new flexible lifetime distributions that possess powerful physical explications applied in areas like industrial and biological studies. The IELoPS class comprises the inverse Lomax power series as a new subclass as well as several new flexible compounded lifetime distributions. For the proposed class, some characteristics and properties are derived such as hazard rate function, limiting behavior, quantile function, Lorenz and Bonferroni curves, mean residual life, mean inactivity time, and some measures of information. The methods of maximum likelihood and Bayesian estimations are used to estimate the model parameters of one optional model. The Bayesian estimators of parameters are discussed under squared error and linear exponential loss functions. The asymptotic confidence intervals, as well as Bayesian credible intervals, of parameters, are constructed. Simulations for a one‐selective model, say inverse exponentiated Lomax Poisson (IELoP) distribution, are designed to assess and compare different estimates. Results of the study emphasized the merit of produced estimates. In addition, they appeared the superiority of Bayesian estimate under regarded priors compared to the corresponding maximum likelihood estimate. Finally, we examine medical and reliability data to demonstrate the applicability, flexibility, and usefulness of IELoP distribution. For the suggested two real data sets, the IELoP distribution fits better than Kumaraswamy–Weibull, Poisson–Lomax, Poisson inverse Lomax, Weibull–Lomax, Gumbel–Lomax, odd Burr–Weibull–Poisson, and power Lomax–Poisson distributions.

A l’aube de la 5ème génération de la transformation digitale industrielle, le processus « Achat 5.0 » connait, lui aussi, une mutation profonde en passant d’abord par ses acheteurs, appelés « acheteurs augmentés ». Face aux défis de l’automatisation induite par cette transformation, les travaux s’accentuent et tentent de converger vers des techniques plus avancées de l’Intelligence Artificielle (IA) pour faire face au problème complexe de la sélection multifournisseurs. Les risques liés à la volatilité des fournisseurs, encore fragilisés par la crise pandémique COVID-19, ont fortement augmenté en conséquence. L’objectif de cet article est de palier à cette faiblesse. Il propose une nouvelle approche par hybridation d’analyse multicritères et des chat-bots dotés de capacité d’aversion au risque à l’aide de l’apprentissage par renforcement. Un cadre de validation d’un constructeur automobile Français nous sert de scénario préliminaire. Les premiers résultats sont prometteurs et nous encouragent à continuer dans la suite de ces travaux.