A modified butterfly optimization algorithm for mechanical design optimization problems

Arora, Sankalap; Singh, Satvir; Yetilmezsoy, Kaan

doi:10.1007/s40430-017-0927-1

Cited by 69 publications

(50 citation statements)

References 61 publications

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“…Table 3 Comparison of the proposed algorithm MICA with respect to OICA [19] , SAEA [9] , SMES [16] , RCEA [17] , ISEA [26] on 13 benchmark functions. "NA" presents not results Methods Function Optimal Status OICA [19] SAEA [9] SMEA [16] RCEA [17] ISEA [26] MICA The compared results in Table 2 verifies that MICA has the capability in convergence rate, and the compared results in Table 3 reflects the fact that our algorithm is capable of performing a robust and stable search. Furthermore, feasible solutions are consistently found for all test problems in Table 1.…”

Section: Resultsmentioning

confidence: 99%

Multiobjective Imperialist Competitive Algorithm for Solving Nonlinear Constrained Optimization Problems

Chun-an

Jia

2019

Journal of Systems Science and Information

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Nonlinear constrained optimization problem (NCOP) has been arisen in a diverse range of sciences such as portfolio, economic management, airspace engineering and intelligence system etc. In this paper, a new multiobjective imperialist competitive algorithm for solving NCOP is proposed. First, we review some existing excellent algorithms for solving NOCP; then, the nonlinear constrained optimization problem is transformed into a biobjective optimization problem. Second, in order to improve the diversity of evolution country swarm, and help the evolution country swarm to approach or land into the feasible region of the search space, three kinds of different methods of colony moving toward their relevant imperialist are given. Thirdly, the new operator for exchanging position of the imperialist and colony is given similar as a recombination operator in genetic algorithm to enrich the exploration and exploitation abilities of the proposed algorithm. Fourth, a local search method is also presented in order to accelerate the convergence speed. At last, the new approach is tested on thirteen well-known NP-hard nonlinear constrained optimization functions, and the experiment evidences suggest that the proposed method is robust, efficient, and generic when solving nonlinear constrained optimization problem. Compared with some other state-of-the-art algorithms, the proposed algorithm has remarkable advantages in terms of the best, mean, and worst objective function value and the standard deviations.

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Section: Resultsmentioning

confidence: 99%

Multiobjective Imperialist Competitive Algorithm for Solving Nonlinear Constrained Optimization Problems

Chun-an

Jia

2019

Journal of Systems Science and Information

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“…In addition, the global and local search is not effectively controlled due to the use of a simple probability switch [31]. Thus, two other studies introduced limited improvement by including an additional search phase [32] and chaotic maps [31]. The chaotic maps improve the global search slightly; however, adding the extra search step increases the computation time of the algorithm.…”

Section: Related Workmentioning

confidence: 99%

“…Note that the MSE does not reflect the original error because the error is squared (32). To avoid the scaling problem associated with MSE, the root MSE (RMSE) is suggested because it does not treat each error in the same manner.…”

Section: ) Parametric Testsmentioning

confidence: 99%

Quantum Chaotic Butterfly Optimization Algorithm With Ranking Strategy for Constrained Optimization Problems

et al. 2021

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Nature-inspired metaheuristic optimization algorithms, e.g., the butterfly optimization algorithm (BOA), have become increasingly popular. The BOA, which adapts the food foraging and social behaviors of butterflies, involves randomly defined, algorithmic-dependent parameters that affect the exploration and exploitation strategies, which negatively influences the overall performance of the algorithm. To address this issue and improve performance, this paper proposes a modified BOA, i.e., the quantum chaos BOA (QCBOA), that relies on chaos theory and quantum computing techniques. Chaos mapping of unpredictable and divergent behavior helps tune critical parameters, and the quantum wave concept helps the representative butterflies in the algorithm explore the search space more effectively. The proposed QCBOA also implements a ranking strategy to maintain balance between the exploration and exploitation phases, which is lacking in conventional BOAs. To evaluate reliability and efficiency, the proposed QCBOA is tested against a well-utilized set of 20 benchmark functions and travelling salesman problem which belongs to the class of combinatorial optimization problems. Besides, the proposed method is also adopted to photovoltaic system parameter extraction to demonstrate its application to real-word problems. An extensive comparative study was also conducted to compare the performance of QCBOA with that of the conventional BOAs, fine-tuned particle swarm optimization (PSO) algorithm, differential evolution (DE), and genetic algorithm (GA). The results demonstrate that, chaos functions with the quantum wave concept yield better performance for most tested cases and comparative results in the rest of the cases. The speed of convergence also increased compared to the conventional BOAs. The proposed QCBOA is expected to provide better results in other real-word optimization problems and benchmark functions.

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“…Mostly often, constraint handling optimization algorithm used in classical optimization methods can be classified into two types: one is generic methods that do not exploit the mathematical structure of the constraint, such as the penalty function method [5], lagrange multiple method [6], and some intelligence optimization search heuristic algorithms, e.g., enhanced grey wolf optimization algorithm [7], surrogate-assisted evolutionary optimization method [8], modified butterfly optimization algorithm [9] chaotic grey wolf optimization algorithm [10], and enhanced grey wolf optimisation algorithm [11] and the other is special methods that used to solve these problems with specific types of constraints, such as the cutting place method [12] the gradient projection method [13] the quasi-Newton method [14] and the steepest descent method [15].…”

Section: Introductionmentioning

confidence: 99%

“…Comparison of the proposed algorithm MICA with respect to OICA[19], SAEA[9], SMES[16], RCEA[17], ISEA[26] on 13 benchmark functions. "NA" presents not results.…”

mentioning

confidence: 99%

Multiobjective Imperialist Competitive Algorithm for Solving Nonlinear Constrained Optimization Problems

Liu¹,

Jia²

2018

J Swarm Intel Evol Comput

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Nonlinear Constrained Optimization Problem (NCOP) has been arisen in a diverse range of sciences such as portfolio, economic management, airspace engineering and intelligence system etc. In this paper, a new multiobjective imperialist competitive algorithm for solving NCOP is proposed. First, we review some existing excellent algorithms for solving NOCP; then, the nonlinear constrained optimization problem is transformed into a bi objective optimization problem. Second, in order to improve the diversity of evolution country swarm and help the evolution country swarm to approach or land into the feasible region of the search space, three kinds of different methods of colony moving toward their relevant imperialist are given. Thirdly, the new operator for exchanging position of the imperialist and colony is given similar as a recombination operator in genetic algorithm to enrich the exploration and exploitation abilities of the proposed algorithm. Fourth, a local search method is also presented in order to accelerate the convergence speed. At last, the new approach is tested on thirteen well-known NP-hard nonlinear constrained optimization functions, and the experiment evidences suggest that the proposed method is robust, efficient, and generic when solving nonlinear constrained optimization problem. Compared with some other state of the art algorithms, the proposed algorithm has remarkable advantages in terms of the best, mean, and worst objective function value and the standard deviations.

show abstract

A modified butterfly optimization algorithm for mechanical design optimization problems

Cited by 69 publications

References 61 publications

Multiobjective Imperialist Competitive Algorithm for Solving Nonlinear Constrained Optimization Problems

Multiobjective Imperialist Competitive Algorithm for Solving Nonlinear Constrained Optimization Problems

Quantum Chaotic Butterfly Optimization Algorithm With Ranking Strategy for Constrained Optimization Problems

Multiobjective Imperialist Competitive Algorithm for Solving Nonlinear Constrained Optimization Problems

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