The Gambler's Ruin Problem, Genetic Algorithms, and the Sizing of Populations

Harik, G.R.; Cantú‐Paz, Erick; Goldberg, David E.; Miller, Brad L.

doi:10.1162/evco.1999.7.3.231

Cited by 287 publications

(235 citation statements)

References 2 publications

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“…However, the larger population was necessary to solve the 5-bit trap problem since more samples (chromosomes) were needed to accurately cover each trap block. This observation is consistent with previous work where the necessary population size was shown to increase exponentially with the size of the trap [19,25]. Consequently, the ignorant algorithms would be likely to find the optimum solution if permitted additional fitness function evaluations by an order of magnitude or more.…”

Section: Deceptive Trap Functionssupporting

confidence: 91%

MARLEDA: Effective distribution estimation through Markov random fields

Miikkulainen

Alden

2016

Theoretical Computer Science

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Many problems within the biological sciences, such as DNA sequencing, protein structure prediction, and molecular docking, are being approached computationally. These problems require sophisticated solution methods that understand the complex natures of biological domains. Traditionally, such solution methods are problem specific, but recent advances in generic problem-solvers furnish hope for a new breed of computational tools. The challenge is to develop methods that can automatically learn or acquire an understanding of a complex problem domain.Estimation of Distribution Algorithms (EDAs) are generic search methods that use statistical models to learn the structure of a problem domain.EDAs have been successfully applied to many difficult search problems, such as circuit design, optimizing Ising spin glasses, and various scheduling tasks. Computational biology is a computational science that promises tangible, life-altering benefits. Research in fields such as genomics, protein structure prediction, and molecular docking, finds application in pharmacology and gene therapy. Consequently, day-to-day medicine and health have been improved, with the greatest breakthroughs still to come. These fields directly depend on advances in computer hardware and software, and there is great demand for effective computational problem-solving methods.Research in computational biology produces computational models of real-world objects or phenomena, such as molecular interactions or phylogenetic trees. The computational models can be studied, adjusted, and experimented with to generate predictions about their real-world counterparts. In 2 turn, real-world experiments help form the basis for new computational models. There is an interplay between real-world and computational research; each informs and refines the other. While a computational formulation of real-world problems is useful and convenient, there are drawbacks.The key difficulty of many computational problems, such as DNA sequence alignment, selecting key attributes for data mining, or optimizing antenna design, is that no analytic solution methods exist. There are also problems that do have analytic solutions, but those methods are too computationally expensive to be practical. Without the ability to construct an ideal solution efficiently, we are often reduced to a procedure of guess-and-check.Such a procedure, formally known as search, tries to identity the best solution(s) among a set of candidates by systematically evaluating alternatives.Search algorithms are, in many cases, a relatively easy and effective means of producing near-optimal solutions to difficult problems. However, in complex domains search is often inefficient, taking too long to be practical. This dissertation develops a search method that handles complexity better by statistically modeling the problem domain. ApproachFortunately, even when analytical methods are not available, for many computational problems it is relatively easy to test the "correctness" of a potential solution. For example, t...

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Section: Deceptive Trap Functionssupporting

confidence: 91%

MARLEDA: Effective distribution estimation through Markov random fields

Miikkulainen

Alden

2016

Theoretical Computer Science

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“…However, they assumed that if wrong BBs were chosen in the first generation, the GAs would be unable to recover from the error. Harik, Cantú-Paz, Goldberg, and Miller (Harik, Cantú-Paz, Goldberg, & Miller, 1999) refined the above model by incorporating cumulative effects of decision making over time rather than in first generation only. Harik et al (Harik, Cantú-Paz, Goldberg, & Miller, 1999) modeled the decision making between competing BBs as a gambler's ruin problem.…”

Section: Population-sizing Modelmentioning

confidence: 99%

Let’s Get Ready to Rumble: Crossover Versus Mutation Head to Head

Sastry

Goldberg

2004

Genetic and Evolutionary Computation – GECCO 2004

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This paper analyzes the relative advantages between crossover and mutation on a class of deterministic and stochastic additively separable problems. 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 additively separable deterministic problems, the BB-wise mutation is more efficient than crossover, while the crossover outperforms the mutation on additively separable problems perturbed with additive Gaussian noise. The results show that the speed-up of using BB-wise mutation on deterministic problems is O( √ k log m), where k is the BB size, and m is the number of BBs. Likewise, the speed-up of using crossover on stochastic problems with fixed noise variance is O(m √ k/ log m).

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“…The success of these techniques is based on the maintenance of genetic diversity, for which it is necessary to work with large populations. The population size that guarantees an optimal solution in a short time has been a topic of intense research [2], [3]. Large populations generally converge to better solutions, but they require more computational cost and memory requirements.…”

Section: Introductionmentioning

confidence: 99%

“…They further enhanced the equation which allows accurate statistical decision making among competing building blocks (BBs) [2]. Extending the decision model presented in [2], Harik et al [3] tried to determine an adequate population size which guarantees a solution with the desired quality. To show the real importance of the population size in Evolutionary Algorithms (EAs) He and Yao [5] showed that the introduction of a non random population decreases convergence time.…”

Section: Introductionmentioning

confidence: 99%

An Experimental Comparative Study for Interactive Evolutionary Computation Problems

Sáez

Isasi

Segovia

et al. 2006

Lecture Notes in Computer Science

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Abstract. This paper presents an objective experimental comparative study between four algorithms: the Genetic Algorithm, the Fitness Prediction Genetic Algorithm, the Population Based Incremental Learning algorithm and the purposed method based on the Chromosome Appearance Probability Matrix. The comparative is done with a non subjective evaluation function. The main objective is to validate the efficiency of several methods in Interactive Evolutionary Computation environments. The most important constraint of working within those environments is the user interaction, which affects the results adding time restrictions for the experimentation stage and subjectivity to the validation. The experiments done in this paper replace user interaction with several approaches avoiding user limitations. So far, the results show the efficiency of the purposed algorithm in terms of quality of solutions and convergence speed, two known keys to decrease the user fatigue.

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The Gambler's Ruin Problem, Genetic Algorithms, and the Sizing of Populations

Cited by 287 publications

References 2 publications

MARLEDA: Effective distribution estimation through Markov random fields

MARLEDA: Effective distribution estimation through Markov random fields

Let’s Get Ready to Rumble: Crossover Versus Mutation Head to Head

An Experimental Comparative Study for Interactive Evolutionary Computation Problems

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