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## Hybridizing differential evolution and particle swarm optimization to design powerful optimizers: A review and taxonomy

Venue: | IEEE Transactions on Systems, Man, and Cybernetics, Part C: Applications and Reviews |

Citations: | 3 - 0 self |

### Citations

10040 |
Genetic Algorithms
- Goldberg
- 1989
(Show Context)
Citation Context ...e functions. Besides, many stochastic optimizers have good performance in global optimization. In the family of stochastic optimizers, well-known typical optimizers include the genetic algorithm (GA) =-=[2]-=-, evolutionary strategy (ES) [3] (CMA-ES [4] in particular), evolutionary programming (EP) [5], simulated annealing (SA) [6], ant-colony optimization (ACO) [7], particle swarm optimization (PSO) [8], ... |

5028 | Optimization by simulated annealing
- Kirkpatrick, Gelatt, et al.
- 1983
(Show Context)
Citation Context ...ptimizers, well-known typical optimizers include the genetic algorithm (GA) [2], evolutionary strategy (ES) [3] (CMA-ES [4] in particular), evolutionary programming (EP) [5], simulated annealing (SA) =-=[6]-=-, ant-colony optimization (ACO) [7], particle swarm optimization (PSO) [8], differential evolution (DE) [9], estimation of distribution algorithm (EDA) [10], and so on. All of them have many variants,... |

3520 | Particle swarm optimization
- Kennedy, Eberhart
- 1995
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Citation Context ...) [2], evolutionary strategy (ES) [3] (CMA-ES [4] in particular), evolutionary programming (EP) [5], simulated annealing (SA) [6], ant-colony optimization (ACO) [7], particle swarm optimization (PSO) =-=[8]-=-, differential evolution (DE) [9], estimation of distribution algorithm (EDA) [10], and so on. All of them have many variants, which have excellent performance. These variants are based on various imp... |

1247 |
programming and extensions
- Linear
- 1963
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Citation Context ...Therefore, it is not unusual to see that numerous optimizers have emerged since Dantzig proposed the simplex method for the linear programming problem in 1947 as an inception of optimization research =-=[1]-=-. Now, increasingly, problems turn out to be nonlinear, nonconvex, multimodal, discontinuous, and even dynamic. For these complicated problems, stochastic optimizers become favored as they have no dep... |

1021 | Ant Colony Optimization
- Dorigo, Stützle
- 2004
(Show Context)
Citation Context ...izers include the genetic algorithm (GA) [2], evolutionary strategy (ES) [3] (CMA-ES [4] in particular), evolutionary programming (EP) [5], simulated annealing (SA) [6], ant-colony optimization (ACO) =-=[7]-=-, particle swarm optimization (PSO) [8], differential evolution (DE) [9], estimation of distribution algorithm (EDA) [10], and so on. All of them have many variants, which have excellent performance. ... |

812 | The particle swarm-explosion, stability, and convergence in a multidimensional complex space
- Clerc, Kennedy
- 2002
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Citation Context ...n [0,1]. The PSO parameter w is the so-called inertia weight, and a common setting of this parameter is w∗ = 0.7298, which corresponds to the constriction factor that is proposed by Clerc and Kennedy =-=[45]-=-. Concerning another setting that is frequently adopted in the literature, the inertia weight is dynamically adjusted, decreasing from a number around 1 to a smaller number around zero [46], [47]. c1 ... |

647 | Tabu search—part I
- Glover
- 1989
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Citation Context ...metaheuristics, Taillard et al. set forth a unifying view from the perspective of adaptive memory-based programming [58]. Although the concept of memory is usually regarded as a kernel in tabu search =-=[59]-=- and it is usually not stressed in the DE and PSO literature, both DE and PSO have to maintain a memory to record personal best information. Calégari et al. proposed a taxonomy of EAs, taking into ac... |

413 |
Differential Evolution: A Practical Approach to Global Optimization
- Price, Storn, et al.
- 2005
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Citation Context ...worthy of future research. In Section VI, we conclude the paper. II. DIFFERENTIAL EVOLUTION AND PARTICLE SWARM OPTIMIZATION A. Classical Differential Evolution The DE proposed by Storn and Price [9], =-=[30]-=- is a formidable PO, which has been widely applied in practice [30]–[35]. It was established on the framework of GAs and inspired by the Nelder–Mead simplex method [30]. It has three operators— mutati... |

376 |
Differential Evolution–A Simple and Efficient Heuristic for global Optimization over Continuous Spaces, Journal of Global Optimization 11 (4
- Storn, Price
- 1997
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Citation Context ... [3] (CMA-ES [4] in particular), evolutionary programming (EP) [5], simulated annealing (SA) [6], ant-colony optimization (ACO) [7], particle swarm optimization (PSO) [8], differential evolution (DE) =-=[9]-=-, estimation of distribution algorithm (EDA) [10], and so on. All of them have many variants, which have excellent performance. These variants are based on various improvement strategies. Hybridizatio... |

361 |
Estimation of Distribution Algorithms: A New Tool for Evolutionary Computation
- Larrañaga, Lozano
- 2001
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Citation Context ...ogramming (EP) [5], simulated annealing (SA) [6], ant-colony optimization (ACO) [7], particle swarm optimization (PSO) [8], differential evolution (DE) [9], estimation of distribution algorithm (EDA) =-=[10]-=-, and so on. All of them have many variants, which have excellent performance. These variants are based on various improvement strategies. Hybridization is one of the most efficient strategies to impr... |

327 | Evolutionary programming made faster
- Yao, Liu, et al.
- 1999
(Show Context)
Citation Context ... In the family of stochastic optimizers, well-known typical optimizers include the genetic algorithm (GA) [2], evolutionary strategy (ES) [3] (CMA-ES [4] in particular), evolutionary programming (EP) =-=[5]-=-, simulated annealing (SA) [6], ant-colony optimization (ACO) [7], particle swarm optimization (PSO) [8], differential evolution (DE) [9], estimation of distribution algorithm (EDA) [10], and so on. A... |

294 | Metaheuristics in combinatorial optimization: Overview and conceptual comparison
- Blum, Roli
(Show Context)
Citation Context ...s-level hybridization (HELH) means that the OLs of parents are different. For example, regarding the hybridization between a PO and a trajectory search method (TSM), i.e., singlepoint-based optimizer =-=[17]-=-, in which the PO usually operates at population level, the TSM will be regarded to be hybridized with the PO at individual level if a TSM manipulates only one solution at each generation. As a rule, ... |

241 | Comparing inertia weights and constriction factors in particle swarm optimization
- Eberhart, Shi
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Citation Context ...n experiences about the problem space and, meanwhile, learn from each other according to their fitness values. The iteration equations for the velocity and position in PSO with inertia weight (PSO-w) =-=[44]-=- are given as follows: vk+1i,d = w · vki,d ︸ ︷︷ ︸ inertia + c1 · rand1 · (pbestki,d − xki,d) ︸ ︷︷ ︸ individual cognition + c2 · rand2 · (nbestki,d − xki,d) ︸ ︷︷ ︸ social learning (6) xk+1i,d = x k i,d... |

222 | On the adaptation of arbitrary normal mutation distributions in evolution strategies: The generating set adaptation
- Hansen, Ostermeier, et al.
- 1995
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Citation Context ...zers have good performance in global optimization. In the family of stochastic optimizers, well-known typical optimizers include the genetic algorithm (GA) [2], evolutionary strategy (ES) [3] (CMA-ES =-=[4]-=- in particular), evolutionary programming (EP) [5], simulated annealing (SA) [6], ant-colony optimization (ACO) [7], particle swarm optimization (PSO) [8], differential evolution (DE) [9], estimation ... |

183 | Population structure and particle swarm performance
- Kennedy, Mendes
- 2002
(Show Context)
Citation Context ...ure. The population topology has obvious effects on the spreading speed of information and the convergence of particle swarm [48]. Different population topologies correspond to different PSO versions =-=[49]-=-, [50]. The most well-known topology models are Gbest and Lbest. In the Gbest model, each particle’s neighborhood covers the whole swarm and all particles are connected with each other. Usually, “gbes... |

166 |
A multi-objective genetic local search algorithm and its application to flowshop scheduling
- Isibuchi, Murata
- 1998
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Citation Context ... MAs. Both GQD and GQL are expected to combine the advantage of the GA in exploration with that of QN in exploitation. 3) MOGLS (Multi-Objective Genetic Local Search) Proposed by Ishibuchi and Murata =-=[22]-=-: GA⊕LS〈C,P,S,D〉: [HOLH], [HOOH], [deterministic static alternation], [homogeneous TIT], [TTI:〈S〉, GA 〈x〉⇀↽ 〈x〉 LS]. Inventors’ ideas: A truncated LS is employed with the goal to alleviate the great b... |

149 |
A Cooperative Approach to Particle Swarm Optimization
- Bergh, Engelbrecht
- 2004
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Citation Context ...nd Kennedy [45]. Concerning another setting that is frequently adopted in the literature, the inertia weight is dynamically adjusted, decreasing from a number around 1 to a smaller number around zero =-=[46]-=-, [47]. c1 and c2 are acceleration coefficients, which are also termed as the cognitive factor and the social factor, respectively. Both of them are set to 0.7298× 2.05 ≈ 1.496 in the PSO with the con... |

149 |
Comprehensive learning particle swarm optimizer for global optimization of multimodal functions
- Liang, Qin, et al.
- 2006
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Citation Context ...nedy [45]. Concerning another setting that is frequently adopted in the literature, the inertia weight is dynamically adjusted, decreasing from a number around 1 to a smaller number around zero [46], =-=[47]-=-. c1 and c2 are acceleration coefficients, which are also termed as the cognitive factor and the social factor, respectively. Both of them are set to 0.7298× 2.05 ≈ 1.496 in the PSO with the constrict... |

138 |
worlds and mega-minds: Effects of neighborhood topology on particle swarm performance
- Small
- 1999
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Citation Context ...O with the constriction factor (PSO-cf) [45]. One kernel of PSO is population topology, which is also termed as neighborhood or information topology, specifying the social structure of particle swarm =-=[48]-=-–[50]. Information such as the best position that is found by some particle can only be transferred to its neighbors that are determined by population structure. The population topology has obvious ef... |

114 | A tutorial for competent memetic algorithms: Model, taxonomy, and design issues
- Krasnogor, Smith
- 2005
(Show Context)
Citation Context ...dization contributes to population diversity but the population here means the family of optimizers. There are many successful examples of hybridization in the evolution process of this family (e.g., =-=[19]-=-–[28]). A common template for hybridization is provided by memetic algorithms (MAs), which combine the respective advantages of global search and local search (LS) [19]. Due to excellent performance, ... |

110 |
Self-adapting control parameters in differential evolution: a comparative study on numerical benchmark problems
- Brest, Greiner, et al.
(Show Context)
Citation Context ...gest F ∈ [0.5, 1] as such a setting may result in good optimization effectiveness [9]. In addition, there are many advanced DE variants, which are based on the dynamic tuning of this parameter (e.g., =-=[36]-=- and [37], see also the survey [32] on DE for more introduction). After mutation, a binominal (bin) crossover operates on the vector zi and the target vector xi to generate the final vector ui in the ... |

107 | Differential evolution algorithm with strategy adaptation for global numerical optimization
- Qin, Huang, et al.
(Show Context)
Citation Context ...[0.5, 1] as such a setting may result in good optimization effectiveness [9]. In addition, there are many advanced DE variants, which are based on the dynamic tuning of this parameter (e.g., [36] and =-=[37]-=-, see also the survey [32] on DE for more introduction). After mutation, a binominal (bin) crossover operates on the vector zi and the target vector xi to generate the final vector ui in the following... |

78 | A taxonomy of hybrid metaheuristics
- Talbi
- 2002
(Show Context)
Citation Context ... which have excellent performance. These variants are based on various improvement strategies. Hybridization is one of the most efficient strategies to improve the performance of many optimizers [11]–=-=[15]-=-. In genetics, hybridization is the process to combine different varieties or species of organisms to create a hybrid (biology). In evolutionary algorithms (EAs), hybridization refers to merging two o... |

76 | Particle swarm optimization: basic concepts, variants and applications in power systems - Valle, Venayagamoorthy, et al. - 2008 |

73 | A hybrid of genetic algorithm and particle swarm optimization for recurrent network design
- Juang
- 2004
(Show Context)
Citation Context ...This is one of the important reasons for the success of many efficient hybrid optimizers, especially those that are frequently cited and whose high quality and efficiency have been proved in practice =-=[20]-=-–[27]. Like other population-based global optimizers, DE and PSO stress on exploration and lack exploitation; therefore, many researchers have tried to hybridize them with LS to strike a balance [67]–... |

71 |
Meta-Lamarckian learning in memetic algorithms
- Ong, Keane
- 2004
(Show Context)
Citation Context ...istical learning to choose evolution methods can also be applied to the adaptation of control parameters, evolutionary operators (e.g., the differential mutation [37], [132]), and LS techniques [19], =-=[24]-=-, [133], [134]. B. Embedding-Based DEPSOs A typical embedding-based DEPSO is the PSO with differentially perturbed velocity (namely DEPSO-DKC; PSODV in [110]) that is proposed by Das et al. The embedd... |

65 |
Bare bones particle swarm
- Kennedy
- 2003
(Show Context)
Citation Context ...cularly, Kennedy proposed a simplified PSO version [named barebones PSO (BBPSO)] with an attempt to more concisely reflect the essence of the PSO paradigm, i.e., the social interaction of individuals =-=[54]-=-. In this compact PSO, the velocity formula is eliminated, while the sampling distribution of classical PSO is retained by the employment of a Guassian sampling approach. Kennedy suggests the normal d... |

64 | Hybrid Methods Using Genetic Algorithms for Global Optimization
- Renders, Flasse
- 1996
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Citation Context ...L (hybrid of Genetic Algorithm and Quasi-Newton Inspired by Lamarckian Evolution) and GQD (hybrid of Genetic Algorithm and Quasi-Newton Inspired by Darwinian Evolution) Proposed by Renders and Flasse =-=[21]-=-: GA⊕QN(quasi-Newton method). 758 IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS—PART C: APPLICATIONS AND REVIEWS, VOL. 42, NO. 5, SEPTEMBER 2012 TABLE I (Continued.) Fig. 6. Number of times each ... |

62 | DEPSO: Hybrid Particle Swarm with Differential Evolution Operator
- Zhang, Xie
(Show Context)
Citation Context ...ion contributes to population diversity but the population here means the family of optimizers. There are many successful examples of hybridization in the evolution process of this family (e.g., [19]–=-=[28]-=-). A common template for hybridization is provided by memetic algorithms (MAs), which combine the respective advantages of global search and local search (LS) [19]. Due to excellent performance, MAs h... |

52 |
Accelerating Differential Evolution using an adaptive local search
- Noman, Iba
- 2008
(Show Context)
Citation Context ... First, as mentioned earlier, neither classical DE nor classical PSO employs IMs though there exist several advanced variants of DE and PSO, which incorporate LS techniques as an improvement strategy =-=[67]-=-–[71]. Second, DE takes differential mutation and crossover as its SCM, while the SCM of PSO is a random combination of pbest and nbest. As for the pool, both DE and PSO keep only a pool of pbest info... |

44 | A Hybrid Approach to Modelling Metabolic Systems Using Genetic Algorithms and Simplex Method
- Yen, Liao, et al.
- 1995
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Citation Context ... for the next generation. Therefore, the SA in essence is embedded as a selection mechanism into the GA. Accordingly, this GASA can be categorized into 〈E,P,N,D〉. 7) Simplex-GA Proposed by Yen et al. =-=[26]-=-: GA⊕CPS (concurrent probabilistic simplex), 〈C,S,P,D〉: [HELH (GA’s OL:〈P〉, CPS’s OL:〈S〉)], [HEOH], [heterogeneous TIT], [TTI:〈S〉, GA 〈e〉 ⇀↽ 〈x〉 CPS]. Inventors’ ideas: The hybrid implies a hierarchic... |

43 | Adaptive memory programming: A unified view of metaheuristics
- Taillard, LM, et al.
- 2001
(Show Context)
Citation Context ...cially biased individual learning heuristics [57]. On the implementation of diverse metaheuristics, Taillard et al. set forth a unifying view from the perspective of adaptive memory-based programming =-=[58]-=-. Although the concept of memory is usually regarded as a kernel in tabu search [59] and it is usually not stressed in the DE and PSO literature, both DE and PSO have to maintain a memory to record pe... |

30 |
D.X Huang: Improved Particle Swarm Optimization Combined with Chaos
- Liu, Wang, et al.
- 2005
(Show Context)
Citation Context ... shares the same idea with the GQL that is proposed by Renders and Flasse [21]. In fact, both of them belong to the family of MAs. 4) CPSO (Chaotic Particle Swarm Optimization) Proposed by Liu et al. =-=[23]-=-: PSO⊕CS (chaotic search) 〈C,I,S,D〉: [HELH (PSO’s OL: 〈P〉, CS’s OL: 〈I〉)], [HEOH], [deterministic static alternation], [homogeneous TIT], [TTI: 〈S〉, PSO 〈g〉⇀↽ 〈g〉 CS]. Inventors’ ideas: Chaotic dynami... |

27 |
Exploring dynamic self-adaptive populations in differential evolution
- Teo
- 2006
(Show Context)
Citation Context ...f EAs, taking into account multiple classification criteria, such as population sizing strategy and population structure [60]. Both DE and PSO can adopt a static (constant) or dynamic population size =-=[61]-=-–[65]; howbeit, they differ in terms of population structure as DE originally does not differentiate population topologies. Greistorfer and Voβ proposed a “pool” template to cover diverse classes of m... |

26 | An effective PSO-based memetic algorithm for flow shop scheduling - Liu, Wang, et al. - 2007 |

24 | DE/EDA: A new evolutionary algorithm for global optimization, Information Science (169
- Sun, Zhang, et al.
- 2005
(Show Context)
Citation Context ... subpopulation directly enter the next generation. The CPS is an exploitative optimizer that is expected to search the local space around some high-quality solutions. 8) DE/EDA Proposed by Sun et al. =-=[27]-=-: EDA⊕DE (DE/mid-to-better/1/bin), 〈C,C,S,D〉: [HOLH], [HOOH], [stochastic static alternation], [heterogeneous TIT], [TTI:〈S〉, 〈Sc〉, EDA 〈Sc〉⇀↽ 〈e〉,〈Sc〉 DE]. Inventors’ ideas: DE/EDA combines global in... |

24 |
Neighborhood topologies in fully informed and best-of-neighborhood particle swarm
- Kennedy, Mendes
- 2006
(Show Context)
Citation Context ...h the constriction factor (PSO-cf) [45]. One kernel of PSO is population topology, which is also termed as neighborhood or information topology, specifying the social structure of particle swarm [48]–=-=[50]-=-. Information such as the best position that is found by some particle can only be transferred to its neighbors that are determined by population structure. The population topology has obvious effects... |

23 | Automatic clustering using an improved differential evolution algorithm - Das, Abraham, et al. - 2008 |

19 |
A taxonomy of evolutionary algorithms in combinatorial optimization
- Calègari, Coray, et al.
- 1999
(Show Context)
Citation Context ...ory to record personal best information. Calégari et al. proposed a taxonomy of EAs, taking into account multiple classification criteria, such as population sizing strategy and population structure =-=[60]-=-. Both DE and PSO can adopt a static (constant) or dynamic population size [61]–[65]; howbeit, they differ in terms of population structure as DE originally does not differentiate population topologie... |

18 |
An effective hybrid optimization strategy for jobshop scheduling problems
- Wang, Zheng
- 2001
(Show Context)
Citation Context ...r performance. In contrast, MA-S2 employs a biased roulette wheel scheme to bias the choice of LSs by accumulated knowledge on the performance of each LS candidate. 6) GASA Proposed by Wang and Zheng =-=[25]-=-: GA⊕SA (simulated annealing) 〈C,P,S,D〉: [HOLH], [HOOH], [deterministic static alternation], [homogeneous TIT], [TTI:〈S〉, GA 〈x〉⇀↽ 〈x〉 SA]. XIN et al.: HYBRIDIZING DIFFERENTIAL EVOLUTION AND PARTICLE ... |

18 |
A Combined Swarm Differential Evolution Algorithm for Optimization Problems
- Hendtlass
(Show Context)
Citation Context ...and PSO as the parents of DEPSO. As a burgeoning optimizer, DEPSO has shown its prominent advantage and prosperity, which are witnessed by the diversity of DEPSO variants and their applications [28], =-=[72]-=-–[126]. Besides, DEPSO has been further hybridized with other optimizers, giving birth to more complicated hybrids [127]–[129]. In the past decade, many scholars have made contributions to DEPSO resea... |

16 |
Metaheuristics in combinatorial optimization
- Gendreau, Potvin
(Show Context)
Citation Context ...ybrid optimizers. A. Tradeoff Between Exploration and Exploitation Exploration and exploitation are also referred to as diversification (breadth first) and intensification (depth first), respectively =-=[16]-=-, [148]. In [148], through an extensive investigation of hybrid metaheuristics that are based on EAs, Lozano and Martı́nez concluded that the use of EAs specializing in diversification and intensifica... |

16 | Population size reduction for the differential evolution algorithm - Brest, Maučec - 2008 |

16 |
PSO-based multiobjective optimization with dynamic population size and adaptive local archives
- Leong, Yen
- 2008
(Show Context)
Citation Context ..., taking into account multiple classification criteria, such as population sizing strategy and population structure [60]. Both DE and PSO can adopt a static (constant) or dynamic population size [61]–=-=[65]-=-; howbeit, they differ in terms of population structure as DE originally does not differentiate population topologies. Greistorfer and Voβ proposed a “pool” template to cover diverse classes of metahe... |

15 |
Differential evolution vs. the functions of the 2nd ICEO
- Price
- 1997
(Show Context)
Citation Context ...e also used in the literature. 1) DE/current-to-best/1(DE/target-to-best/1) [30], [37] zi = xi + λ · (xbest − xi) ︸ ︷︷ ︸ base +F · (xr1 − xr2) ︸ ︷︷ ︸ individual difference . (4) 2) DE/mid-to-better/1 =-=[38]-=-, [39] zi = (xi + xbetter)/2 + λ · (xbetter − xi) ︸ ︷︷ ︸ base +F · (xr1 − xr2) ︸ ︷︷ ︸ individual difference . (5) Here, xbetter is an individual that is randomly selected from the DE population, and i... |

14 | A unified view on hybrid metaheuristics
- Raidl, Blum
- 2006
(Show Context)
Citation Context ...ion refers to merging two or more optimization techniques into a single algorithm. In the research field of combinatorial optimization, hybrid optimizers are also termed as hybrid metaheuristics [15]–=-=[18]-=-. In the past decade, hybrid optimizers have attracted persistent attention from scholars that are interested in design of optimizers and their applications [11]–[18]. As Raidl claimed in his unified ... |

14 |
A particle swarm optimization algorithm with differential evolution
- Hao, Guo, et al.
- 2007
(Show Context)
Citation Context ... used in the literature. 1) DE/current-to-best/1(DE/target-to-best/1) [30], [37] zi = xi + λ · (xbest − xi) ︸ ︷︷ ︸ base +F · (xr1 − xr2) ︸ ︷︷ ︸ individual difference . (4) 2) DE/mid-to-better/1 [38], =-=[39]-=- zi = (xi + xbetter)/2 + λ · (xbetter − xi) ︸ ︷︷ ︸ base +F · (xr1 − xr2) ︸ ︷︷ ︸ individual difference . (5) Here, xbetter is an individual that is randomly selected from the DE population, and its fit... |

14 |
Hybrid particle swarm with differential evolution for multimodal image registration
- Talbi, Batouche
(Show Context)
Citation Context ...ui,d = { zi,d , if randdi ≤ CR or d == rni pbesti,d , otherwise (9) where the denotations are the same as those in (2) and (3). DEPSO-ZX has been successfully applied in multimodal image registration =-=[74]-=-, modeling of gene regulatory networks [75], structure optimization of a high-temperature superconducting cable [76], and design of finite-impulse response filters [77]. Besides, DEPSO-ZX was even fur... |

13 | Efficient population utilization strategy for particle swarm optimizer - Hsieh, T, et al. - 2009 |

11 | Special Issue on Memetic Algorithm - Ong, Krasnogor, et al. - 2007 |

11 |
Hybridizing particle swarm optimization with differential evolution for constrained numerical and engineering optimization
- Liu, Cai, et al.
(Show Context)
Citation Context ...sis issue of mechanics parameters in engineering projects. Other analogs of DEPSO-ZX include the DEPSO-LCW proposed by Liu et al. to handle constrained numerical and engineering optimization problems =-=[81]-=-, and the DEPSO-XXW proposed by Xu et al. for partitional clustering [82]. In [83], a similar scheme of evolution of the personal experience of particles (pbest) by DE is proposed (the resultant DEPSO... |

9 |
Modeling of gene regulatory networks with hybrid differential evolution and particle swarm optimization
- Xu, Venayagamoorthy, et al.
(Show Context)
Citation Context ...pbesti,d , otherwise (9) where the denotations are the same as those in (2) and (3). DEPSO-ZX has been successfully applied in multimodal image registration [74], modeling of gene regulatory networks =-=[75]-=-, structure optimization of a high-temperature superconducting cable [76], and design of finite-impulse response filters [77]. Besides, DEPSO-ZX was even further hybridized with PSO and ES to form a m... |

9 |
Differential evolution particle swarmoptimization for digital filter design
- Luitel, Venayagamoorthy
- 2008
(Show Context)
Citation Context ...n multimodal image registration [74], modeling of gene regulatory networks [75], structure optimization of a high-temperature superconducting cable [76], and design of finite-impulse response filters =-=[77]-=-. Besides, DEPSO-ZX was even further hybridized with PSO and ES to form a more complicated hybrid [128], [129]. In [78], Moore and Venayamoorthy proposed a DEPSO (namely DEPSO-MV), which shares the sa... |

9 |
Evolving digital circuit using hybrid particle swarm optimizaiton and differential evolution
- Moore, Venayagamoorthy
- 2006
(Show Context)
Citation Context ...rature superconducting cable [76], and design of finite-impulse response filters [77]. Besides, DEPSO-ZX was even further hybridized with PSO and ES to form a more complicated hybrid [128], [129]. In =-=[78]-=-, Moore and Venayamoorthy proposed a DEPSO (namely DEPSO-MV), which shares the same idea with DEPSO-ZX, but its DE and PSO parents are DE/rand/2/bin and a modified PSO with “Ring” topology, respective... |

8 |
Evolution strategies: a family of nonlinear optimization techniques based on imitating some principles of organic evolution
- Schwefel
- 1984
(Show Context)
Citation Context ...astic optimizers have good performance in global optimization. In the family of stochastic optimizers, well-known typical optimizers include the genetic algorithm (GA) [2], evolutionary strategy (ES) =-=[3]-=- (CMA-ES [4] in particular), evolutionary programming (EP) [5], simulated annealing (SA) [6], ant-colony optimization (ACO) [7], particle swarm optimization (PSO) [8], differential evolution (DE) [9],... |

8 | Mean and variance of the sampling distribution of particle swarm optimizers during stagnation
- Poli
- 2009
(Show Context)
Citation Context ... generation scheme to approximate the distribution [52]. Poli analyzed the sampling distribution of a classical PSO with the assumption of stagnation and used it to explain the search behavior of PSO =-=[53]-=-. Particularly, Kennedy proposed a simplified PSO version [named barebones PSO (BBPSO)] with an attempt to more concisely reflect the essence of the PSO paradigm, i.e., the social interaction of indiv... |

8 | Evolving cognitive and social experience in Particle Swarm Optimization through Differential Evolution
- Epitropakis, Vrahatis
(Show Context)
Citation Context ...ZX include the DEPSO-LCW proposed by Liu et al. to handle constrained numerical and engineering optimization problems [81], and the DEPSO-XXW proposed by Xu et al. for partitional clustering [82]. In =-=[83]-=-, a similar scheme of evolution of the personal experience of particles (pbest) by DE is proposed (the resultant DEPSOs are all named DEPSO-EPV); however, DE will only be applied to the personal best ... |

8 |
Super-fit control adaptation in memetic differential evolution frameworks
- Caponio, Neri, et al.
- 2009
(Show Context)
Citation Context ...uns first, and DE/best/2/bin follows to improve the current positions of particles. Caponio et al. designed a DEPSO (namely DEPSO-CNT) by the use of PSO to provide DE a so-called super-fit individual =-=[87]-=-. DEPSO-CNT was established on a DE framework that is hybridized with PSO and two local searchers. PSO works only XIN et al.: HYBRIDIZING DIFFERENTIAL EVOLUTION AND PARTICLE SWARM OPTIMIZATION TO DESI... |

8 | Population-based algorithmportfolios for numerical optimization
- Peng, Tang, et al.
- 2010
(Show Context)
Citation Context ...ce of common individuals. Recently, Peng et al. proposed a general coevolutionary framework, namely population-based algorithm portfolio (PAP), to combine different population-based search algorithms =-=[99]-=-. Four optimizers, which involve a self-adaptive DE and classical PSO, are chosen as candidate parent optimizers to test the efficiency of PAP. Within the PAP framework, parents exchange the elite sol... |

8 |
Differential evolution based particle swarm optimization
- Omran, Engelbrecht, et al.
- 2007
(Show Context)
Citation Context ... as well as modulate particle velocities, and PSO follows to regulate the current positions of particles. DEPSODRKC was employed to maximize camera coverage area in the coordination of robot ants. In =-=[103]-=-, two DEPSOs are presented. The first DEPSO (namely DEPSO-OES1) is somewhat similar to DEPSO-HGH. The DE (DE/rand/1/bin) and PSO (PSO-cf) in it also alternate in a stochastic way, but both DE and PSO ... |

7 | Nonlinear System Control Using Adaptive Neural Fuzzy Networks Based on a Modified Differential Evolution
- Chen
- 2009
(Show Context)
Citation Context ...FERENTIAL EVOLUTION AND PARTICLE SWARM OPTIMIZATION A. Classical Differential Evolution The DE proposed by Storn and Price [9], [30] is a formidable PO, which has been widely applied in practice [30]–=-=[35]-=-. It was established on the framework of GAs and inspired by the Nelder–Mead simplex method [30]. It has three operators— mutation, crossover, and selection—which are similar to GAs. However, the muta... |

7 |
An effective PSO-based hybrid algorithm for multiobjective permutation flow shop scheduling
- Li, Wang, et al.
- 2008
(Show Context)
Citation Context ...t, as mentioned earlier, neither classical DE nor classical PSO employs IMs though there exist several advanced variants of DE and PSO, which incorporate LS techniques as an improvement strategy [67]–=-=[71]-=-. Second, DE takes differential mutation and crossover as its SCM, while the SCM of PSO is a random combination of pbest and nbest. As for the pool, both DE and PSO keep only a pool of pbest informati... |

7 |
Environmental/economic power dispatch using a hybrid multi-objective optimization algorithm
- GONG, ZHANG, et al.
- 2010
(Show Context)
Citation Context ...achieve the final exploitation of promising regions. Gong et al. hybridized DE/best/2/bin with a PSO variant, which removes traditional velocity terms and adopts timevariant acceleration coefficients =-=[89]-=-. Their DEPSO (namely DEPSO-GZQ) was proposed to solve multiobjective environmental/economic power dispatch problems. The motivation behind DEPSO-GZQ is an effective synergy of PSO’s exploration abili... |

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editors. Hybrid Metaheuristics: An Emerging Approach to Optimization, volume 114
- Blum, Blesa, et al.
- 2008
(Show Context)
Citation Context ...ants, which have excellent performance. These variants are based on various improvement strategies. Hybridization is one of the most efficient strategies to improve the performance of many optimizers =-=[11]-=-–[15]. In genetics, hybridization is the process to combine different varieties or species of organisms to create a hybrid (biology). In evolutionary algorithms (EAs), hybridization refers to merging ... |

6 |
A hybrid of cooperative particle swarm optimization and cultural algorithm for neural fuzzy networks and its prediction applications
- Lin, Chen, et al.
- 1982
(Show Context)
Citation Context ...ennedy and Eberhart is also a powerful tool in search and optimization [8]. During the past decade, PSO has been successfully and widely applied in the practice of science and engineering (e.g., [40]–=-=[43]-=-), which demonstrates the superiority of this algorithm. Originally, PSO was inspired by the cooperative behavior of animal groups, such as bird flocks. In PSO, many particles form a swarm, which flie... |

6 | SWAF: Swarm algorithm framework for numerical optimization
- Xie, Zhang
- 2004
(Show Context)
Citation Context ...ariant shares some similarity with the Gbest PSO in terms of the sampling approach. XIN et al.: HYBRIDIZING DIFFERENTIAL EVOLUTION AND PARTICLE SWARM OPTIMIZATION TO DESIGN POWERFUL OPTIMIZERS 747 In =-=[57]-=-, Xie and Zhang proposed a swarm algorithm framework (SWAF) that is realized by agent-based modeling, regarding each individual (agent) as a barebones cognitive architecture, which gains knowledge by ... |

5 | An effective hybrid DE-based algorithm for multi-objective flow shop scheduling with limited buffers - Qian, Wang, et al. |

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A hybrid particle swarm optimization approach with prior crossover differential evolution
- Xu, Gu
- 2009
(Show Context)
Citation Context ... PSO in each generation to change the current positions of particles. Xu and Gu also proposed a collaboration-based DEPSO, namely DEPSO-XG, in which PSO and DE evolve the whole population alternately =-=[85]-=-. In particular, Xu and Gu incorporated the average pbest position and velocity of particles into the velocity regulation of the classical PSO [cf., (10)]. The DE operations in DEPSO-XG involve two po... |

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A Novel PSO-DE-Based Hybrid Algorithm for Global Optimization
- Li, Xue, et al.
- 2008
(Show Context)
Citation Context ...L, employing DE and PSO to evolve their respective subpopulations. Its DE parent (DE/rand/1/bin) and PSO parent (classical Gbest PSO) interact by sharing the global best solution that is found so far =-=[92]-=-, [93]. The same idea was also adopted by Zhang et al. who created a chaotic coevolutionary DEPSO (namely DEPSO-ZZS) [94]. In particular, DEPSO-ZZS employs Tent-map-based chaotic perturbation, which f... |

5 |
Cooperative evolutionary algorithm for space trajectory optimization
- Sentinella, M, et al.
(Show Context)
Citation Context ...ion. Another analog is the DEPSO-SC that is proposed by Sentinella and Casalino, incorporating three EAs, which include the GA, PSO, and DE, to solve spacecraft trajectory optimization problems [96], =-=[97]-=-. The three optimizers work in parallel and, periodically, let their best individuals migrate to other subpopulations. Yang et al. hybridized a quantum-behaved PSO with DE/rand/2/bin to create a coevo... |

4 | Evolutionary tristate pso for strategic bidding of pumped-storage hydroelectric plant - Kanakasabapathy, Swarup - 2010 |

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A differential free point generation scheme in the differential evolution algorithm
- Ali, Fatti
(Show Context)
Citation Context ...uct the sampling probability distribution from which the next population is generated [51]. Regarding the sampling distribution of DE and PSO, several scholars have conducted some pioneering research =-=[52]-=-–[55]. Ali et al. derived the probability distribution of trial points in DE and proposed a point generation scheme to approximate the distribution [52]. Poli analyzed the sampling distribution of a c... |

4 | Self-adaptive population sizing for a tune-free differential evolution,” Soft Computing – A Fusion of Foundations - Teng, Teo, et al. - 2009 |

4 | Memetic compact differential evolution for cartesian robot control - Neri, Mininno - 2010 |

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Combined Hybrid Differential Particle Swarm Optimization Approach for Economic Dispatch Problems
- Ramesh, Jayabarathi, et al.
(Show Context)
Citation Context ...re, the DE algorithm is DE/rand/1/bin, and the PSO algorithm is a variant of the Gbest PSO. A very similar DEPSO (namely DEPSO-RJAMB) was proposed by Ramesh et al. to solve economic dispatch problems =-=[73]-=-. Its DE and PSO parents share and update the current positions of particles in their respective manners. Ramesh et al. claimed that DEPSORJAMB combines the vibrancy and explorative nature of PSO with... |

3 |
Designing neural networks using hybrid particle swarm optimization
- Liu, Wang, et al.
- 2005
(Show Context)
Citation Context ...-ZX, but its DE and PSO parents are DE/rand/2/bin and a modified PSO with “Ring” topology, respectively. DEPSO-MV is used in the multiobjective optimization of combinational logic circuits design. In =-=[79]-=-, a DEPSO (namely DEPSO-LWJH) that is similar to DEPSO-ZX is proposed and it is used to train artificial neural networks. Like DEPSO-ZX, the PSO in this hybrid is also based on the Gbest model. Differ... |

3 |
Clustering with differential evolution particle swarm optimization
- Xu, Xu, et al.
- 2010
(Show Context)
Citation Context ...of DEPSO-ZX include the DEPSO-LCW proposed by Liu et al. to handle constrained numerical and engineering optimization problems [81], and the DEPSO-XXW proposed by Xu et al. for partitional clustering =-=[82]-=-. In [83], a similar scheme of evolution of the personal experience of particles (pbest) by DE is proposed (the resultant DEPSOs are all named DEPSO-EPV); however, DE will only be applied to the perso... |

3 |
Hybrid evolutionary algorithm for the optimization of interplanetary trajectories
- Sentinella, M, et al.
(Show Context)
Citation Context ...evolution. Another analog is the DEPSO-SC that is proposed by Sentinella and Casalino, incorporating three EAs, which include the GA, PSO, and DE, to solve spacecraft trajectory optimization problems =-=[96]-=-, [97]. The three optimizers work in parallel and, periodically, let their best individuals migrate to other subpopulations. Yang et al. hybridized a quantum-behaved PSO with DE/rand/2/bin to create a... |

3 |
Cultural algorithmbased quantum-behaved particle swarm optimization
- Yang, Maginu, et al.
- 2010
(Show Context)
Citation Context ... et al. hybridized a quantum-behaved PSO with DE/rand/2/bin to create a coevolutionary DEPSO (namely DEPSO-YMN) in which the DE parent evolves elite individuals and the PSO evolves common individuals =-=[98]-=-. The evolution of common individuals is guided by the pbest of elite solutions, while the DE-based evolution of elites contains the perturbation based on the difference of common individuals. Recentl... |

2 | Hybridizing metaheuristics: The road to success in problem solving,” in 6th Eur - Voβ - 2006 |

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Differential evolution: A survey of the state of the art
- Das, Suganthan
- 2011
(Show Context)
Citation Context ... may result in good optimization effectiveness [9]. In addition, there are many advanced DE variants, which are based on the dynamic tuning of this parameter (e.g., [36] and [37], see also the survey =-=[32]-=- on DE for more introduction). After mutation, a binominal (bin) crossover operates on the vector zi and the target vector xi to generate the final vector ui in the following way: ui,d = { zi,d , if r... |

2 | Timetable synchronization of mass rapid transit system using multiobjective evolutionary approach - Kwan, Chang - 2008 |

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A unified optimization framework for population-based methods
- Sun, Zhao, et al.
- 2008
(Show Context)
Citation Context ...ultiple solutions in parallel. Sun et al. pointed out that the essence of population-based optimizers is to construct the sampling probability distribution from which the next population is generated =-=[51]-=-. Regarding the sampling distribution of DE and PSO, several scholars have conducted some pioneering research [52]–[55]. Ali et al. derived the probability distribution of trial points in DE and propo... |

2 |
The particle swarm as collaborative sampling of the search space
- Kennedy
- 2007
(Show Context)
Citation Context ...he sampling probability distribution from which the next population is generated [51]. Regarding the sampling distribution of DE and PSO, several scholars have conducted some pioneering research [52]–=-=[55]-=-. Ali et al. derived the probability distribution of trial points in DE and proposed a point generation scheme to approximate the distribution [52]. Poli analyzed the sampling distribution of a classi... |

2 |
Self-adaptive barebones differential evolution
- Omran, Engelbrecht, et al.
- 2007
(Show Context)
Citation Context ...ng approach still encompasses the collaborative interaction of population members [55]. Omran et al. borrowed the idea of Kennedy’s BBPSO to design a self-adaptive barebones DE based on DE/rand/1/bin =-=[56]-=-. The base vector and individual difference of DE/rand/1/bin are taken as the mean and standard deviation of the Gaussian sampling distribution for the barebones DE, respectively. In terms of the samp... |

2 |
Controlled pool maintenance for metaheuristics,” in Metaheuristic Optimization via Memory and Evolution
- Greistorfer, Voß
- 2005
(Show Context)
Citation Context ... differ in terms of population structure as DE originally does not differentiate population topologies. Greistorfer and Voβ proposed a “pool” template to cover diverse classes of metaheuristics [18], =-=[66]-=-. The template uses the metaphor of “pool” to describe the set of candidate solutions that are possibly chosen as ingredients for subsequent recombination methods or as start solutions for improvement... |

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Robust optimization in HTS cable based on DEPSO and design for six sigma
- Wang, Liu, et al.
- 2008
(Show Context)
Citation Context ...2) and (3). DEPSO-ZX has been successfully applied in multimodal image registration [74], modeling of gene regulatory networks [75], structure optimization of a high-temperature superconducting cable =-=[76]-=-, and design of finite-impulse response filters [77]. Besides, DEPSO-ZX was even further hybridized with PSO and ES to form a more complicated hybrid [128], [129]. In [78], Moore and Venayamoorthy pro... |

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The back analysis of mechanics parameters based on DEPSO algorithm and parallel
- Huang, Wei, et al.
- 2009
(Show Context)
Citation Context ...est/1/bin. In particular, DEPSO-LWJH adopts a chaotic LS to improve its local exploitation ability. Huang et al. also adopted the same hybridization strategy to design their DEPSO (namely DEPSO-HWLR) =-=[80]-=-. Besides, DEPSO-HWLR incorporates the technique of the parallel finite-element method (PFEM) to address the back-analysis issue of mechanics parameters in engineering projects. Other analogs of DEPSO... |

2 |
Multistage inventory hybrid intelligent optimization under grey fuzzy uncertainty
- Liu, Huang, et al.
- 2006
(Show Context)
Citation Context ...o the personal best positions, which have been improved as compared with previous generation. Liu et al. used DE to perturb the positions of particles with the purpose of keeping population diversity =-=[84]-=-. In their DEPSO (namely DEPSO-LHTC), DE follows PSO in each generation to change the current positions of particles. Xu and Gu also proposed a collaboration-based DEPSO, namely DEPSO-XG, in which PSO... |

2 |
Differential evolution based particle swarm optimizer for neural network learning
- Ning, Zhang, et al.
- 2008
(Show Context)
Citation Context ...pbestki , d PS and vkd = ∑P S i = 1 vk i , d PS . Ning et al. introduced differential mutation operator into a basic PSO in order to alleviate the so-called premature convergence of the classical PSO =-=[86]-=-. At each generation of their DEPSO (namely DEPSO-NZL) [86], PSO runs first, and DE/best/2/bin follows to improve the current positions of particles. Caponio et al. designed a DEPSO (namely DEPSO-CNT)... |

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Inserting information sharing mechanism of PSO to improve the convergence of DE
- Ali, Pant, et al.
- 2009
(Show Context)
Citation Context ...ptimal drive design for a direct current motor and the design of a digital filter. Ali et al. also proposed a two-phase DEPSO (namely DEPSO-APA) in which DE mainly in charge of exploration runs first =-=[88]-=-. DEPSO-APA will switch from DE/rand/1/bin to basic PSO (Gbest topology) according to a predefined threshold for the identification of DE’s convergence. Once the fitness difference of the best and wor... |

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Hybridizing PSO and DE for improved vector evaluated multi-objective optimization
- Grobler, Engelbrecht
- 2009
(Show Context)
Citation Context ...multiobjective space, is utilized to differentiate the quality of nondominated solutions. Grobler and Engelbrecht also proposed a DEPSO, namely DEPSO-GE, to solve multiobjective optimization problems =-=[90]-=-. Like DEPSO-GZQ, the DE and PSO parents of DEPSO-GE also interact via an external archive. However, they are assigned different objectives to optimize. Another DEPSO for multiobjective optimization i... |

2 |
A novel hybrid particle swarm optimization for multi-objective problems
- Jiang, Cai
- 2009
(Show Context)
Citation Context ...-GE also interact via an external archive. However, they are assigned different objectives to optimize. Another DEPSO for multiobjective optimization is the DEPSO-JC that is proposed by Jiang and Cai =-=[91]-=-, employing PSO and DE as regeneration methods. A new acceptance rule that is called distance/volume fitness was proposed to update the external archive of the multiobjective DEPSO. Niu and Li propose... |

2 |
Design of T–S fuzzy model based on PSODE algorithm
- Niu, Li
- 2008
(Show Context)
Citation Context ...loying DE and PSO to evolve their respective subpopulations. Its DE parent (DE/rand/1/bin) and PSO parent (classical Gbest PSO) interact by sharing the global best solution that is found so far [92], =-=[93]-=-. The same idea was also adopted by Zhang et al. who created a chaotic coevolutionary DEPSO (namely DEPSO-ZZS) [94]. In particular, DEPSO-ZZS employs Tent-map-based chaotic perturbation, which follows... |

2 |
Chaotic co-evolutionary algorithm based on differential evolution and particle swarm optimization
- Zhang, Zhang, et al.
- 2009
(Show Context)
Citation Context ...l Gbest PSO) interact by sharing the global best solution that is found so far [92], [93]. The same idea was also adopted by Zhang et al. who created a chaotic coevolutionary DEPSO (namely DEPSO-ZZS) =-=[94]-=-. In particular, DEPSO-ZZS employs Tent-map-based chaotic perturbation, which follows both DE (DE/current-to-best/1/bin) and PSO (Gbest) to update DE individuals and particle positions, respectively. ... |

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Research on hybrid PSODE with triple populations based on multiple differential evolutionary models
- Wang, Yang, et al.
- 2010
(Show Context)
Citation Context ...rticle positions, respectively. Wang et al. also proposed a similar DEPSO (namely DEPSO-WYZ), which maintains three subpopulations that are evolved, respectively, by classical PSO and two DE variants =-=[95]-=-. The three subpopulations share the global best solution during their evolution. Another analog is the DEPSO-SC that is proposed by Sentinella and Casalino, incorporating three EAs, which include the... |

2 |
Diploid hybrid particle swarm optimization with differential evolution for open vehicle routing problem
- Hu, Wu
- 2010
(Show Context)
Citation Context ...he homogeneous parallel hybridization of any parent optimizer. Peng et al. also pointed out that the complementarity of parents is a key issue to ensure the superior performance of their PAP [99]. In =-=[100]-=-, a novel coevolutionary DEPSO (namely DEPSOHW) is proposed based on diploid genetic theory to solve the open vehicle routing problem. In DEPSO-HW, PSO evolves the so-called dominant chromosomes, whil... |

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A hybrid optimization method of particle swarm optimization and cultural algorithm
- Wu, Gao, et al.
- 2010
(Show Context)
Citation Context ...o opposite subpopulations. Wu et al. proposed a distinctive coevolutionary DEPSO (namely DEPSO-WGHZ) by introducing the mutation operator of DE within the framework of the cultural algorithm into PSO =-=[101]-=-. The average fitness of all particles is utilized to divide the whole swarm into two subpopulations, which are evolved, respectively, by PSO and DE [101]. The DE parent of DEPSO-WGHZ resembles DE/ran... |

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An evolutionary SPDE breeding-based hybrid particle swarm optimizer: application in coordination of robot ants for camera coverage area optimization
- De, Ray, et al.
- 2005
(Show Context)
Citation Context ...component of the global best position gbest at the kth generation, and it is required that the fitness of xr1 is not worse than that of xi . The DEPSO that is designed by De et al. (namely DEPSODRKC) =-=[102]-=- combined the self-adaptive Pareto DE that is proposed by Abbass et al. [131] and a basic PSO with random inertia weight. In the evolutionary loop of DEPSO-DRKC, DE operates on some selected dimension... |

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An integrated method of particle swarm optimization and differential evolution
- Kim, Lee
- 2009
(Show Context)
Citation Context ...ts current position (DE or PSO). Besides, the probability of selecting an updating method and the scaling factor in DE are dynamic and adaptive. A similar DEPSO (DEPSO-KL) was proposed by Kim and Lee =-=[104]-=-. At each generation, each individual selects the updating method of its current position, either PSO-cf or DE/best/1/bin, according to a predefined probability. Kim and Lee also employed the reinforc... |