Don't Evaluate, Inherit

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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.

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Don't Evaluate, Inherit

Don't Evaluate, Inherit

Don't Evaluate, Inherit

Don't Evaluate, Inherit

Don't Evaluate, Inherit

Don't Evaluate, Inherit

Don't Evaluate, Inherit

Don't Evaluate, Inherit

Don't Evaluate, Inherit

Don't Evaluate, Inherit

Don't Evaluate, Inherit

Don't Evaluate, Inherit

Don't Evaluate, Inherit

Don't Evaluate, Inherit

Don't Evaluate, Inherit

Don't Evaluate, Inherit

Don't Evaluate, Inherit

Don't Evaluate, Inherit

Don't Evaluate, Inherit

Don't Evaluate, Inherit

Don't Evaluate, Inherit

Don't Evaluate, Inherit

Don't Evaluate, Inherit

Don't Evaluate, Inherit

Don't Evaluate, Inherit

Don't Evaluate, Inherit

Don't Evaluate, Inherit

Don't Evaluate, Inherit

Don't Evaluate, Inherit

Don't Evaluate, Inherit

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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(<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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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.

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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 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(k0.5logm)—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.

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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). With sporadic model building, the structure of the probabilistic model is updated once 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 that decreases the asymptotic time complexity of model building in hBOA by a factor of Θ(n0.26) to Θ(n0.65), where n is the problem size. On the other hand, sporadic model building also increases the number of evaluations until convergence; nonetheless, for decomposable problems, the evaluation slowdown is insignificant compared to the gains in the asymptotic complexity of model building.

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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.

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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.

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Ensuring building-block (BB) mixing is critical to the success of genetic and evolutionary algorithms. There has been a growing interest in analyzing and understanding BB mixing and it is necessary to organize and categorize representative literature. This paper presents an exhaustive survey of studies on one or more aspects of mixing. In doing so, a classification of the literature based on the role of recombination operators assumed by those studies is developed. Such a classification not only highlights the significant results and unifies existing work, but also provides a foundation for future research in understanding mixing in genetic algorithms.

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Ensuring building-block (BB) mixing is critical to the success of genetic and evolutionary algorithms. This study develops facetwise models to predict the BB mixing time and the population sizing dictated by BB mixing for single-point crossover. Empirical results are used to validate these models. The population-sizing model suggests that for moderate-to-large problems, BB mixing—instead of BB decision making and BB supply—bounds the population size required to obtain a solution of constant quality. Furthermore, the population sizing for single-point crossover scales as O(2km1.5), where k is the BB size and m is the number of BBs.

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This paper describes a probabilistic model building genetic programming (PMBGP) developed based on the extended compact genetic algorithm (eCGA). Unlike traditional genetic programming, which use fixed recombination operators, the proposed PMBGA adapts linkages. The proposed algorithms, called the extended compact genetic programming (eCGP) adaptively identifies and exchanges non-overlapping building blocks by constructing and sampling probabilistic models of promising solutions. The results show that eCGP scales-up polynomially with the problem size (the number of functionals and terminals) on both GP-easy problem and boundedly difficult GP-hard problem.

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This paper derives a population sizing relationship for genetic programming (GP). Following the population-sizing derivation for genetic algorithms in Goldberg, Deb, and Clark (1992), it considers building block decision making as a key facet. The analysis yields a GP-unique relationship because it has to account for bloat and for the fact that GP solutions often use subsolutions multiple times. The population-sizing relationship depends upon tree size, solution complexity, problem difficulty and building block expression probability. The relationship is used to analyze and empirically investigate population sizing for three model GP problems named ORDER, ON-OFF and LOUD. These problems exhibit bloat to differing extents and differ in whether their solutions require the use of a building block multiple times.

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

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Automated alphabet reduction with evolutionary algorithms for protein structu...

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Fast and accurate reaction dynamics via multiobjective genetic algorithm opti...

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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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Efficient Cluster Optimization Using A Hybrid Extended Compact Genetic Algori...

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Evaluation Relaxation as an Efficiency-Enhancement Technique: Handling Varian...

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Analysis of Mixing in Genetic Algorithms: A Survey

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Analysis of Mixing in Genetic Algorithms: A Survey

Scalability of Selectorecombinative Genetic Algorithms for Problems with Tigh...

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Scalability of Selectorecombinative Genetic Algorithms for Problems with Tigh...

Probabilistic Model Building and Competent Genetic Programming

Probabilistic Model Building and Competent Genetic Programming

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Inducing Sequentiality Using Grammatical Genetic Codes

Inducing Sequentiality Using Grammatical Genetic Codes

Inducing Sequentiality Using Grammatical Genetic Codes

Population Sizing for Genetic Programming Based Upon Decision Making

Population Sizing for Genetic Programming Based Upon Decision Making

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W.D. Gann Theory Complete Information.pdf

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