By Maurice Clerc (auth.), Bijaya Ketan Panigrahi, Yuhui Shi, Meng-Hiot Lim (eds.)

ISBN-10: 3642173896

ISBN-13: 9783642173899

ISBN-10: 364217390X

ISBN-13: 9783642173905

From nature, we detect swarming habit within the type of ant colonies, chicken flocking, animal herding, honey bees, swarming of micro organism, and plenty of extra. it is just lately that researchers have taken detect of such usual swarming structures as fruits of a few type of innate collective intelligence, albeit swarm intelligence (SI) - a metaphor that conjures up a myriad of computational problem-solving concepts. In computational intelligence, swarm-like algorithms were effectively utilized to unravel many real-world difficulties in engineering and sciences. This guide quantity serves as an invaluable foundational in addition to consolidatory state-of-art number of articles within the box from quite a few researchers all over the world. It has a wealthy number of contributions concerning the theoretical and empirical examine of unmarried and multi-objective variations of swarm intelligence dependent algorithms like particle swarm optimization (PSO), ant colony optimization (ACO), bacterial foraging optimization algorithm (BFOA), honey bee social foraging algorithms, and harmony search (HS). With chapters describing quite a few purposes of SI concepts in real-world engineering difficulties, this guide could be a precious source for researchers and practitioners, giving an in-depth taste of what SI is in a position to achieving.

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Proceeding in the same way we can deduce the system of differential equations for the second order moments: ⎞ ⎞ ⎛ ⎛ Var (x (t)) Var (x (t)) d ⎝ Cov (x (t) , x (t)) ⎠ = Aσ ⎝ Cov (x (t) , x (t)) ⎠ + bσ (t) , (11) dt Var (x (t)) Var (x (t)) where and ⎞ 0 2 0 ⎠, Aσ = ⎝ −φ ω − 1 1 0 −2φ 2 (ω − 1) ⎛ ⎞ 0 bσ (t) = ⎝ φ Cov (x (t) , o (t)) ⎠ . 2φ Cov (x (t) , o (t)) ⎛ Thus, bσ (t) includes the statistical similarity functions between processes x (t) , x (t) and the oscillation center o (t). The second order trajectories will depend on the type of eigenvalues of matrix Aσ and on the similarity functions E (x (t) o (t)) and E (x (t) o (t)) .

Each station mk has two coordinates (mk,1 , mk,2 ). These are the 2M variables of the problem. e. (i, j) , i ∈ {0, 1, . . , 100} , j ∈ {0, 1, . . , 100}. On each lattice point, the field induced by the station mk is given by fi,j,mk = 2 1 2 (i − mk,1 ) + (j − mk,2 ) + 1 (34) and we want to have at least one field that is not too weak. Finally, the function to be minimised is 1 f = 100 100 (35) i=1 j=1 maxk (fi,j,mk ) In this chapter, we set M = 10 . Therefore the dimension of the problem is 20.

Actually, for this simplified problem, more efficient methods do exist (Delaunay’s tesselation, for example), but those can not be used as soon as we introduce a third dimension and more constraints. 32 M. Clerc D Results Table 3. Results with the PSO variants discussed in this chapter. In each cell, we have the mean best value over 100 runs (including the values for Rosenbrock, although it is questionable as shown in E), the success rate if not null, and the mean number of fitness evaluations if the success rate is 100%.

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Handbook of Swarm Intelligence: Concepts, Principles and Applications by Maurice Clerc (auth.), Bijaya Ketan Panigrahi, Yuhui Shi, Meng-Hiot Lim (eds.)

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