Efficiency Enhancement of Estimation of Distribution Algorithms

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Martin Pelikan

Economy & Finance Education

Efficiency Enhancement of Estimation of Distribution Algorithms

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Estimation of distribution algorithms (EDAs) are stochastic optimization techniques that explore the space of potential solutions by building and sampling explicit probabilistic models of promising candidate solutions. While the primary goal of applying EDAs is to discover the global optimum or at least its accurate approximation, besides this, any EDA provides us with a sequence of probabilistic models, which in most cases hold a great deal of information about the problem. Although using problem-specific knowledge has been shown to significantly improve performance of EDAs and other evolutionary algorithms, this readily available source of problem-specific information has been practically ignored by the EDA community. This paper takes the first step towards the use of probabilistic models obtained by EDAs to speed up the solution of similar problems in future. More specifically, we propose two approaches to biasing model building in the hierarchical Bayesian optimization algorithm (hBOA) based on knowledge automatically learned from previous hBOA runs on similar problems. We show that the proposed methods lead to substantial speedups and argue that the methods should work well in other applications that require solving a large number of problems with similar structure.

Using Previous Models to Bias Structural Learning in the Hierarchical BOA

Martin Pelikan

This paper proposes the incremental Bayesian optimization algorithm (iBOA), which modifies standard BOA by removing the population of solutions and using incremental updates of the Bayesian network. iBOA is shown to be able to learn and exploit unrestricted Bayesian networks using incremental techniques for updating both the structure as well as the parameters of the probabilistic model. This represents an important step toward the design of competent incremental estimation of distribution algorithms that can solve difficult nearly decomposable problems scalably and reliably.

iBOA: The Incremental Bayesian Optimization Algorithm

Martin Pelikan

Initial-Population Bias in the Univariate Estimation of Distribution Algorithm

Martin Pelikan

An automated technique has recently been proposed to transfer learning in the hierarchical Bayesian optimization algorithm (hBOA) based on distance-based statistics. The technique enables practitioners to improve hBOA efficiency by collecting statistics from probabilistic models obtained in previous hBOA runs and using the obtained statistics to bias future hBOA runs on similar problems. The purpose of this paper is threefold: (1) test the technique on several classes of NP-complete problems, including MAXSAT, spin glasses and minimum vertex cover; (2) demonstrate that the technique is effective even when previous runs were done on problems of different size; (3) provide empirical evidence that combining transfer learning with other efficiency enhancement techniques can often yield nearly multiplicative speedups.

Transfer Learning, Soft Distance-Based Bias, and the Hierarchical BOA

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Using Problem-Specific Knowledge and Learning from Experience in Estimation o...

Martin Pelikan

The hierarchical Bayesian optimization algorithm (hBOA) can solve nearly decomposable and hierarchical problems of bounded difficulty in a robust and scalable manner by building and sampling probabilistic models of promising solutions. This paper analyzes probabilistic models in hBOA on two common test problems: concatenated traps and 2D Ising spin glasses with periodic boundary conditions. We argue that although Bayesian networks with local structures can encode complex probability distributions, analyzing these models in hBOA is relatively straightforward and the results of such analyses may provide practitioners with useful information about their problems. The results show that the probabilistic models in hBOA closely correspond to the structure of the underlying optimization problem, the models do not change significantly in subsequent iterations of BOA, and creating adequate probabilistic models by hand is not straightforward even with complete knowledge of the optimization problem.

Analyzing Probabilistic Models in Hierarchical BOA on Traps and Spin Glasses

Martin Pelikan

This work studies the utility of using substructural neighborhoods for local search in the Bayesian optimization algorithm (BOA). The probabilistic model of BOA, which automatically identifies important problem substructures, is used to define the structure of the neighborhoods used in local search. Additionally, a surrogate fitness model is considered to evaluate the improvement of the local search steps. The results show that performing substructural local search in BOA significatively reduces the number of generations necessary to converge to optimal solutions and thus provides substantial speedups.

The Bayesian Optimization Algorithm with Substructural Local Search

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It has been shown that model building in the hierarchical Bayesian optimization algorithm (hBOA) can be efficiently parallelized by randomly generating an ancestral ordering of the nodes of the network prior to learning the network structure and allowing only dependencies consistent with the generated ordering. However, it has not been thoroughly shown that this approach to restricting probabilistic models does not affect scalability of hBOA on important classes of problems. This presentation demonstrates that although the use of a random ancestral ordering restricts the structure of considered models to allow efficient parallelization of model building, its effects on hBOA performance and scalability are negligible.

Order Or Not: Does Parallelization of Model Building in hBOA Affect Its Scala...

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Probabilistic model-building algorithms (PMBGAs), also called estimation of distribution algorithms (EDAs) and iterated density estimation algorithms (IDEAs), replace traditional variation of genetic and evolutionary algorithms by (1) building a probabilistic model of promising solutions and (2) sampling the built model to generate new candidate solutions. PMBGAs are also known as estimation of distribution algorithms (EDAs) and iterated density-estimation algorithms (IDEAs). Replacing traditional crossover and mutation operators by building and sampling a probabilistic model of promising solutions enables the use of machine learning techniques for automatic discovery of problem regularities and exploitation of these regularities for effective exploration of the search space. Using machine learning in optimization enables the design of optimization techniques that can automatically adapt to the given problem. There are many successful applications of PMBGAs, for example, Ising spin glasses in 2D and 3D, graph partitioning, MAXSAT, feature subset selection, forest management, groundwater remediation design, telecommunication network design, antenna design, and scheduling. This tutorial provides a gentle introduction to PMBGAs with an overview of major research directions in this area. Strengths and weaknesses of different PMBGAs will be discussed and suggestions will be provided to help practitioners to choose the best PMBGA for their problem. The video of this tutorial presented at GECCO-2008 can be found at http://medal.cs.umsl.edu/blog/?p=293

Estimation of Distribution Algorithms Tutorial

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Using Previous Models to Bias Structural Learning in the Hierarchical BOA

iBOA: The Incremental Bayesian Optimization Algorithm

Initial-Population Bias in the Univariate Estimation of Distribution Algorithm

Transfer Learning, Soft Distance-Based Bias, and the Hierarchical BOA

Using Problem-Specific Knowledge and Learning from Experience in Estimation o...

Analyzing Probabilistic Models in Hierarchical BOA on Traps and Spin Glasses

The Bayesian Optimization Algorithm with Substructural Local Search

Order Or Not: Does Parallelization of Model Building in hBOA Affect Its Scala...

Estimation of Distribution Algorithms Tutorial

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This paper proposes a hybrid genetic algorithm to perform image segmentation based on applying the q-state Potts spin glass model to a grayscale image. First, the image is converted to a set of weights for a q-state spin glass and then a steady-state genetic algorithm is used to evolve candidate segmented images until a suitable candidate solution is found. To speed up the convergence to an adequate solution, hierarchical local search is used on each evaluated solution. The results show that the hybrid genetic algorithm with hierarchical local search is able to efficiently perform image segmentation. The necessity of hierarchical search for these types of problems is also clearly demonstrated.

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For many optimization problems it is possible to define a distance metric between problem variables that correlates with the likelihood and strength of interactions between the variables. For example, one may define a metric so that the dependencies between variables that are closer to each other with respect to the metric are expected to be stronger than the dependencies between variables that are further apart. The purpose of this paper is to describe a method that combines such a problem-specific distance metric with information mined from probabilistic models obtained in previous runs of estimation of distribution algorithms with the goal of solving future problem instances of similar type with increased speed, accuracy and reliability. While the focus of the paper is on additively decomposable problems and the hierarchical Bayesian optimization algorithm, it should be straightforward to generalize the approach to other model-directed optimization techniques and other problem classes. Compared to other techniques for learning from experience put forward in the past, the proposed technique is both more practical and more broadly applicable.

Distance-based bias in model-directed optimization of additively decomposable...

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The linkage tree genetic algorithm (LTGA) identifies linkages between problem variables using an agglomerative hierarchical clustering algorithm and linkage trees. This enables LTGA to solve many decomposable problems that are difficult with more conventional genetic algorithms. The goal of this paper is two-fold: (1) Present a thorough empirical evaluation of LTGA on a large set of problem instances of additively decomposable problems and (2) speed up the clustering algorithm used to build the linkage trees in LTGA by using a pairwise and a problem-specific metric. http://medal.cs.umsl.edu/files/2011001.pdf

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This study focuses on the problem of finding ground states of random instances of the Sherrington-Kirkpatrick (SK) spin-glass model with Gaussian couplings. While the ground states of SK spin-glass instances can be obtained with branch and bound, the computational complexity of branch and bound yields instances of not more than about 90 spins. We describe several approaches based on the hierarchical Bayesian optimization algorithm (hBOA) to reliably identifying ground states of SK instances intractable with branch and bound, and present a broad range of empirical results on such problem instances. We argue that the proposed methodology holds a big promise for reliably solving large SK spin-glass instances to optimality with practical time complexity. The proposed approaches to identifying global optima reliably can also be applied to other problems and they can be used with many other evolutionary algorithms. Performance of hBOA is compared to that of the genetic algorithm with two common crossover operators.

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We discuss the computational complexity of random 2D Ising spin glasses, which represent an interesting class of constraint satisfaction problems for black box optimization. Two extremal cases are considered: (1) the +/- J spin glass, and (2) the Gaussian spin glass. We also study a smooth transition between these two extremal cases. The computational complexity of all studied spin glass systems is found to be dominated by rare events of extremely hard spin glass samples. We show that complexity of all studied spin glass systems is closely related to Frechet extremal value distribution. In a hybrid algorithm that combines the hierarchical Bayesian optimization algorithm (hBOA) with a deterministic bit-flip hill climber, the number of steps performed by both the global searcher (hBOA) and the local searcher follow Frechet distributions. Nonetheless, unlike in methods based purely on local search, the parameters of these distributions confirm good scalability of hBOA with local search. We further argue that standard performance measures for optimization algorithms---such as the average number of evaluations until convergence---can be misleading. Finally, our results indicate that for highly multimodal constraint satisfaction problems, such as Ising spin glasses, recombination-based search can provide qualitatively better results than mutation-based search.

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