Success in evolutionary computation by Cipriano Galindo, Juan-Antonio Fernández-Madrigal, Javier

By Cipriano Galindo, Juan-Antonio Fernández-Madrigal, Javier Gonzalez

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This also illustrates that our system consists of components that can be expanded or plugged in depending on the specific problem. The population size was decreased to 25 because of the large computational expense of learning and evolution, and the archive in which non-dominated individuals are stored externally in SPEA was set to be the same size as the population. The maximum number of generations was fixed at 50, and all networks trained for 200 epochs with RPROP, a variant of error backpropagation which has been shown to be very effective in previous research [39].

Table 3 summarizes the experimental results. Minimum hidden nodes is the smallest number of hidden nodes found during an experiment, and numbers in the parentheses show the theoretically minimum number of nodes possible In an n-partition problem [SEQUENCE 5_xor [SEQUENCE 5_xor [PARALLEL Input [PARALLEL Input [LAYER in [LAYER in1 [SIZE 2][CONNECT h1 out1]] [NUM_LAYER 5] [LAYER in2 [SIZE 2][CONNECT h1]] [SIZE 2] [LAYER in3 [SIZE 2][CONNECT h2]] [CONNECT [LAYER in4 [SIZE 2][CONNECT h3 out4]] [EVOLVE Hidden Output]]] [LAYER in5 [SIZE 2][CONNECT h4 out5]]] [COLLECTION Hidden [PARALLEL Hidden1 [LAYER h [LAYER h1 [SIZE 5][CONNECT out1 out2]] [PARALLEL Hidden2 [NUM_LAYER [EVOLVE 0 10]] [LAYER h2 [SIZE 2][CONNECT out3]] [SIZE [EVOLVE 1 5]] [LAYER h3 [SIZE 1][CONNECT out4]] [CONNECT [LAYER h4 [SIZE 1][CONNECT out5]]]] [EVOLVE Hidden Output]]]] [PARALLEL Output [PARALLEL Output [LAYER out1 [SIZE 1]] [LAYER out [LAYER out2 [SIZE 1]] [NUM_LAYER 5] [LAYER out3 [SIZE 1]] [SIZE 1]]] [LAYER out4 [SIZE 1]] ] [LAYER out5 [SIZE 1]]]] (a) (b) in1 out1 in2 out2 in3 out3 in4 out4 in5 out5 (c) Fig.

Kitano H (1994) Neurogenetic learning: An integrated method of designing and training neural networks using genetic algorithms. Physica D 75:225–238 30. Koza J, Bennett F, Andre D, Keane M (1999) Genetic Programming III: Darwinian Invention and Problem Solving. Morgan Kaufmann, San Francisco, CA 31. Lehmann KA, Kaufmann M (2005) Evolutionary algorithms for the selforganized evolution of networks. In: GECCO ’05: Proceedings of the 2005 conference on Genetic and evolutionary computation, ACM, New York, NY, USA, pp.

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