This paper studies fitness inheritance as an efficiency enhancement technique for a class of competent genetic algorithms called estimation distribution algorithms. Probabilistic models of important sub-solutions are developed to estimate the fitness of a proportion of individuals in the population, thereby avoiding computationally expensive function evaluations. The effect of fitness inheritance on the convergence time and population sizing are modeled and the speed-up obtained through inheritance is predicted. The results show that a fitness-inheritance mechanism which utilizes information on building-block fitnesses provides significant efficiency enhancement. For additively separable problems, fitness inheritance reduces the number of function evaluations to about half and yields a speed-up of about 1.75–2.25.

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 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. Categories and Subject Descriptors

We propose a sub-structural niching method that fully exploits the problem decomposition capability of linkagelearning methods such as the estimation distribution algorithms and concentrate on maintaining diversity at the sub-structural level. The proposed method consists of three key components: (1) Problem decomposition and sub-structure identification, (2) sub-structure fitness estimation, and (3) sub-structural niche preservation. The substructural niching method is compared to restricted tournament selection (RTS)—a niching method used in hierarchical Bayesian optimization algorithm—with special emphasis on sustained preservation of multiple global solutions of a class of boundedly-difficult, additively-separable multimodal problems. The results show that sub-structural niching successfully maintains multiple global optima over large number of generations and does so with significantly less population than RTS. Additionally, the market share of each of the niche is much closer to the expected level in sub-structural niching when compared to RTS.

Genetic algorithms (GAs) are search methods based on principles of natural selection and genetics (Fraser, 1957; Bremermann, 1958; Holland, 1975). We start with a brief introduction to simple genetic algorithms and associated terminology. GAs encode

Efficiency enhancement techniques—such as parallelization and hybridization—are among the most important ingredients of practical applications of genetic and evolutionary algorithms and that is why this research area represents an important niche of evolutionary computation. This paper describes and analyzes sporadic model building, which can be used to enhance the efficiency of the hierarchical Bayesian optimization algorithm (hBOA) and other estimation of distribution algorithms (EDAs) that use complex multivariate probabilistic models. With sporadic model building, the structure of the probabilistic model is updated once in every few iterations (generations), whereas in the remaining iterations, only model parameters (conditional and marginal probabilities) are updated. Since the time complexity of updating model parameters is much lower than the time complexity of learning the model structure, sporadic model building decreases the overall time complexity of model building. The paper shows that for boundedly difficult nearly decomposable and hierarchical optimization problems, sporadic model building leads to a significant model-building speedup, which decreases the asymptotic time complexity of model building in hBOA by a factor of Θ(n 0.26) to Θ(n 0.5), where n is the problem size. On the other hand, sporadic model building also increases the number of evaluations until convergence; nonetheless, if model building is the bottleneck, the evaluation slowdown is insignificant compared to the gains in the asymptotic complexity of model building. The paper also presents a dimensional model to provide a heuristic for scaling the structurebuilding period, which is the only parameter of the proposed sporadic model-building approach. The paper then tests the proposed method and the rule for setting the structure-building period on the problem of finding ground states of 2D and 3D Ising spin glasses.

Abstract. This paper presents two different efficiency-enhancement techniques for probabilistic model building genetic algorithms. The first technique proposes the use of a mutation operator which performs local search in the sub-solution neighborhood identified through the probabilistic model. The second technique proposes building and using an internal probabilistic model of the fitness along with the probabilistic model of variable interactions. The fitness values of some offspring are estimated using the probabilistic model, thereby avoiding computationally expensive function evaluations. The scalability of the aforementioned techniques are analyzed using facetwise models for convergence time and population sizing. The speed-up obtained by each of the methods is predicted and verified with empirical results. The results show that for additively separable problems the competent mutation operator requires O ( √ k log m)—where k is the building-block size, and m is the number of building blocks—less function evaluations than its selectorecombinative counterpart. The results also show that the use of an internal probabilistic fitness model reduces the required number of function evaluations to as low as 1-10 % and yields a speed-up of 2–50. 1

The paper presents an evaluation-relaxation scheme where a fitness surrogate automatically adapts to the problem structure and the partial contributions of subsolutions to the fitness of an individual are estimated efficiently and accurately. In particular, the probabilistic model built by extended compact genetic algorithm is used to infer the structural form of the surrogate and a least squares method is used to estimate the coefficients of the surrogate. Using the surrogate avoids the need for expensive fitness evaluation for some of the solutions, and thereby yields significant efficiency enhancement. Results show that a surrogate, which automatically adapts to problem knowledge mined from probabilistic models, yields substantial speedup (1.75–3.1) on a class of boundedly-difficult additively-decomposable problems with and without additive Gaussian noise. The speedup provided by the surrogate increases with the number of substructures, substructure complexity, and noise-to-signal ratio.

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.

One benefit of using probabilistic model-building genetic algorithms is the possibility of creating cheap and accurate surrogate models. Learning classifier systems—and genetics-based machine learning in general—can greatly benefit from such surrogates which can replace the costly matching procedure of a rule against large data sets. In this paper we investigate the accuracy of such surrogate fitness function when coupled with the probabilistic models evolved by the χ-ary extended compact classifier system (χeCCS). We present results showing how functional alignment between the probabilistic model of χeCCS and the surrogate fitness is required. We also present a transformation of populations of rules based on the dependency structure matrix genetic algorithm (DSMGA) that allows building accurate models of overlapping building blocks—a necessary condition to accurately estimate the fitness of the evolved rules. 1

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