A fully multivariate DEUM algorithm

Shakya, Siddhartha; Brownlee, Alexander E. I.; McCall, John; Fournier, Francois A.; Owusu, Gilbert

doi:10.1109/cec.2009.4982984

Cited by 19 publications

(15 citation statements)

References 27 publications

(45 reference statements)

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“…This section describes the equivalence between the weights of a HEDA and the second order Walsh coefficients. The important finding is that the weights of an exhaustively trained HEDA, W are equal to the second order Walsh coefficients, as stated in equation 23.…”

Section: Analysis Of Network Weightsmentioning

confidence: 99%

“…The connections in the BMDA are conditional probabilities, making the model more akin to a Bayesian network, whereas the HEDA structure is more like that of a Markov Random Field. A recent example of a high order EDA can be found in the multi-variate DEUM model, [23]. DEUM performs distribution estimation using Markov random fields (MRF).…”

Section: Comparison With Other Edasmentioning

confidence: 99%

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An Analysis of the Local Optima Storage Capacity of Hopfield Network Based Fitness Function Models

Swingler

Smith

2014

Transactions on Computational Collective Intelligence XVII

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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.

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Section: Analysis Of Network Weightsmentioning

confidence: 99%

Section: Comparison With Other Edasmentioning

confidence: 99%

An Analysis of the Local Optima Storage Capacity of Hopfield Network Based Fitness Function Models

Swingler

Smith

2014

Transactions on Computational Collective Intelligence XVII

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“…Listing the ranks for a function f gives the class C f as in Eqn. 16. Two functions, f and g, are said to be rank-…”

Section: Rank-equivalence Classesmentioning

confidence: 99%

“…EDAs such as the DEUM algorithm [16] use a Markov random field (MRF) model based on Walsh coefficients. This is an appropriate representation because any fitness function on bit strings may be rewritten using the Walsh-Hadamard transform, and the non-zero Walsh coefficients are indicative of the structure of the function [6].…”

Section: Walsh-hadamard Transformmentioning

confidence: 99%

Minimal walsh structure and ordinal linkage of monotonicity-invariant function classes on bit strings

Christie

McCall

Lonie

2014

Proceedings of the 2014 Annual Conference on Genetic and Evolutionary Computation

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CopyrightItems in 'OpenAIR@RGU', Robert Gordon University Open Access Institutional Repository, are protected by copyright and intellectual property law. If you believe that any material held in 'OpenAIR@RGU' infringes copyright, please contact openair-help@rgu.ac.uk with details. The item will be removed from the repository while the claim is investigated. ABSTRACTProblem structure, or linkage, refers to the interaction between variables in a black-box fitness function. Discovering structure is a feature of a range of algorithms, including estimation of distribution algorithms (EDAs) and perturbation methods (PMs). The complexity of structure has traditionally been used as a broad measure of problem difficulty, as the computational complexity relates directly to the complexity of structure. The EDA literature describes necessary and unnecessary interactions in terms of the relationship between problem structure and the structure of probabilistic graphical models discovered by the EDA. In this paper we introduce a classification of problems based on monotonicity invariance. We observe that the minimal problem structures for these classes often reveal that significant proportions of detected structures are unnecessary. We perform a complete classification of all functions on 3 bits. We consider nonmonotonicity linkage discovery using perturbation methods and derive a concept of directed ordinal linkage associated to optimization schedules. The resulting refined classification factored out by relabeling, shows a hierarchy of nine directed ordinal linkage classes for all 3-bit functions. We show that this classification allows precise analysis of computational complexity and parallelizability and conclude with a number of suggestions for future work.

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“…The most widely known is probably the Bayesian optimization algorithm (BOA) [3], which relies on a Bayesian network to learn the model and sample solutions, but there are more, like DEUM (Distribution Estimation Using Markov network) [5] and dtEDA (dependency-tree EDA) [4]. HMM-EDA is a novel approach which uses a Hidden Markov Model (HMM) [2] as the underlying distribution.…”

mentioning

confidence: 99%

Estimation of distribution algorithm based on hidden Markov models for combinatorial optimization

Gardner

Gagné

Parizeau

2013

Proceedings of the 15th Annual Conference Companion on Genetic and Evolutionary Computation

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Estimation of Distribution Algorithms (EDAs) have been successfully applied to a wide variety of problems. The algorithmic model of EDA is generic and can virtually be used with any distribution model, ranging from the mere Bernoulli distribution to the sophisticated Bayesian network. The Hidden Markov Model (HMM) is a well-known graphical model useful for modelling populations of variable-length sequences of discrete values. Surprisingly, HMMs have not yet been used as distribution estimators for an EDA, even though it is a very powerful tool especially designed for modelling sequences. We thus propose a new method, called HMM-EDA, implementing this idea. Preliminary comparative results on two classical combinatorial optimization problems show that HMM-EDA is indeed a promising approach for problems that have sequential representations. Categories and Subject Descriptors KeywordsEstimation of distribution algorithms; Hidden Markov models; Combinatorial optimization Several graphical models have been used in EDAs. The most widely known is probably the Bayesian optimization algorithm (BOA) [3], which relies on a Bayesian network to learn the model and sample solutions, but there are more, like DEUM (Distribution Estimation Using Markov network) [5] and dtEDA (dependency-tree EDA) [4]. HMM-EDA is a novel approach which uses a Hidden Markov Model (HMM) [2] as the underlying distribution. While its versatility may allow it to model various kinds of distributions, the focus of this work is on combinatorial optimization problems.The proposed approach integrates an HMM in the generic EDA model, using it to directly estimate the distribution of the samples making up the population. Using an HMM for that purpose is quite versatile, as it only assumes that the samples are sequences of discrete values. Such a model should be useful in a wide variety of optimization problems, including problems where solutions can be modelled as bit strings. HMM should be able to capture complex interactions between the elements of sequences, not only the first order relations captured in observable Markov models. Our intuition is that hidden states of the HMM can capture intrinsic sequential patterns that characterize populations, and link these patterns together in various ways to produce better individuals, through transitions between the hidden states.The HMM-EDA algorithm interprets individuals as sequences. Each possible value of the problem's "alphabet" is mapped to a possible observation of the HMM. For instance, with the travelling salesman problem, there would be as many possible observations as the number of cities in the tour. Given that HMMs can easily handle up to several dozens of observable emissions, the implementation is quite straightforward for many problems. The HMM is trained with the best individuals, and then produces a new generation, effectively leading to an offspring population with, hopefully, a better average fitness than the parent population. In the process, the probabilistic nature of the HMM will a...

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A fully multivariate DEUM algorithm

Cited by 19 publications

References 27 publications

An Analysis of the Local Optima Storage Capacity of Hopfield Network Based Fitness Function Models

An Analysis of the Local Optima Storage Capacity of Hopfield Network Based Fitness Function Models

Minimal walsh structure and ordinal linkage of monotonicity-invariant function classes on bit strings

Estimation of distribution algorithm based on hidden Markov models for combinatorial optimization

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