Improved gene expression programming to solve the inverse problem for ordinary differential equations

Li, Kangshun; Chen, Yan; Li, Wei; He, Jun; Xue, Yu

doi:10.1016/j.swevo.2017.07.005

Cited by 33 publications

(11 citation statements)

References 22 publications

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“…Compared with other optimization algorithms, its structure is simple and easy to implement, and after a long period of theory and practice, the algorithm has good reliability and strong robustness. It is widely used to solve numerical optimization problems in various fields 4‐12 …”

Section: Research Backgroundmentioning

confidence: 99%

A dynamic population reduction differential evolution algorithm combining linear and nonlinear strategy piecewise functions

Wang

et al. 2021

Concurrency and Computation

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The population size has a great impact on the performance of the Differential Evolution (DE) algorithm, but in many classic DE algorithms, the population size is usually determined by the user based on the experience value, and it remains unchanged during the evolution process, which greatly affect the performance of DE. To this end, a dynamic population reduction differential evolution algorithm (DPSHADE) that combines linear and nonlinear strategy piecewise functions is proposed. The algorithm uses a dynamic population size reduction method to dynamically adjust the population size during operation, and construct a combination of linear and nonlinear piecewise functions for dynamic scale adaptive adjustment. In this paper, we proposed the DPSHADE algorithm and is compared with the four traditional algorithms in the CEC2017 benchmark set. The experimental results show that DPSHADE performs better in overall performance, which is significant better than the performance of SHADE.

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Section: Research Backgroundmentioning

confidence: 99%

A dynamic population reduction differential evolution algorithm combining linear and nonlinear strategy piecewise functions

Wang

et al. 2021

Concurrency and Computation

Self Cite

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“…When manipulating the chromosomes, the gene expression programing is more similar to GA than GP. Like GP, the representation is tree like whereas performing manipulations; crossover operator is taken from the GA [39]. The primary base of the differential evolution is vector differences and hence this technique is majorly more suitable for solving optimization problems of numerical representation.…”

Section: Related Workmentioning

confidence: 99%

An Enhanced Firefly Algorithm Using Pattern Search for Solving Optimization Problems

et al. 2020

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Firefly Algorithm (FA) is one of the most recently introduced stochastic, nature-inspired, meta-heuristic approaches used for solving optimization problems. The conventional FA use randomization factor during generation of solution search space and fireflies position changing, which results in imbalanced relationship between exploration and exploitation. This imbalanced relationship causes in incapability of FA to find the most optimum values at termination stage. In the proposed model, this issue has been resolved by incorporating PS at the termination stage of standard FA. The optimized values obtained from the FA are set as the initial starting points for the PS algorithm and the values are further optimized by PS to get the most optimal values or at least better values than the values obtained by conventional FA during its maximum number of iterations. The performance of the newly developed FA-PS model has been tested on eight minimization functions and six maximization functions by considering various performance evaluation parameters. The results obtained have been compared with other optimization algorithms namely genetic algorithm (GA), standard FA, artificial bee colony (ABC), ant colony optimization (ACO), differential equations (DE), bat algorithm (BA), grey wolf optimization (GWO), Self-Adaptive Step Firefly Algorithm (SASFA), and FA-Cross algorithm in terms of convergence rate and various numerical performance evaluation parameters. A significant improvement has been observed in the solution quality by embedding PS in the standard FA at the termination stage. The result behind this improvement is the better exploration and exploitation of the solution search space at this stage.

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“…How to solve these problems has become a hotspot of scientific research [36,38]. Compared with the traditional mathematical programming methods, evolutionary algorithms (EAs) are widely applied to solve MaOPs [7,[21][22][23], because they do not need to carry out complex mathematical reasoning and they can obtain a set of approximately optimal solutions in one single run.…”

Section: Introductionmentioning

confidence: 99%

A collaborative decomposition-based evolutionary algorithm integrating normal and penalty-based boundary intersection for many-objective optimization

Wu¹,

Wei²,

Ying³

et al. 2022

Preprint

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Decomposition-based evolutionary algorithms have become fairly popular for many-objective optimization owing to their excellent selection pressure in recent years. However, the existing decomposition methods still are quite sensitive to the various shapes of frontiers of many-objective optimization problems (MaOPs). On the one hand, the cone decomposition methods such as the penalty-based boundary intersection (PBI) are incapable of acquiring uniform frontiers due to the radial spatial distribution of their reference lines for MaOPs with very convex frontiers. On the other hand, the parallel reference lines of the parallel decomposition methods including the normal boundary intersection (NBI) might result in poor diversity because of under-sampling near the boundaries for MaOPs with concave frontiers. In this paper, a collaborative decomposition method is first proposed to integrate the advantages of parallel decomposition and cone decomposition to overcome their respective disadvantages. This method inherits the NBI-style Tchebycheff function as a convergence measure to heighten the convergence and uniformity of distribution of the PBI method. Moreover, this method also adaptively tunes the extent of rotating an NBI reference line towards a PBI reference line for every subproblem to enhance the diversity of distribution of the NBI method. Furthermore, a collaborative decomposition-based evolutionary algorithm (CoDEA) is presented for many-objective optimization. A collaborative decomposition-based environmental selection mechanism is primarily designed in CoDEA to rank all the individuals associated with the same PBI reference line in the boundary layer and pick out the best ranks. The proposed algorithm is compared with several popular many-objective evolutionary algorithms on 85 benchmark test instances. The experimental results show that CoDEA achieves high competitiveness benefiting from the collaborative decomposition maintaining a good balance among the convergence, uniformity, and diversity of distribution.

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Improved gene expression programming to solve the inverse problem for ordinary differential equations

Cited by 33 publications

References 22 publications

A dynamic population reduction differential evolution algorithm combining linear and nonlinear strategy piecewise functions

A dynamic population reduction differential evolution algorithm combining linear and nonlinear strategy piecewise functions

An Enhanced Firefly Algorithm Using Pattern Search for Solving Optimization Problems

A collaborative decomposition-based evolutionary algorithm integrating normal and penalty-based boundary intersection for many-objective optimization

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