A Global Optimization Algorithm for Unconstrained Non-linear Optimization Problems Using Chaotic Neuron Map and Golden Number

This paper presents aninnovative global multi-variable optimization algorithm using one of the best chaotic sequences, the neuron map, a description of which is also provided in the paper. The algorithm uses neuron map in the first stage to move near the global minimum point, as well as in each iteration of the second stage of local search that is done using the N-dimensional golden section search algorithm. The generation and mapping of the neuron variables to the optimization variables along with the stagewise search for the global minimum is explained conscientiously in the work. Numerical results on some benchmark functions and the comparison with a latest state-of-the-art algorithm ispresented in order to demonstrate the efficiency of the proposed algorithm.

Quantification of thermal energy generation in annular hyperbolic porous-finned heat sinks using inverse optimization

The present paper introduces an accurate numerical procedure to assess the internal thermal energy generation in an annular porous-finned heat sink from the sole assessment of surface temperature profile using the golden section search technique. All possible heat transfer modes and temperature dependence of all thermal parameters are accounted for in the present nonlinear model. At first, the direct problem is numerically solved using the Runge–Kutta method, whereas for predicting the prevailing heat generation within a given generalized fin domain an inverse method is used with the aid of the golden section search technique. After simplifications, the proposed scheme is credibly verified with other methodologies reported in the existing literature. Numerical predictions are performed under different levels of Gaussian noise from which accurate reconstructions are observed for measurement error up to 20%. The sensitivity study deciphers that the surface temperature field in itself is a strong function of the surface porosity, and the same is controlled through a joint trade-off among heat generation and other thermo-geometrical parameters. The present results acquired from the golden section search technique-assisted inverse method are proposed to be suitable for designing effective and robust porous fin heat sinks in order to deliver safe and enhanced heat transfer along with significant weight reduction with respect to the conventionally used systems. The present inverse estimation technique is proposed to be robust as it can be easily tailored to analyse all possible geometries manufactured from any material in a more accurate manner by taking into account all feasible heat transfer modes.

Generalized Fibonacci Search Method in One-Dimensional Unconstrained Non-Linear Optimization

In this paper, we develop a generalized Fibonacci search method for one-dimensional unconstrained non-linear optimization of unimodal functions. This method uses the idea of the “ratio length of 1” from the golden section search. Our method takes successive lower Fibonacci numbers as the initial ratio and does not specify beforehand, the number of iterations to be used. We evaluated the method using Microsoft Excel with nine one-dimensional benchmark functions. We found that our generalized Fibonacci search method out-performed the golden section and other Fibonacci-type search methods such as the Fibonacci, Lucas and Pell approaches.

GOLDEN EXPONENTIAL SMOOTHING: A SELF-ADJUSTED METHOD FOR IDENTIFYING OPTIMUM ALPHA

The conventional double exponential smoothing is a forecasting method that troubles the forecaster with a tremendous choice of its parameter, alpha. The choice of alpha would greatly influence the accuracy of prediction. In this paper, an integrated forecasting method named Golden Exponential Smoothing (GES) was proposed to solve the problem. The conventional method was reformed and interposed with golden section search such that an optimum alpha which minimizes the errors of forecasting could be identified in the algorithm training process. Numerical simulations of four sets of times series data were employed to test the efficiency of GES model. The findings show that the GES model was self-adjusted according to the situation and converged fast in the algorithm training process. The optimum alpha, which was identified from the algorithm training stage, demonstrated good performance in the stage of Model Testing and Usage.

Image-Based Feedback Control for a Coaxial Spray

Optimization of jet engine sprays has the potential to improve efficiency and reduce environmental impact. Sprays can be continually optimized in multivariate scenarios using real-time feedback control, but a method of controlling the sprays based on physical properties must first be established. In this study, a spray controller was developed to optimize the spray angle obtained from shadowgraphs, with the assumption that the largest angle is desired. The spray angle was used as an example, as it is a physically important parameter which is easily found through shadowgraph imaging. Varying ratios of swirled air to straight air, determined by the image-based feedback controller were introduced into the air portion of a coaxial airblast nozzle while keeping the total air flow rate constant. A golden section search converged on the swirled air ratio that provided the largest angle and was validated from the distribution of spray angle versus swirled air ratio. The ratio that produced a spray with the greatest angle of 25.8 ± 2 deg was found at a swirled air ratio of 0.66 ± 0.03 for a spray with a momentum ratio of 6. The successful design and implementation of this image-based feedback controller is intended to provide a foundation for developing real-time active feedback controllers for sprays.