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Journal Article•DOI•

Chaos-enhanced accelerated particle swarm optimization

Amir H. Gandomi1, Gun Jin Yun1, Xin-She Yang2, Siamak Talatahari3•
University of Akron1, University of Cambridge2, University of Tabriz3
01 Feb 2013-Communications in Nonlinear Science and Numerical Simulation (Elsevier)-Vol. 18, Iss: 2, pp 327-340
TL;DR: This study introduces chaos into the APSO in order to further enhance its global search ability, and shows that the CAPSO with an appropriate chaotic map can clearly outperform standard APSO, with very good performance in comparison with other algorithms and in application to a complex problem.
About: This article is published in Communications in Nonlinear Science and Numerical Simulation.The article was published on 2013-02-01. It has received 336 citations till now. The article focuses on the topics: Particle swarm optimization & Chaotic.
Citations
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Book•
Nature-Inspired Optimization Algorithms

[...]

Xin-She Yang
17 Feb 2014
TL;DR: This book can serve as an introductory book for graduates, doctoral students and lecturers in computer science, engineering and natural sciences, and researchers and engineers as well as experienced experts will also find it a handy reference.
Abstract: Nature-Inspired Optimization Algorithms provides a systematic introduction to all major nature-inspired algorithms for optimization. The book's unified approach, balancing algorithm introduction, theoretical background and practical implementation, complements extensive literature with well-chosen case studies to illustrate how these algorithms work. Topics include particle swarm optimization, ant and bee algorithms, simulated annealing, cuckoo search, firefly algorithm, bat algorithm, flower algorithm, harmony search, algorithm analysis, constraint handling, hybrid methods, parameter tuning and control, as well as multi-objective optimization. This book can serve as an introductory book for graduates, doctoral students and lecturers in computer science, engineering and natural sciences. It can also serve a source of inspiration for new applications. Researchers and engineers as well as experienced experts will also find it a handy reference.Discusses and summarizes the latest developments in nature-inspired algorithms with comprehensive, timely literatureProvides a theoretical understanding as well as practical implementation hintsProvides a step-by-step introduction to each algorithm

901 citations

Journal Article•DOI•
Butterfly optimization algorithm: a novel approach for global optimization

[...]

Sankalap Arora1, Satvir Singh1•
Punjab Technical University1
01 Feb 2019
TL;DR: A new nature-inspired algorithm, namely butterfly optimization algorithm (BOA) that mimics food search and mating behavior of butterflies, to solve global optimization problems and results indicate that the proposed BOA is more efficient than other metaheuristic algorithms.
Abstract: Real-world problems are complex as they are multidimensional and multimodal in nature that encourages computer scientists to develop better and efficient problem-solving methods. Nature-inspired metaheuristics have shown better performances than that of traditional approaches. Till date, researchers have presented and experimented with various nature-inspired metaheuristic algorithms to handle various search problems. This paper introduces a new nature-inspired algorithm, namely butterfly optimization algorithm (BOA) that mimics food search and mating behavior of butterflies, to solve global optimization problems. The framework is mainly based on the foraging strategy of butterflies, which utilize their sense of smell to determine the location of nectar or mating partner. In this paper, the proposed algorithm is tested and validated on a set of 30 benchmark test functions and its performance is compared with other metaheuristic algorithms. BOA is also employed to solve three classical engineering problems (spring design, welded beam design, and gear train design). Results indicate that the proposed BOA is more efficient than other metaheuristic algorithms.

865 citations

Cites background or methods from "Chaos-enhanced accelerated particle..."

  • ...The heuristic methods that have been adopted to optimize this problem are: Chaotic variant of Accelerated PSO (CAPSO) (Gandomi et al. 2013b), Table 7 Comparison results of welded beam design problem Algorithm Optimum variables Optimum cost h l t b BOA 0.1736 2.9690 8.7637 0.2188 1.6644 GWO 0.2056…...

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  • ...The heuristic methods that have been adopted to optimize this problem are: Chaotic variant of Accelerated PSO (CAPSO) (Gandomi et al. 2013b), Table 7 Comparison results of welded beam design problem Algorithm Optimum variables Optimum cost h l t b BOA 0.1736 2.9690 8.7637 0.2188 1.6644 GWO 0.2056 3.4783 9.0368 0.2057 1.7262 GSA 0.1821 3.8569 10.0000 0.2023 1.8799 GA1 N/A N/A N/A N/A 1.8245 GA2 N/A N/A N/A N/A 2.3800 GA3 0.2489 6.1730 8.1789 0.2533 2.4331 HS 0.2442 6.2231 8.2915 0.2443 2.3807 Random 0.4575 4.7313 5.0853 0.6600 4.1185 Simplex 0.2792 5.6256 7.7512 0.2796 2.5307 David 0.2434 6.2552 8.2915 0.2444 2.3841 Approx 0.2444 6.2189 8.2915 0.2444 2.3815 Fig....

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  • ...CS is a metaheuristic algorithm based on the obligate brood parasitic behavior of some cuckoo species in which the cuckoo bird lay their eggs in the nests of birds of different species (Gandomi et al. 2013a)....

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  • ...10 Schematic representation of gear CS (Gandomi et al. 2013a), PSO (Parsopoulos and Vrahatis 2005), Genetic Adaptive Search (GeneAS) (Deb and Goyal 1996) and Simulated annealing (Zhang and Wang 1993)....

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Journal Article•DOI•
Bat algorithm: literature review and applications

[...]

Xin-She Yang1, Xingshi He2•
Middlesex University1, Xi'an Polytechnic University2
01 Jul 2013-International Journal of Bio-inspired Computation
TL;DR: A timely review of the bat algorithm and its new variants and a wide range of diverse applications and case studies are reviewed and summarised briefly here.
Abstract: Bat algorithm BA is a bio-inspired algorithm developed by Xin-She Yang in 2010 and BA has been found to be very efficient. As a result, the literature has expanded significantly in the last three years. This paper provides a timely review of the bat algorithm and its new variants. A wide range of diverse applications and case studies are also reviewed and summarised briefly here. In addition, we also discuss the essence of an algorithm and the links between algorithms and self-organisation. Further research topics are also discussed.

791 citations

Cites background or methods from "Chaos-enhanced accelerated particle..."

  • ...In the rest of the paper, we will briefly highlight some of the applications (Yang, 2010;Parpinelli and Lopes, 2011; Yang et al., 2012a; Yang, 2012; Yang, 2013; Gandomi et al., 2013)....

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  • ...Furthermore, cuckoo search (CS) was based on the brooding behaviour of some cuckoo species (Yang and Deb, 2009; Gandomi et al, 2013) which was combined with Lévy flights....

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Journal Article•DOI•
Chaotic Krill Herd algorithm

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Gai-Ge Wang1, Lihong Guo2, Amir H. Gandomi3, Guo-Sheng Hao1, Heqi Wang2 •
Jiangsu Normal University1, Chinese Academy of Sciences2, University of Akron3
01 Aug 2014-Information Sciences
TL;DR: The chaos theory is introduced into the KH optimization process with the aim of accelerating its global convergence speed and shows that the performance of CKH, with an appropriate chaotic map, is better than or comparable with the KH and other robust optimization approaches.

473 citations

Journal Article•DOI•
Chaotic bat algorithm

[...]

Amir H. Gandomi1, Xin-She Yang2•
University of Akron1, Middlesex University2
01 Mar 2014-Journal of Computational Science
TL;DR: Chaos is introduced into Bat algorithm so as to increase its global search mobility for robust global optimization and results show that some variants of chaotic BAs can clearly outperform the standard BA for these benchmarks.

445 citations

References
More filters
Proceedings Article•DOI•
Particle swarm optimization

[...]

James Kennedy, Russell C. Eberhart
06 Aug 2002
TL;DR: A concept for the optimization of nonlinear functions using particle swarm methodology is introduced, and the evolution of several paradigms is outlined, and an implementation of one of the paradigm is discussed.
Abstract: A concept for the optimization of nonlinear functions using particle swarm methodology is introduced. The evolution of several paradigms is outlined, and an implementation of one of the paradigms is discussed. Benchmark testing of the paradigm is described, and applications, including nonlinear function optimization and neural network training, are proposed. The relationships between particle swarm optimization and both artificial life and genetic algorithms are described.

35,104 citations

Journal Article•DOI•
The particle swarm - explosion, stability, and convergence in a multidimensional complex space

[...]

M. Clerc1, James Kennedy2•
Orange S.A.1, Bureau of Labor Statistics2
01 Feb 2002-IEEE Transactions on Evolutionary Computation
TL;DR: This paper analyzes a particle's trajectory as it moves in discrete time, then progresses to the view of it in continuous time, leading to a generalized model of the algorithm, containing a set of coefficients to control the system's convergence tendencies.
Abstract: The particle swarm is an algorithm for finding optimal regions of complex search spaces through the interaction of individuals in a population of particles. This paper analyzes a particle's trajectory as it moves in discrete time (the algebraic view), then progresses to the view of it in continuous time (the analytical view). A five-dimensional depiction is developed, which describes the system completely. These analyses lead to a generalized model of the algorithm, containing a set of coefficients to control the system's convergence tendencies. Some results of the particle swarm optimizer, implementing modifications derived from the analysis, suggest methods for altering the original algorithm in ways that eliminate problems and increase the ability of the particle swarm to find optima of some well-studied test functions.

8,287 citations

"Chaos-enhanced accelerated particle..." refers methods in this paper

  • ...For example, Clerc and Kennedy [17] provided a detailed analysis of PSO using a simplified dynamical system by considering a 1D particle system with a global best p and transforming k 1⁄4 ðb þ aÞ and ut = p x(t + 1)....

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  • ...Among more than two dozen variants of PSO, the most noticeable improvement is possibly the use of an inertia function h(t) so that v i is replaced by hðtÞv i v tþ1 i 1⁄4 hðtÞv i þ ar1ðx i xi Þ þ br2ðg xi Þ ð3Þ where h 2 (0,1) [17]....

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Particle Swarm Optimization.

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James Kennedy
01 Jan 2010

6,571 citations

Journal Article•DOI•
Simple mathematical models with very complicated dynamics

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Robert M. May1, Robert M. May2•
University of Cambridge1, Princeton University2
10 Jun 1976-Nature
TL;DR: This is an interpretive review of first-order difference equations, which can exhibit a surprising array of dynamical behaviour, from stable points, to a bifurcating hierarchy of stable cycles, to apparently random fluctuations.
Abstract: First-order difference equations arise in many contexts in the biological, economic and social sciences. Such equations, even though simple and deterministic, can exhibit a surprising array of dynamical behaviour, from stable points, to a bifurcating hierarchy of stable cycles, to apparently random fluctuations. There are consequently many fascinating problems, some concerned with delicate mathematical aspects of the fine structure of the trajectories, and some concerned with the practical implications and applications. This is an interpretive review of them.

6,118 citations

"Chaos-enhanced accelerated particle..." refers background in this paper

  • ...The iterative chaotic map with infinite collapses [23] is expressed by:...

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  • ...The piecewise map is defined as follows [23]:...

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Book•
Chaos in dynamical systems

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Edward Ott1•
University of Maryland, College Park1
01 Jan 1993
TL;DR: In the new edition of this classic textbook, the most important change is the addition of a completely new chapter on control and synchronization of chaos as mentioned in this paper, which will be of interest to advanced undergraduates and graduate students in science, engineering and mathematics taking courses in chaotic dynamics, as well as to researchers in the subject.
Abstract: Over the past two decades scientists, mathematicians, and engineers have come to understand that a large variety of systems exhibit complicated evolution with time. This complicated behavior is known as chaos. In the new edition of this classic textbook Edward Ott has added much new material and has significantly increased the number of homework problems. The most important change is the addition of a completely new chapter on control and synchronization of chaos. Other changes include new material on riddled basins of attraction, phase locking of globally coupled oscillators, fractal aspects of fluid advection by Lagrangian chaotic flows, magnetic dynamos, and strange nonchaotic attractors. This new edition will be of interest to advanced undergraduates and graduate students in science, engineering, and mathematics taking courses in chaotic dynamics, as well as to researchers in the subject.

3,890 citations

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[...]

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01 Dec 1997-Journal of Global Optimization
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Nature-Inspired Metaheuristic Algorithms

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01 Feb 2008
Xin-She Yang
Biogeography-Based Optimization

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01 Dec 2008-IEEE Transactions on Evolutionary Computation
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Cuckoo search algorithm: a metaheuristic approach to solve structural optimization problems

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01 Jan 2013-Engineering With Computers
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