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An analysis of the local optima storage capacity of Hopfield network based fitness function models

Citation
Swingler K & Smith L (2014) An analysis of the local optima storage capacity of Hopfield network based fitness function models. In: Nguyen N, Kowalczyk R, Fred A & Joaquim F (eds.) Transactions on Computational Collective Intelligence XVII. Lecture Notes in Computer Science, 8790. Berlin Heidelberg: Springer, pp. 248-271. http://link.springer.com/chapter/10.1007/978-3-662-44994-3_13; https://doi.org/10.1007/978-3-662-44994-3_13

Abstract
A Hopfield Neural Network (HNN) with a new weight update rule can be treated as a second order Estimation of Distribution Algorithm (EDA) or Fitness Function Model (FFM) for solving optimisation problems. The HNN models promising solutions and has a capacity for storing a certain number of local optima as low energy attractors. Solutions are generated by sampling the patterns stored in the attractors. The number of attractors a network can store (its capacity) has an impact on solution diversity and, consequently solution quality. This paper introduces two new HNN learning rules and presents the Hopfield EDA (HEDA), which learns weight values from samples of the fitness function. It investigates the attractor storage capacity of the HEDA and shows it to be equal to that known in the literature for a standard HNN. The relationship between HEDA capacity and linkage order is also investigated.

Keywords
Dynamical systems; Hopfield neural networks; Optimization Energy attractors; Fitness function modeling; Fitness functions; Hopfield Networks; Hopfield neural networks (HNN); Optimisation problems; Solution quality; Storage capacity

StatusPublished
Author(s)Swingler, Kevin; Smith, Leslie
Title of seriesLecture Notes in Computer Science
Number in series8790
Publication date31/12/2014
Publication date online30/09/2014
URLhttp://hdl.handle.net/1893/22466
PublisherSpringer
Publisher URLhttp://link.springer.com/…3-662-44994-3_13
Place of publicationBerlin Heidelberg
ISSN of series0302-9743
ISBN978-3-662-44993-6
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