New filled functions for nonsmooth global optimization

Zhang, Ying; Zhang, Liansheng; Xu, Yuelei

doi:10.1016/j.apm.2008.10.015

Cited by 27 publications

(11 citation statements)

References 21 publications

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“…To solve this problem, some filled functions have been designed (e.g., [12]- [15]). In this paper, we integrate a filled function P -function [15] into the proposed EA.…”

Section: Filled Functionmentioning

confidence: 99%

“…Choose a positive real numbers β large enough, σ = ∞, f (x * 0 ) = f (x 0 ) = ∞, ε is a tolerance threshold. 2 Perform the grouping strategy AVG, and obtained M iterations k1 in SaNSDE, the current best solution x k and second-best solution x k−1 in this subcomponent optimization, and the number of function evaluation SF Es in SaNSDE, then update F Es = F Es + SF Es, andδ = f (x k−1 ) − f (x k ); 11if δ ≤ ε then12 construct a filled function P (x, x k ) at x k , then obtain a current best solution x * k by minimizing this filled function;update δ = f (x k ) − f (x * k ); best solution x * K = x * k , and σ = f (x * K ) − f (x *the maximum number of function evaluations MaxFEs is met; 21 x * = x * K , and f (x * ) = f (x * K ); 22 return x * and f (x * ).…”

mentioning

confidence: 99%

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A novel cooperative coevolution for large scale global optimization

Wei

Wang

Zong

2014

2014 IEEE International Conference on Systems, Man, and Cybernetics (SMC)

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For large scale global optimization problems, the efficiency and effectiveness of evolutionary algorithms (EAs) will be much reduced with the dimension increasing. In this paper, a novel evolutionary algorithm is proposed in order to improve the performance of EAs. In the proposed algorithm, on one hand, a variable grouping strategy is introduced. It can group all variables into several subcomponents, while the variables in each subcomponent are non-separable. In this way, a large scale problem can be decomposed into several small scale problems. On the other hand, a filled function with one parameter is integrated into EAs, which can help algorithm to escape from the current local optimal solution and find a better one. The simulations are made on the standard benchmark suite in CEC'2013, and the proposed algorithm is compared with several well performed algorithms. The results indicate the proposed algorithm is more efficient and effective.

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“…To solve this problem, some filled functions have been designed (e.g., [12]- [15]). In this paper, we integrate a filled function P -function [15] into the proposed EA.…”

Section: Filled Functionmentioning

confidence: 99%

mentioning

confidence: 99%

A novel cooperative coevolution for large scale global optimization

Wei

Wang

Zong

2014

2014 IEEE International Conference on Systems, Man, and Cybernetics (SMC)

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“…This is more difficult to be guaranteed. Therefore, many improvements in the definition are given in the literatures ( [6,14,28], e.g. ), which make it more convenient to construct a new filled function.…”

Section: A New Filled Function and Its Propertiesmentioning

confidence: 99%

A New Filled Function Method with One Parameter for Global Optimization

Wei

Wang

2013

Mathematical Problems in Engineering

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The filled function method is an effective approach to find the global minimizer of multidimensional multimodal functions. The conventional filled functions are numerically unstable due to exponential or logarithmic term and sensitive to parameters. In this paper, a new filled function with only one parameter is proposed, which is continuously differentiable and proved to satisfy all conditions of the filled function definition. Moreover, this filled function is not sensitive to parameter, and the overflow can not happen for this function. Based on these, a new filled function method is proposed, and it is numerically stable to the initial point and the parameter variable. The computer simulations indicate that the proposed filled function method is efficient and effective.

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“…The filled function method was introduced by Ge [56,57]. It has had increasing interest in filled methods in the last few years [58][59][60].…”

Section: Global Optimization Approachesmentioning

confidence: 99%

A Direct Search Algorithm for Global Optimization

2016

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Abstract:A direct search algorithm is proposed for minimizing an arbitrary real valued function. The algorithm uses a new function transformation and three simplex-based operations. The function transformation provides global exploration features, while the simplex-based operations guarantees the termination of the algorithm and provides global convergence to a stationary point if the cost function is differentiable and its gradient is Lipschitz continuous. The algorithm's performance has been extensively tested using benchmark functions and compared to some well-known global optimization algorithms. The results of the computational study show that the algorithm combines both simplicity and efficiency and is competitive with the heuristics-based strategies presently used for global optimization.

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New filled functions for nonsmooth global optimization

Cited by 27 publications

References 21 publications

A novel cooperative coevolution for large scale global optimization

A novel cooperative coevolution for large scale global optimization

A New Filled Function Method with One Parameter for Global Optimization

A Direct Search Algorithm for Global Optimization

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