Chaotic gravitational constants for the gravitational search algorithm
01 Apr 2017-Vol. 53, pp 407-419
TL;DR: Ten chaotic maps are embedded into the gravitational constant of the recently proposed population-based meta-heuristic algorithm called Gravitational Search Algorithm (GSA) and it is demonstrated that sinusoidal map is the best map for improving the performance of GSA significantly.
Abstract: Display Omitted Chaotic maps have been embedded into Gravitational Search Algorithms (GSA) for the first time.The problem of trapping in local minima in GSA has been improved by the chaotic maps.The convergence rate of GSA has been improved.The statistical test allowed us to judge about the significance of the results.An adaptive normalization is proposed to smoothly transit from the exploration phase to the exploitation phase. In a population-based meta-heuristic, the search process is divided into two main phases: exploration versus exploitation. In the exploration phase, a random behavior is fruitful to explore the search space as extensive as possible. In contrast, a fast exploitation toward the promising regions is the main objective of the latter phase. It is really challenging to find a proper balance between these two phases because of the stochastic nature of population-based meta-heuristic algorithms. The literature shows that chaotic maps are able to improve both phases. This work embeds ten chaotic maps into the gravitational constant (G) of the recently proposed population-based meta-heuristic algorithm called Gravitational Search Algorithm (GSA). Also, an adaptive normalization method is proposed to transit from the exploration phase to the exploitation phase smoothly. As case studies, twelve shifted and biased benchmark functions evaluate the performance of the proposed chaos-based GSA algorithms in terms of exploration and exploitation. A statistical test called Wilcoxon rank-sum is done to judge about the significance of the results as well. The results demonstrate that sinusoidal map is the best map for improving the performance of GSA significantly.
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TL;DR: The most popular heuristic and meta-heuristic optimization algorithms are studied in this paper, and implementation of the optimization procedures for the solution of CHPED problem taking into account the objective functions and different constrains are discussed.
Abstract: Combined heat and power economic dispatch (CHPED) aims to minimize the operational cost of heat and power units satisfying several equality and inequality operational and power network constraints. The CHPED should be handled considering valve-point loading impact of the conventional thermal plants, power transmission losses of the system, generation capacity limits of the production units, and heat-power dependency constraints of the cogeneration units. Several conventional optimization algorithms have been firstly presented for providing the optimal production scheduling of power and heat generation units. Recently, experience-based algorithms, which are called heuristic and meta-heuristic optimization procedures, are introduced for solving the CHPED optimization problem. In this paper, a comprehensive review on application of heuristic optimization algorithms for the solution of CHPED problem is provided. In addition, the most popular heuristic and meta-heuristic optimization algorithms are studied in this paper, and implementation of the optimization procedures for the solution of CHPED problem taking into account the objective functions and different constrains are discussed. The main contributions of the reviewed papers are studied and discussed in details. Additionally, main considerations of equality and inequality constraints handled by different research studies are reported in this paper. Five test systems are considered for evaluating the performance of different optimization techniques. Optimal solutions obtained by employment of multiple heuristic and meta-heuristic optimization methods for test instances are demonstrated and the introduced methods are compared in terms of convergence speed, attained optimal solutions, and constrains. The best optimal solutions for five test systems are provided in terms of operational cost by employment of different optimization methods.
184 citations
TL;DR: A novel GSA-based algorithm with evolutionary crossover and mutation operators is proposed to deal with feature selection (FS) tasks and the extensive results and comparisons demonstrate the superiority of the proposed algorithm in solving FS problems.
165 citations
TL;DR: The numerical simulations of the proposed ChASO-FOPID and ASO-fOPID controllers for the dc motor speed control system demonstrated the superior performance of both the chaotic ASO and the original ASO, respectively.
Abstract: In this paper, atom search optimization (ASO) algorithm and a novel chaotic version of it [chaotic ASO (ChASO)] are proposed to determine the optimal parameters of the fractional-order proportional+integral+derivative (FOPID) controller for dc motor speed control. The ASO algorithm is simple and easy to implement, which mathematically models and mimics the atomic motion model in nature, and is developed to address a diverse set of optimization problems. The proposed ChASO algorithm, on the other hand, is based on logistic map chaotic sequences, which makes the original algorithm be able to escape from local minima stagnation and improve its convergence rate and resulting precision. First, the proposed ChASO algorithm is applied to six unimodal and multimodal benchmark optimization problems and the results are compared with other algorithms. Second, the proposed ChASO-FOPID, ASO-FOPID, and ASO-PID controllers are compared with GWO-FOPID, GWO-PID, IWO-PID, and SFS-PID controllers using the integral of time multiplied absolute error (ITAE) objective function for a fair comparison. Comparisons were also made for the integral of time multiplied squared error (ITSE) and Zwe-Lee Gaing's (ZLG) objective function as the most commonly used objective functions in the literature. Transient response analysis, frequency response (Bode) analysis, and robustness analysis were all carried out. The simulation results are promising and validate the effectiveness of the proposed approaches. The numerical simulations of the proposed ChASO-FOPID and ASO-FOPID controllers for the dc motor speed control system demonstrated the superior performance of both the chaotic ASO and the original ASO, respectively.
156 citations
Cites background from "Chaotic gravitational constants for..."
...In [35], ten chaotic maps, namely Chebyshev, circle, Gauss/mouse, iterative, logistic, piecewise, sine, singer, sinusoidal, and tent, are embedded into the gravitational constant of gravitational search algorithm (GSA), which improved the performance of the original GSA significantly....
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128 citations
01 Oct 2018
TL;DR: The results show that the proposed hybrid metaheuristic algorithms outperform the best existing techniques on the majority of case studies.
Abstract: Nowadays, operation managers usually need efficient supply chain networks including important design factors such as economic and social considerations The recent decade has seen a rapid development of controlling the uncertainty in supply chain configurations along with proposing novel solution approaches By investigating the related studies, this paper shows that most of the current studies consider the economic aspects and just a few works present the two-stage stochastic programming as well as social considerations to design a closed-loop supply chain network This motivated our attempts to consider economic and social aspects simultaneously by using the mentioned suppositions among the first studies Another main contribution of this paper is the hybridization and tuning of a number of recent algorithms to address the problem The results show that the proposed hybrid metaheuristic algorithms outperform the best existing techniques on the majority of case studies
121 citations
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TL;DR: A framework is developed to explore the connection between effective optimization algorithms and the problems they are solving and a number of "no free lunch" (NFL) theorems are presented which establish that for any algorithm, any elevated performance over one class of problems is offset by performance over another class.
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TL;DR: A new parameter, called inertia weight, is introduced into the original particle swarm optimizer, which resembles a school of flying birds since it adjusts its flying according to its own flying experience and its companions' flying experience.
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9,373 citations