Population Sizing for Genetic Programming Based Upon Decision Making

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Population Sizing for Genetic Programming Based Upon Decision Making

Population Sizing for Genetic Programming Based Upon Decision Making

Population Sizing for Genetic Programming Based Upon Decision Making

Population Sizing for Genetic Programming Based Upon Decision Making

Population Sizing for Genetic Programming Based Upon Decision Making

Population Sizing for Genetic Programming Based Upon Decision Making

Population Sizing for Genetic Programming Based Upon Decision Making

Population Sizing for Genetic Programming Based Upon Decision Making

Population Sizing for Genetic Programming Based Upon Decision Making

Population Sizing for Genetic Programming Based Upon Decision Making

Population Sizing for Genetic Programming Based Upon Decision Making

Population Sizing for Genetic Programming Based Upon Decision Making

Population Sizing for Genetic Programming Based Upon Decision Making

Population Sizing for Genetic Programming Based Upon Decision Making

Population Sizing for Genetic Programming Based Upon Decision Making

Population Sizing for Genetic Programming Based Upon Decision Making

Population Sizing for Genetic Programming Based Upon Decision Making

Population Sizing for Genetic Programming Based Upon Decision Making

Population Sizing for Genetic Programming Based Upon Decision Making

Population Sizing for Genetic Programming Based Upon Decision Making

Population Sizing for Genetic Programming Based Upon Decision Making

Population Sizing for Genetic Programming Based Upon Decision Making

Population Sizing for Genetic Programming Based Upon Decision Making

Population Sizing for Genetic Programming Based Upon Decision Making

Population Sizing for Genetic Programming Based Upon Decision Making

Population Sizing for Genetic Programming Based Upon Decision Making

Population Sizing for Genetic Programming Based Upon Decision Making

Population Sizing for Genetic Programming Based Upon Decision Making

Population Sizing for Genetic Programming Based Upon Decision Making

Population Sizing for Genetic Programming Based Upon Decision Making

Population Sizing for Genetic Programming Based Upon Decision Making

Population Sizing for Genetic Programming Based Upon Decision Making

Population Sizing for Genetic Programming Based Upon Decision Making

Population Sizing for Genetic Programming Based Upon Decision Making

Population Sizing for Genetic Programming Based Upon Decision Making

Population Sizing for Genetic Programming Based Upon Decision Making

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Effective and efficient multiscale modeling is essential to advance both the science and synthesis in a wide array of fields such as physics, chemistry, materials science, biology, biotechnology and pharmacology. This study investigates the efficacy and potential of using genetic algorithms for multiscale materials modeling and addresses some of the challenges involved in designing competent algorithms that solve hard problems quickly, reliably and accurately.

Genetic Algorithms and Genetic Programming for Multiscale Modeling

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Genetic Algorithms and Genetic Programming for Multiscale Modeling

This paper presents a highly efficient, fully parallelized implementation of the compact genetic algorithm to solve very large scale problems with millions to billions of variables. The paper presents principled results demonstrating the scalable solution of a difficult test function on instances over a billion variables using a parallel implementation of compact genetic algorithm (cGA). The problem addressed is a noisy, blind problem over a vector of binary decision variables. Noise is added equaling up to a tenth of the deterministic objective function variance of the problem, thereby making it difficult for simple hillclimbers to find the optimal solution. The compact GA, on the other hand, is able to find the optimum in the presence of noise quickly, reliably, and accurately, and the solution scalability follows known convergence theories. These results on noisy problem together with other results on problems involving varying modularity, hierarchy, and overlap foreshadow routine solution of billion-variable problems across the landscape of search problems.

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This paper analyzes the behavior of a selectorecombinative genetic algorithm (GA) with an ideal crossover on a class of random additively decomposable problems (rADPs). Specifically, additively decomposable problems of order k whose subsolution fitnesses are sampled from the standard uniform distribution U[0,1] are analyzed. The scalability of the selectorecombinative GA is investigated for 10,000 rADP instances. The validity of facetwise models in bounding the population size, run duration, and the number of function evaluations required to successfully solve the problems is also verified. Finally, rADP instances that are easiest and most difficult are also investigated.

Empirical Analysis of ideal recombination on random decomposable problems

Empirical Analysis of ideal recombination on random decomposable problems

Empirical Analysis of ideal recombination on random decomposable problems

This paper presents a population-sizing model for the entropy-based model building in genetic algorithms. Specifically, the population size required for building an accurate model is investigated. The effect of the selection pressure on population sizing is also incorporated. The proposed model indicates that the population size required for building an accurate model scales as Θ(m log m), where m is the number of substructures and proportional to the problem size. Experiments are conducted to verify the derivations, and the results agree with the proposed model.

Population sizing for entropy-based model buliding In genetic algorithms

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This paper analyzes the relative advantages between crossover and mutation on a class of deterministic and stochastic additively separable problems with substructures of non-uniform salience. This study assumes that the recombination and mutation operators have the knowledge of the building blocks (BBs) and effectively exchange or search among competing BBs. Facetwise models of convergence time and population sizing have been used to determine the scalability of each algorithm. The analysis shows that for deterministic exponentially-scaled additively separable, problems, the BB-wise mutation is more efficient than crossover yielding a speedup of Θ(l logl), where l is the problem size. For the noisy exponentially-scaled problems, the outcome depends on whether scaling on noise is dominant. When scaling dominates, mutation is more efficient than crossover yielding a speedup of Θ(l logl). On the other hand, when noise dominates, crossover is more efficient than mutation yielding a speedup of Θ(l).

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In this paper, we derive models of the selection pressure in XCS for proportionate (roulette wheel) selection and tournament selection. We show that these models can explain the empirical results that have been previously presented in the literature. We validate the models on simple problems showing that, (i) when the model assumptions hold, the theory perfectly matches the empirical evidence; (ii) when the model assumptions do not hold, the theory can still provide qualitative explanations of the experimental results.

Modeling selection pressure in XCS for proportionate and tournament selection

Modeling selection pressure in XCS for proportionate and tournament selection

Modeling selection pressure in XCS for proportionate and tournament selection

This paper analyzes the scalability of the population size required in XCS to maintain niches that are infrequently activated. Facetwise models have been developed to predict the effect of the imbalance ratio—ratio between the number of instances of the majority class and the minority class that are sampled to XCS—on population initialization, and on the creation and deletion of classifiers of the minority class. While theoretical models show that, ideally, XCS scales linearly with the imbalance ratio, XCS with standard configuration scales exponentially. The causes that are potentially responsible for this deviation from the ideal scalability are also investigated. Specifically, the inheritance procedure of classifiers’ parameters, mutation, and subsumption are analyzed, and improvements in XCS’s mechanisms are proposed to effectively and efficiently handle imbalanced problems. Once the recommendations are incorporated to XCS, empirical results show that the population size in XCS indeed scales linearly with the imbalance ratio.

Modeling XCS in class imbalances: Population sizing and parameter settings

Modeling XCS in class imbalances: Population sizing and parameter settings

Modeling XCS in class imbalances: Population sizing and parameter settings

This paper presents a learning methodology based on a substructural classification model to solve decomposable classification problems. The proposed method consists of three important components: (1) a structural model that represents salient interactions between attributes for a given data, (2) a surrogate model which provides a functional approximation of the output as a function of attributes, and (3) a classification model which predicts the class for new inputs. The structural model is used to infer the functional form of the surrogate and its coefficients are estimated using linear regression methods. The classification model uses a maximally-accurate, least-complex surrogate to predict the output for given inputs. The structural model that yields an optimal classification model is searched using an iterative greedy search heuristic. Results show that the proposed method successfully detects the interacting variables in hierarchical problems, group them in linkages groups, and build maximally accurate classification models. The initial results on non-trivial hierarchical test problems indicate that the proposed method holds promise and have also shed light on several improvements to enhance the capabilities of the proposed method.

Substructrual surrogates for learning decomposable classification problems: i...

Substructrual surrogates for learning decomposable classification problems: i...

Substructrual surrogates for learning decomposable classification problems: i...

This paper analyzes the relative advantages between crossover and mutation on a class of deterministic and stochastic additively separable problems with substructures of non-uniform salience. This study assumes that the recombination and mutation operators have the knowledge of the building blocks (BBs) and effectively exchange or search among competing BBs. Facetwise models of convergence time and population sizing have been used to determine the scalability of each algorithm. The analysis shows that for deterministic exponentially-scaled additively separable, problems, the BB-wise mutation is more efficient than crossover yielding a speedup of Θ(<em>l</em> log<em>l</em>), where <em>l</em> is the problem size. For the noisy exponentially-scaled problems, the outcome depends on whether scaling on noise is dominant. When scaling dominates, mutation is more efficient than crossover yielding a speedup of Θ(<em>l</em> log<em>l</em>). On the other hand, when noise dominates, crossover is more efficient than mutation yielding a speedup of Θ(<em>l</em>).

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Let's get ready to rumble redux: Crossover versus mutation head to head on ex...

Let's get ready to rumble redux: Crossover versus mutation head to head on ex...

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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

Analyzing probabilistic models in hierarchical BOA on traps and spin glasses

Analyzing probabilistic models in hierarchical BOA on traps and spin glasses

In this paper, we derive models of the selection pressure in XCS for proportionate (roulette wheel) selection and tournament selection. We show that these models can explain the empirical results that have been previously presented in the literature. We validate the models on simple problems showing that, (i) when the model assumptions hold, the theory perfectly matches the empirical evidence; (ii) when the model assumptions do not hold, the theory can still provide qualitative explanations of the experimental results.

Modeling selection pressure in XCS for proportionate and tournament selection

Modeling selection pressure in XCS for proportionate and tournament selection

Modeling selection pressure in XCS for proportionate and tournament selection

This paper analyzes the scalability of the population size required in XCS to maintain niches that are infrequently activated. Facetwise models have been developed to predict the effect of the imbalance ratio—ratio between the number of instances of the majority class and the minority class that are sampled to XCS—on population initialization, and on the creation and deletion of classifiers of the minority class. While theoretical models show that, ideally, XCS scales linearly with the imbalance ratio, XCS with standard configuration scales exponentially. The causes that are potentially responsible for this deviation from the ideal scalability are also investigated. Specifically, the inheritance procedure of classifiers’ parameters, mutation, and subsumption are analyzed, and improvements in XCS’s mechanisms are proposed to effectively and efficiently handle imbalanced problems. Once the recommendations are incorporated to XCS, empirical results show that the population size in XCS indeed scales linearly with the imbalance ratio.

Modeling XCS in class imbalances: Population size and parameter settings

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On Extended Compact Genetic Algorithm

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Silicon Cluster Optimization Using Extended Compact Genetic Algorithm

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Silicon Cluster Optimization Using Extended Compact Genetic Algorithm

This paper develops the theory that can enable the design of genetic algorithms and choose the parameters such that the proportion of the best building blocks grow. A practical schema theorem has been used for this purpose and its ramification for the choice of selection operator and parameterization of the algorithm is explored. In particular stochastic universal selection, tournament selection, and truncation selection schemes are employed to verify the results. Results agree with the schema theorem and indicate that it must be obeyed in order to ascertain sustained growth of good building blocks. The analysis suggests that schema theorem alone is insufficient to guarantee the success of a selectorecombinative genetic algorithm.

A Practical Schema Theorem for Genetic Algorithm Design and Tuning

A Practical Schema Theorem for Genetic Algorithm Design and Tuning

A Practical Schema Theorem for Genetic Algorithm Design and Tuning

This study addresses the issue of building-block supply in the initial population. Facetwise models for supply of a single building block as well as for supply of all schemata in a partition have been developed. An estimate for the population size required to ensure the presence of all raw building blocks has been derived using these facetwise models. The facetwise models and the population-sizing estimate are verified with computational results.

On the Supply of Building Blocks

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On the Supply of Building Blocks

This paper studies fitness inheritance as an efficiency enhancement technique for genetic and evolutionary algorithms. Convergence and population-sizing models are derived and compared with experimental results. These models are optimized for greatest speed-up and the optimal inheritance proportion to obtain such a speed-up is derived. Results on OneMax problems show that when the inheritance effects are considered in the population-sizing model, the number of function evaluations are reduced by 20% with the use of fitness inheritance. Results indicate that for a fixed population size, the number of function evaluations can be reduced by 70% using a simple fitness inheritance technique.

Don't Evaluate, Inherit

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Don't Evaluate, Inherit

This paper analyzes the effects of tournament selection with replacement on the convergence time and population sizing for selectorecombinative genetic algorithms. This paper empirically demonstrates that the run duration remains the same and is not affected whether the tournament selection is performed with or without replacement. However, the population size required is more if tournament selection is performed with replacement rather than without replacement to attain the same level of accuracy. An approximate population-sizing model is derived based on apparent added noise for the case of tournament selection with replacement. The proposed model is verified with experimental results.

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