Chaotic Optimization Method Research Articles

Three Chaotic Strategies for Enhancing the Self-Adaptive Harris Hawk Optimization Algorithm for Global Optimization

Harris Hawk Optimization (HHO) is a well-known nature-inspired metaheuristic model inspired by the distinctive foraging strategy and cooperative behavior of Harris Hawks. As with numerous other algorithms, HHO is susceptible to getting stuck in local optima and has a sluggish convergence rate. Several techniques have been proposed in the literature to improve the performance of metaheuristic algorithms (MAs) and to tackle their limitations. Chaos optimization strategies have been proposed for many years to enhance MAs. There are four distinct categories of Chaos strategies, including chaotic mapped initialization, randomness, iterations, and controlled parameters. This paper introduces SHHOIRC, a novel hybrid algorithm designed to enhance the efficiency of HHO. Self-adaptive Harris Hawk Optimization using three chaotic optimization methods (SHHOIRC) is the proposed algorithm. On 16 well-known benchmark functions, the proposed hybrid algorithm, authentic HHO, and five HHO variants are evaluated. The computational results and statistical analysis demonstrate that SHHOIRC exhibits notable similarities to other previously published algorithms. The proposed algorithm outperformed the other algorithms by 81.25%, compared to 18.75% for the prior algorithms, by obtaining the best average solutions for 13 benchmark functions. Furthermore, the proposed algorithm is tested on a real-life problem, which is the maximum coverage problem of Wireless Sensor Networks (WSNs), and compared with pure HHO, and two well-known algorithms, Grey Wolf Optimization (GWO) and Whale Optimization Algorithm (WOA). For the maximum coverage experiments, the proposed algorithm demonstrated superior performance, surpassing other algorithms by obtaining the best coverage rates of 95.4375% and 97.125% for experiments 1 and 2, respectively.

A chaotic optimization method based on logistic-sine map for numerical function optimization

Meta-heuristic optimization algorithms have been used to solve mathematically unidentifiable problems. The main purpose of the optimization methods on problem-solving is to choose the best solution in predefined conditions. To increase performance of the optimization methods, chaotic maps for instance Logistic, Singer, Sine, Tent, Chebyshev, Circle have been widely used in the literature. However, hybrid 1D chaotic maps have higher performance than the 1D chaotic maps. The hybrid chaotic maps have not been used in the optimization process. In this article, 1D hybrid chaotic map (logistic-sine map)-based novel swarm optimization method is proposed to achieve higher numerical results than other optimization methods. Logistic-sine map has good statistical result, and this advantage is used directly to calculate global optimum value in this study. The proposed algorithm is a swarm-based optimization algorithm, and the seed value of the logistic-sine map is generated from local best solutions to reach global optimum. In order to test the proposed hybrid chaotic map-based optimization method, widely used numerical benchmark functions are chosen. The proposed chaotic optimization method is also tested on compression spring design problem. Results and comparisons clearly show that the proposed chaotic optimization method is successful.

Parameter identification of Jiles–Atherton model using the chaotic optimization method

PurposeThe purpose of this paper is to propose a chaotic optimization method for identifying the parameters of the Jiles–Atherton (J-A) hysteresis model.Design/methodology/approachThe J-A model has five parameters which are assigned with physical meaning and whose determination is demanding. To determine these parameters, the fitness function, which represents the difference between the measured and the modeled hysteresis loop, is formed. Optimal parameter values are the values that minimize the fitness function.FindingsThe parameters of J-A model for three magnetic materials are determined. The model with the optimal parameters is validated using measured data and comparison with particle swarm optimization algorithm, genetic algorithm, pattern search and simulated annealing algorithm. The results show that the proposed method provides better agreement between measured and modeled hysteresis loop than other methods used for comparison. The proposed method is also suitable for simultaneous optimization of multiple hysteresis loops.Originality/valueChaotic optimization method is implemented for the first time for J-A model parameter identification. Numerical comparisons with results obtained with other optimization algorithms demonstrate that this method is a suitable alternative in parameters identification of J-A hysteresis model. Furthermore, this method is easy to implement and set up.

Chaotic Self-Tuning PID Controller Based on Fuzzy Wavelet Neural Network Model

PID controller has been quite successful when its parameters are tuned properly. However, it fails in varying situations. This is even more critical where the system is not known. In this paper, after illustrating the capability of fuzzy wavelet neural network (FWNN) in modeling of nonlinear systems, a self-tuning PID controller based on this model has been designed. The auto-tuner effectively handles the limitation of PID controller in unpredictable conditions such as environmental changes. Chaotic optimization method which is a robust algorithm of escaping from local minimum is applied for tuning of the controller parameters. This supports finding optimal values of controller parameters in a short time which enables online implementation. Unlike most of the researches in this area, the tuning rules could be begun without any trial and error. Since it contains no extra parameters, it has the feature of simplicity in the tuning. The proposed method with few parameters has the ability to increase the speed of tracking with very little steady-state error. The capability of FWNN in the modeling of nonlinear systems with a few rules and susceptibility of the proposed controller will be shown by simulation.

A novel binary bat algorithm with chaos and Doppler effect in echoes for analog fault diagnosis

A novel modified binary bat algorithm (MBBA) with chaos and Doppler effect in echoes is presented in this paper to deal with the fault diagnosis problem of analog circuits with tolerance. The proposed method focuses on further mimicking the bats' behaviors and improving the binary bat algorithm (BBA) in view of biology. The proposed algorithm utilizes the bats' self-adaptive compensation for Doppler effect in echoes and the chaotic optimization method to improve the BBA. The elitist strategy is also used to store all the possible global best solutions, which will provide us with more possible choices in practice. Since single feature extraction method has limitations during fault diagnosis of analog circuits with tolerance, several kinds of feature extraction methods are used together to build a big feature set firstly in our method, and then, the new proposed MBBA is used to select the optimal feature subset simultaneously optimize the classifier parameters for the analog fault diagnosis. Three analog circuits' examples are given to demonstrate the effectiveness and generalization ability of our method, and other methods are also used to do comparisons. The results indicate that combining different kinds of feature extraction method together to optimally select the feature subset simultaneously optimize the classifier parameters by MBBA can obtain better performance in dealing with analog fault diagnosis problems, and our proposed method provides a better tradeoff between fault diagnosis accuracy and total cost, which is superior to other methods. Therefore, it is an effective method for analog fault diagnosis and has broad application prospects in practice.

A novel collaborative optimization algorithm in solving complex optimization problems

To overcome the deficiencies of weak local search ability in genetic algorithms (GA) and slow global convergence speed in ant colony optimization (ACO) algorithm in solving complex optimization problems, the chaotic optimization method, multi-population collaborative strategy and adaptive control parameters are introduced into the GA and ACO algorithm to propose a genetic and ant colony adaptive collaborative optimization (MGACACO) algorithm for solving complex optimization problems. The proposed MGACACO algorithm makes use of the exploration capability of GA and stochastic capability of ACO algorithm. In the proposed MGACACO algorithm, the multi-population strategy is used to realize the information exchange and cooperation among the various populations. The chaotic optimization method is used to overcome long search time, avoid falling into the local extremum and improve the search accuracy. The adaptive control parameters is used to make relatively uniform pheromone distribution, effectively solve the contradiction between expanding search and finding optimal solution. The collaborative strategy is used to dynamically balance the global ability and local search ability, and improve the convergence speed. Finally, various scale TSP are selected to verify the effectiveness of the proposed MGACACO algorithm. The experiment results show that the proposed MGACACO algorithm can avoid falling into the local extremum, and takes on better search precision and faster convergence speed.

Application of Chaotic Time-Series Optimization Algorithm in Solving the Parameters of Leakage Aquifer

Applied the chaotic time-series optimization algorithm to solve hydrogeological parameters through analysis the pumping test data of the first type leakage aquifer, then explored the influence of the initial value of aquifer parameters and other factors on the convergence and results of the algorithm. The results shown that: ①chaotic time-series optimization algorithm could be effectively applied to the calculation problem of aquifer parameters; ②the initial value of the coefficient of storage and conductivity don’t have too much obvious effect on the search and results of the algorithm; ③The upper limit of algorithm had no obvious effect on the search ability but reduce the accuracy of results. Compared with other methods, the chaotic optimization method had such advantages as simple in principle of algorithm, easy to make program and to conduct, and the precision of aquifer parameters calculated was not affected by artificial subjective factors.

Optimization of clay material mixture ratio and filling process in gypsum mine goaf

Because there is neither waste rock nor mill tailings in the gypsum mine, and the buildings on the goaf of gypsum mine are needed to be protected, the research proposed the scheme of the clay filling technology. Gypsum, cement, lime and water glass were used as adhesive, and the strength of different material ratios were investigated in this study. The influence factors of clay strength were obtained in the order of cement, gypsum, water glass and lime. The results show that the cement content is the determinant influence factor, and gypsum has positive effects, while the water glass can enhance both clay strength and the fluidity of the filing slurry. Furthermore, combining chaotic optimization method with neural network, the optimal ratio of composite cementing agent was obtained. The results show that the optimal ratio of water glass, cement, lime and clay (in quality) is 1.17:6.74:4.17:87.92 in the process of bottom self-flow filling, while the optimal ratio is 1.78:9.58:4.71:83.93 for roof-contacted filling. A novel filling process to fill in gypsum mine goaf with clay is established. The engineering practice shows that the filling cost is low, thus, notable economic benefit is achieved.

Global optimization using a multipoint type quasi-chaotic optimization method

This paper proposes a new global optimization method called the multipoint type quasi-chaotic optimization method. In the proposed method, the simultaneous perturbation gradient approximation is introduced into a multipoint type chaotic optimization method in order to carry out optimization without gradient information. The multipoint type chaotic optimization method, which has been proposed recently, is a global optimization method for solving unconstrained optimization problems in which multiple search points which implement global searches driven by a chaotic gradient dynamic model are advected to their elite search points (best search points among the current search histories). The chaotic optimization method uses a gradient to drive search points. Hence, its application is restricted to a class of problems in which the gradient of the objective function can be computed. In this paper, the simultaneous perturbation gradient approximation is introduced into the multipoint type chaotic optimization method in order to approximate gradients so that the chaotic optimization method can be applied to a class of problems for which only the objective function values can be computed. Then, the effectiveness of the proposed method is confirmed through application to several unconstrained multi-peaked, noisy, or discontinuous optimization problems with 100 or more variables, comparing to other major meta-heuristics.

Chaotic Sequence Optimization Algorithm for Estimation of Aquifer Parameters from Data of Pumping Test

Abstract With chaotic sequence optimization algorithm,the function optimization problem for analyzing data pumping test conducted in aquifer to estimate such aquifer parameters as transmissivity and storage coefficient was to be solved. With such different key parameters of the algorithm as the number of coarse search loops, the length of chaotic sequence and the initial guess value ranges of transmissivity of aquifer, simulation experiment was conducted to explore the effect of these key parameters on the convergence of the algorithm. The results show: 1) that chaotic sequence optimization algorithm may be successfully applied to solve the function optimization problem to analyses pumping test data for determining aquifer parameters of aquifer, 2) that the longer sequence length of chaotic sequence and the larger number of coarse search loops may not effectively improve the convergence of algorithm, 3) and that the range of initial guess value of transmissivity of aquifer may brings some influence on the convergence of algorithm, but does not affect the final result of computation. Compared with current methods, the chaotic sequence optimization method is of such advantages as that the principle of algorithm is easy to understand, the procedure of the algorithm is easier to be programmed and conducted,and the precision of aquifer parameters calculated may not be affected by artificial subjective factors. Finally, it is necessary to point out that this method is of wider scope of application.

Fuzzy system identification via chaotic ant swarm

In this paper, we introduce a chaotic optimization method, called CAS (chaotic ant swarm), to solve the problem of designing a fuzzy system to identify dynamical systems. The position vector of each ant in the CAS algorithm corresponds to the parameter vector of the selected fuzzy system. At each learning time step, the CAS algorithm is iterated to give the optimal parameters of fuzzy systems based on the fitness theory. Then the corresponding CAS-designed fuzzy system is built and applied to the identification of the unknown nonlinear dynamical systems. Numerical simulation results are provided to show the effectiveness and feasibility of the developed CAS-designed fuzzy system.

Chaotic Optimization Method and Its Advances

Chaotic Optimization Method and Its Advances

目的関数変換による分岐調整を利用したカオス最適化手法：大域的最適化手法「水抜き法」の提案

目的関数変換による分岐調整を利用したカオス最適化手法：大域的最適化手法「水抜き法」の提案

Chaotic optimization method combined with coordinate transformation

We propose a nonlinear optimization method based on a combination of chaotic dynamics and a coordinate transformation. The coordinate transformation serves to make small eigenvalues of the curvature matrix of the objective function, which is defined for each optimization problem. Then, the objective function becomes flat so that the chaotic dynamics is able to search for possible solutions over a wide domain. We apply our method to a chaotic version of the doubly constrained network model (DCN) that solves quadratic assignment problems. As a result, our new method achieves solution improvements. © 2000 Scripta Technica, Electron Comm Jpn Pt 3, 84(2): 12–20, 2001