Analyzing probabilistic models in hierarchical BOA on traps and spin glasses

Hauschild, Mark W.; Pelikán, Martin; Lima, Cláudio F.; Sastry, Kumara

doi:10.1145/1276958.1277070

Cited by 34 publications

(36 citation statements)

References 29 publications

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“…Truncation selection for n = 201 needs a population size of N = 90000 compared to N = 1900 with SDS! For all other problems truncation selection is numerically more efficient (see also the discussion of the importance of selection in Hauschild et al (2007)). In any case, the numerical determined sample size is N ∈ O(n) at most.…”

Section: Discussionmentioning

confidence: 99%

“…He observes that MN-EDA f is by far the best algorithm among the algorithm he compared. For BOA and hBOA the scaling of the sample size and the number of function evaluations has been intensively investigated by Pelikan and his coworkers (Pelikan and Goldberg, 2006;Pelikan and Hartmann, 2006;Hauschild et al, 2007). But even in very good experimental work sometimes unjustified conclusions are made.…”

Section: Discussionmentioning

confidence: 99%

“…Recently an investigation of the networks computed by the successor program hBOA appeared in Hauschild et al (2007). hBOA generates sparser networks than BOA.…”

Section: Investigation Of the Learned Bayesian Networkmentioning

confidence: 99%

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Convergence Theorems of Estimation of Distribution Algorithms

Mühlenbein

2012

Adaptation, Learning, and Optimization

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Estimation of Distribution Algorithms (EDAs) have been proposed as an extension of genetic algorithms. We assume that the function to be optimized is additively decomposed (ADF). The interaction graph of the ADF is used to create exact or approximate factorizations of the Boltzmann distribution. Convergence of the algorithm MN-GIBBS is proven. MN-GIBBS uses a Markov network easily derived from the ADF and Gibbs sampling. The Factorized Distribution Algorithm (FDA) uses a less general representation , a Bayesian network and probabilistic logic sampling (PLS). We shortly describe the algorithm LFDA which learns a Bayesian network from data. The relation between the network computed by LFDA and the optimal network used by FDA is investigated. Convergence of FDA to the optima is shown for finite samples if the factorization fulfills the running intersection property. The sample size is bounded by O(nm ln nm) where n is the size of the problem and m the number of sub-functions. For the proof results from statistical learning theory and Probably Approximately Correct (PAC) learning are used. Numerical experiments show that even for difficult test functions a sample size which scales linearly with n is often sufficient. We also show that a good approximation of the true distribution is not necessary, it suffices to use a factorization where the global optima have a large enough probability. This explains the success of EDAs in practical applications.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

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Convergence Theorems of Estimation of Distribution Algorithms

Mühlenbein

2012

Adaptation, Learning, and Optimization

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“…Some parts of model structure have been called unnecessary if they are undesirable with the aim of minimizing model complexity [8] and maximizing mixing [18] or if the structure discovered by the probabilistic graphical model is surplus to accurate modeling of the fitness function [15]. In our work, we argue that structure is unnecessary when the same ordering of solutions could be maintained without it.…”

Section: Necessary Walsh Structurementioning

confidence: 94%

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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“…It is known that not all interactions which are present in a problem will necessarily be required in the model for the algorithm to rank individuals by fitness and find a global optimum. This observation is related to the concepts of necessary and unnecessary interactions [19] and benign and malign interactions [23]. This is also related to spurious correlations [45], false relationships in the model resulting from selection.…”

Section: Model Structurementioning

confidence: 99%

The Markov Network Fitness Model

Brownlee

McCall

Shakya

2012

Adaptation, Learning, and Optimization

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Fitness modelling is an area of research which has recently received much interest among the evolutionary computing community. Fitness models can improve the efficiency of optimisation through direct sampling to generate new solutions, guiding of traditional genetic operators or as surrogates for a noisy or long-running fitness functions. In this chapter we discuss the application of Markov networks to fitness modelling of black-box functions within evolutionary computation, accompanied by discussion on the relationship between Markov networks and Walsh analysis of fitness functions. We review alternative fitness modelling and approximation techniques and draw comparisons with the Markov network approach. We discuss the applicability of Markov networks as fitness surrogates which may be used for constructing guided operators or more general hybrid algorithms. We conclude with some observations and issues which arise from work conducted in this area so far.

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Analyzing probabilistic models in hierarchical BOA on traps and spin glasses

Cited by 34 publications

References 29 publications

Convergence Theorems of Estimation of Distribution Algorithms

Convergence Theorems of Estimation of Distribution Algorithms

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

The Markov Network Fitness Model

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