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Published in A Vasuki, Nature-Inspired Optimization Algorithms, 2020
Ackley functionf(X)=−20exp[−151d∑i=1dxi2]−exp[1d∑i=1dcos(2πxi)]+20+e
Spiral Dynamics Algorithms
Published in Nazmul Siddique, Hojjat Adeli, Nature-Inspired Computing, 2017
To investigate and verify the search performance and identify the parameter properties of SpDO algorithm, SpDO algorithm has been applied, firstly, to a number of standard benchmark functions and then to some industrial and real-world problems. The functions such as (i) Rosenbrock function, (ii) 2n minima, (iii) Rastrigin function, (iv) Schwefel function, (v) Griewank function, (vi) Sphere function, and (vii) Ackley function are benchmark functions commonly used to verify optimization problems. These functions are defined in the following.
Synthesis of Concentric Circular Antenna Array Using Whale Optimization Algorithm
Published in IETE Journal of Research, 2022
Krishanu Kundu, Rajesh Bera, Narendra Nath Pathak
The Ackley function (non-convex in nature) is one of the widely used bench mark function employed for testing the functionality of optimization algorithms. The Ackley function was presented by David Ackley in the year of 1987 at his PhD dissertation. In its two-dimensional form, the Ackley function is categorized using a nearly flat outer section and at the same time having a hefty hole at the center. Equation (10) the mathematical representation of the Ackley function suggested variable standards are as follows: a = 20, b = 0.2, and c = 2π. Mostly the Ackley function is estimated over the hypercube xi ∈ [−32.768, 32.768], for all i = 1, … , d, besides it may be constrained to a smaller domain also. Its global optimum point is at
Parameter Identification of Single-Phase Inverter Based on Improved Moth Flame Optimization Algorithm
Published in Electric Power Components and Systems, 2019
Zhongqiang Wu, Dandan Shen, Mengyao Shang, Songqi Qi
Among them, The Schwefel 1.2 and Rosenbrock function are unimodal functions. The global optimal point of the Rosenbrock function is located in a smooth, narrow parabolic valley. Because the information provided by the function for the optimization algorithm is limited, it is difficult to identify the search direction and find the optimal solution. Rastrigin is a function of multiple local optimum value. The peak appears to be undulating and erratic, so it is difficult to search for the global optimal value. Griewangk function is a typical example of non-linear multimodal function. It is usually considered as a complex problem because its extensive search spaces and multiple extremes. Penalized function is a nonlinear multi-valued function with strong oscillations. There are many local extreme values. Ackley function has multiple local minima, and the corresponding abscissas are in the neighborhood of each other.
Parameters optimisation on active disturbance rejection control of a bearingless induction motor
Published in International Journal of Electronics, 2022
Guangxin Wang, Zebin Yang, Xiaodong Sun, Qifeng Ding, Wenxin Fang
For example, the Ackley function is a classical complex optimisation problem with multiple local extremums, which can effectively verify the optimisation ability of the algorithm. The global optimum of the Rosenbrock function is located in a narrow and smooth parabolic valley. The information obtained in the process of finding the optimal solution is very little, and the difficulty of finding the global optimal solution is huge, which is usually used to verify the efficiency of the algorithm. The Griewank function is a univariate multi-peaked function with severe effects and significant correlation between the variables. The Rastrigin function has a wide search space and multiple local extremum points, which makes it difficult to optimise.