New extensions of Rayleigh distribution based on inverted-Weibull and Weibull distributions

The Rayleigh distribution was proposed in the fields of acoustics and optics by lord Rayleigh. It has wide applications in communication theory, such as description of instantaneous peak power of received radio signals, i.e. study of vibrations and waves. It has also been used for modeling of wave propagation, radiation, synthetic aperture radar images, and lifetime data in engineering and clinical studies. This work proposes two new extensions of the Rayleigh distribution, namely the Rayleigh inverted-Weibull (RIW) and the Rayleigh Weibull (RW) distributions. Several fundamental properties are derived in this study, these include reliability and hazard functions, moments, quantile function, random number generation, skewness, and kurtosis. The maximum likelihood estimators for the model parameters of the two proposed models are also derived along with the asymptotic confidence intervals. Two real data sets in communication systems and clinical trials are analyzed to illustrate the concept of the proposed extensions. The results demonstrated that the proposed extensions showed better fitting than other extensions and competing models

Selecting the best stochastic systems for large scale engineering problems

Selecting a subset of the best solutions among large-scale problems is an important area of research. When the alternative solutions are stochastic in nature, then it puts more burden on the problem. The objective of this paper is to select a set that is likely to contain the actual best solutions with high probability. If the selected set contains all the best solutions, then the selection is denoted as correct selection. We are interested in maximizing the probability of this selection; P(CS). In many cases, the available computation budget for simulating the solution set in order to maximize P(CS) is limited. Therefore, instead of distributing these computational efforts equally likely among the alternatives, the optimal computing budget allocation (OCBA) procedure came to put more effort on the solutions that have more impact on the selected set. In this paper, we derive formulas of how to distribute the available budget asymptotically to find the approximation of P(CS). We then present a procedure that uses OCBA with the ordinal optimization (OO) in order to select the set of best solutions. The properties and performance of the proposed procedure are illustrated through a numerical example. Overall results indicate that the procedure is able to select a subset of the best systems with high probability of correct selection using small number of simulation samples under different parameter settings

A Simulated Annealing Algorithm with Constant Temperature for Discrete Stochastic Optimization

We present a modification of the simulated annealing algorithm designed for solving discrete stochastic optimization problems. Like the original simulated annealing algorithm, our method has the hill climbing feature, so it can find global optimal solutions to discrete stochastic optimization problems with many local solutions. However, our method differs from the original simulated annealing algorithm in that it uses a constant (rather than decreasing) temperature. We consider two approaches for estimating the optimal solution. The first approach uses the number of visits the algorithm makes to the different states (divided by a normalizer) to estimate the optimal solution. The second approach uses the state that has the best average estimated objective function value as estimate of the optimal solution. We show that both variants of our method are guaranteed to converge almost surely to the set of global optimal solutions, and discuss how our work applies in the discrete deterministic optimization setting. We also show how both variants can be applied for solving discrete optimization problems when the objective function values are estimated using either transient or steady-state simulation. Finally, we include some encouraging numerical results documenting the behavior of the two variants of our algorithm when applied for solving two versions of a particular discrete stochastic optimization problem, and compare their performance with that of other variants of the simulated annealing algorithm designed for solving discrete stochastic optimization problems.global optimization, discrete parameters, simulated annealing, simulation optimization

Modelling and optimization of outpatient appointment scheduling

We consider the problem of appointment scheduling for outpatient departments in health care systems. The objective is to design an appointment system that minimizes the average waiting time per patient, while at the same time ensuring the effective use of resources, by maximizing doctor utilization and minimizing the average number of patients in the clinic. We model the appointment system problem as a multi-objective optimization problem with three objectives. Several new alternative appointment systems are considered, and the new systems are modelled and simulated using the software Arena. Subsequently, a new version of ranking and selection approaches is used to compare the alternative systems, by constructing a set of Pareto optimal solutions that consists of non-dominated systems with a predetermined level of confidence. Finally, we present the numerical results obtained by implementing the proposed procedure on an outpatient clinic, taking into account the no-show patients as well as the walk-in patients

An adaptive Monte Carlo integration algorithm with general division approach

We propose an adaptive Monte Carlo algorithm for estimating multidimensional integrals over a hyper-rectangular region. The algorithm uses iteratively the idea of separating the domain of integration into 2ssubregions. The proposed algorithm can be applied directly to estimate the integral using an efficient way of storage. We test the algorithm for estimating the value of a 30-dimensional integral using a two-division approach. The numerical results show that the proposed algorithm gives better results than using one-division approach

Optimization of Supercritical Carbon Dioxide Extraction of <i>Saussurea costus</i> Oil and Its Antimicrobial, Antioxidant, and Anticancer Activities

Saussurea costus is a medicinal plant with different bioactive compounds that have an essential role in biomedicine applications, especially in Arab nations. However, traditional extraction methods for oils can lead to the loss of some volatile and non-volatile oils. Therefore, this study aimed to optimize the supercritical fluid extraction (SFE) of oils from S. costus at pressures (10, 20, and 48 MPa). The results were investigated by GC/MS analysis. MTT, DPPH, and agar diffusion methods assessed the extracted oils’ anticancer, antioxidant, and antimicrobial action. GC/MS results showed that elevated pressure from 10 to 20 and 48 MPa led to the loss of some valuable compounds. In addition, the best IC50 values were recorded at 10 MPa on HCT, MCF-7, and HepG-2 cells at about 0.44, 0.46, and 0.74 μg/mL, respectively. In contrast, at 20 MPa, the IC50 values were about 2.33, 6.59, and 19.0 μg/mL, respectively, on HCT, MCF-7, and HepG-2 cells, followed by 48 MPa, about 36.02, 59.5, and 96.9 μg/mL. The oil extract at a pressure of 10 MPa contained much more of á-elemene, dihydro-à-ionone, patchoulene, á-maaliene, à-selinene, (-)-spathulenol, cedran-diol, 8S,13, elemol, eremanthin, á-guaiene, eudesmol, ç-gurjunenepoxide-(2), iso-velleral, and propanedioic acid and had a higher antioxidant activity (IC50 14.4 μg/mL) more than the oil extract at 20 and 48 MPa. In addition, the inhibitory activity of all extracts was higher than gentamicin against all tested bacteria. One of the more significant findings from this study is low pressure in SFE enhancement, the extraction of oils from S. costus, for the first time. As a result, the SFE is regarded as a good extraction technique since it is both quick and ecologically friendly. Furthermore, SFE at 10 MPa increased the production and quality of oils, with high antioxidant activity and a positive effect on cancer cells and pathogens