Optimal correction of infeasible equations system as Ax + B|x|= b using ℓ p-norm regularization

Optimal correction of an infeasible equations system as Ax + B|x|= b leads into a non-convex fractional problem. In this paper, a regularization method(ℓp-norm, 0 < p < 1), is presented to solve mentioned fractional problem. In this method, the obtained problem can be formulated as a non-convex and nonsmooth optimization problem which is not Lipschitz. The objective function of this problem can be decomposed as a difference of convex functions (DC). For this reason, we use a special smoothing technique based on DC programming. The numerical results obtained for generated problem show high performance and the effectiveness of the proposed method.

Forecasting Malaysian Ringgit Using Exponential Smoothing Techniques

Forecasting the foreign currency exchange is a challenging task since it is influenced by political, economic and psychological factors. This paper focuses on the forecasting Malaysian Ringgit (MYR) exchange rate against the United States Dollar (USD) using Exponential Smoothing Techniques which are Single Exponential Smoothing, Double Exponential Smoothing, and Holt’s method. The objectives of this paper are to identify the best Exponential Smoothing Technique that describes MYR for 5 years period and to forecast MYR 12 months ahead by using the best Exponential Smoothing Technique. The comparison between these techniques is also made and the best one will be selected to forecast the MYR exchange rate against USD. The result showed that Holt’s method has the smallest value of error measure which depending on the Mean Square Error (MSE) and Mean Absolute Percentage Error (MAPE) for the evaluation part. The MSE is 1.43915x10-14 and MAPE is 2.5413 x 10-6. Meanwhile, the forecast value of MYR in August 2019 is RM 4.30226.

A Hybrid Parallel Harris Hawks Optimization Algorithm for Reusable Launch Vehicle Reentry Trajectory Optimization With No-fly Zones

Reentry trajectory optimization is a critical optimal control problem for reusable launch vehicle (RLV) with highly nonlinear dynamic characteristics and complex constraints. In this paper, a hybrid parallel harris hawks optimization (HPHHO) algorithm is proposed to address the problem. HPHHO aims to enhance the performance of existing harris hawks optimization (HHO) algorithm by three strategies including oppositional learning, smoothing technique and parallel optimization mechanism. At the beginning of each iteration, the opposite population is calculated from the current population by the oppositional learning strategy. Following that, the individuals in the two populations are arranged in ascending order on the basis of the fitness function values, and the top half of the resulting population is selected as the initial population. The selected initial population is divided into two equal subpopulations which are assigned to the differential evolution and the HHO algorithm, respectively. The both algorithms operate in parallel to search and update the solutions of each subpopulation simultaneously. Then the solutions are smoothed for each iteration by the smoothing technique to reduce fluctuations. As a result, the optimal solution obtained by the parallel optimization mechanism avoids falling into local optima. The performance of HPHHO is evaluated by 4 CEC 2005 benchmark functions and 3 constrained continuous optimal control problems, showing better efficiency and robustness in terms of performance metrics, convergence rate and stability. Finally, the simulation results show that the proposed algorithm is very effective, practical and feasible in solving the RLV reentry trajectory optimization problem.

A Comparative Study of Nearest Neighbor Regression and Nadaraya Watson Regression

Two non-parametric statistical methods are studied in this work. These are the nearest neighbor regression and the Nadaraya Watson kernel smoothing technique. We have proven that under a precise circumstance, the nearest neighborhood estimator and the Nadaraya Watson smoothing produce a smoothed data with a same error level, which means they have the same performance. Another result of the paper is that nearest neighborhood estimator performs better locally, but it graphically shows a weakness point when a large data set is considered on a global scale.

Discrete Wavelet Transform for the Real-Time Smoothing of Wind Turbine Power Using Li-Ion Batteries

Energy Storage Systems (EES) are key to further increase the penetration in energy grids of intermittent renewable energy sources, such as wind, by smoothing out power fluctuations. In order this to be economically feasible; however, the ESS need to be sized correctly and managed efficiently. In the study, the use of discrete wavelet transform (Daubechies Db4) to decompose the power output of utility-scale wind turbines into high and low-frequency components, with the objective of smoothing wind turbine power output, is discussed and applied to four-year Supervisory Control And Data Acquisition (SCADA) real data from multi-MW, on-shore wind turbines provided by the industrial partner. Two main research requests were tackled: first, the effectiveness of the discrete wavelet transform for the correct sizing and management of the battery (Li-Ion type) storage was assessed in comparison to more traditional approaches such as a simple moving average and a direct use of the battery in response to excessive power fluctuations. The performance of different storage designs was compared, in terms of abatement of ramp rate violations, depending on the power smoothing technique applied. Results show that the wavelet transform leads to a more efficient battery use, characterized by lower variation of the averaged state-of-charge, and in turn to the need for a lower battery capacity, which can be translated into a cost reduction (up to −28%). The second research objective was to prove that the wavelet-based power smoothing technique has superior performance for the real-time control of a wind park. To this end, a simple procedure is proposed to generate a suitable moving window centered on the actual sample in which the wavelet transform can be applied. The power-smoothing performance of the method was tested on the same time series data, showing again that the discrete wavelet transform represents a superior solution in comparison to conventional approaches.