Stability analysis of differential evolution

Gopal, Anshul; Bansal, Jagdish Chand

doi:10.1109/iwci.2016.7860370

Cited by 9 publications

(3 citation statements)

References 5 publications

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“…In this study, the mathematical stability analysis of HSOA is performed based on the presented approach by study of [90]. In this approach, the actual solution of problem x_m(n, t) can be considered as a Fourier series solution.…”

Section: Mathematical Framework For Stability Analysismentioning

confidence: 99%

Humboldt Squid Optimization Algorithm (HSOA): A Novel Nature-Inspired Technique for Solving Optimization Problems

Anaraki,

Farzin

2023

IEEE Access

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This study presents a new natural-based algorithm called the Humboldt squid optimization algorithm (HSOA). HSOA is inspired by Humboldt squids hunting, moving, and mating behavior. The HSOA search procedure involves an attack on fish schools, a fish's escape, a successful attack, an attack of bigger squids on smaller ones, and mating, which is the inspiration for creating an algorithm to address existing issues. In HSOA, half of the best populations are Humboldt squid, and the rest are school fish. Individuals connect with each other and cooperate to achieve the optimal response. HSOA is versatile and applicable to mathematical and engineering problems. Solving eighty-four benchmark function problems (twenty-three classic functions, twenty-nine CEC-BC-2017 with 10, 30, 50, and 100 dimensions, ten CEC-C06 2019, ten CEC2020 with 5, 10, 15, and 20 dimensions, and twelve CEC2022 with 10 and 20 dimensions) and twenty-four engineering problems (six CEC2006 and eighteen CEC2011) shows that our proposed algorithm provides proper and acceptable answers to nine algorithms, including well-known (PSO, DE, WOA), recent (AVOA, RW_GWO, HHO and GBO), and state-of-the-art algorithms (LSHADE and EBOwithCMAR). Friedman's rank from HSOA for one hundred and eight problems was 16.45% and 7.45% lower than LSHADE and EBOwithCMAR. Thus, HSOA has the potential to solve various complex problems in the sciences and engineering fields.

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Section: Mathematical Framework For Stability Analysismentioning

confidence: 99%

Humboldt Squid Optimization Algorithm (HSOA): A Novel Nature-Inspired Technique for Solving Optimization Problems

Anaraki,

Farzin

2023

IEEE Access

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“…Finding amplification factor discussed in equation (18). As discussed in section 3.3, amplification factor is calculated by replacing each term x n l of the difference equation ( 15) by v n (k)e ι(kl∆i) and then using equation (16).…”

Section: Appendix Amentioning

confidence: 99%

“…However, a little work has been done in the area of stability analysis of this class of algorithms. Attempts have been made to analyse the stability behaviour of few algorithms which includes Particle Swarm Optimisation (PSO) algorithm using Z-transformation [20] [30] [36], Differential Evolution (DE) algorithm by using Lyapunov's stability theorem and von Neumann stability criterion [12] [18], Bacterial Foraging Optimization (BFO) algorithm using Lyapunov's stability condition and eigen value method [11] [9], Ant Colony Optimization (ACO) algorithm [1] and Gravitational Search algorithm (GSA) using passivity theorem and Lyapunov's stability condition [16].…”

Section: Introductionmentioning

confidence: 99%

Stability analysis of Artificial Bee Colony optimization algorithm

Bansal

Gopal

Nagar

2018

Swarm and Evolutionary Computation

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Theoretical analysis of swarm intelligence and evolutionary algorithms is relatively less explored area of research. Stability and convergence analysis of swarm intelligence and evolutionary algorithms can help the researchers to fine tune the parameter values. This paper presents the stability analysis of a famous Artificial Bee Colony (ABC) optimization algorithm using von Neumann stability criterion for two-level finite difference scheme. Parameter selection for the ABC algorithm is recommended based on the obtained stability conditions. The findings are also validated through numerical experiments on test problems.

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A study of exploratory and stability analysis of artificial electric field algorithm

Sajwan

Yadav

2022

Appl Intell

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Stability analysis of differential evolution

Cited by 9 publications

References 5 publications

Humboldt Squid Optimization Algorithm (HSOA): A Novel Nature-Inspired Technique for Solving Optimization Problems

Humboldt Squid Optimization Algorithm (HSOA): A Novel Nature-Inspired Technique for Solving Optimization Problems

Stability analysis of Artificial Bee Colony optimization algorithm

A study of exploratory and stability analysis of artificial electric field algorithm

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