Toward a Theory of Evolution Strategies: On the Benefits of Sex— the (μ/μ, λ) Theory

1995 ◽  
Vol 3 (1) ◽  
pp. 81-111 ◽  
Author(s):  
Hans-Georg Beyer

The multirecombinant (μ/μ, λ) evolution strategy (ES) is investigated for real-valued, N-dimensional parameter spaces. The analysis includes both intermediate recombination and dominant recombination, as well. These investigations are done for the spherical model first. The problem of the optimal population size depending on the parameter space dimension N is solved. A method extending the results obtained for the spherical model to nonspherical success domains is presented. The power of sexuality is discussed and it is shown that this power does not stem mainly from the “combination” of “good properties” of the mates (building block hypothesis) but rather from genetic repair diminishing the influence of harmful mutations. The dominant recombination is analyzed by introduction of surrogate mutations leading to the concept of species. Conclusions for evolutionary algorithms (EAs), including genetic algorithms (GAs), are drawn.

1993 ◽  
Vol 1 (2) ◽  
pp. 165-188 ◽  
Author(s):  
Hans-Georg Beyer

A method for the determination of the progress rate and the probability of success for the Evolution Strategy (ES) is presented. The new method is based on the asymptotical behavior of the χ-distribution and yields exact results in the case of infinite-dimensional parameter spaces. The technique is demonstrated for the (l,+ λ) ES using a spherical model including noisy quality functions. The results are used to discuss the convergence behavior of the ES.


1994 ◽  
Vol 2 (4) ◽  
pp. 381-407 ◽  
Author(s):  
Hans-Georg Beyer

The multimembered evolution strategy (ES) acting on μ parents and λ offspring is analyzed for real-valued, N-dimensional parameter spaces (N ≳ 30). N-dependent progress rate formulas are derived for (1, λ) and (μ, λ) strategies on spherical models. The analytical results obtained are compared with simulation experiments for the (hyper)sphere and the inclined (hyper)plane.


Author(s):  
Steven M. Corns ◽  
Kenneth M. Bryden ◽  
Daniel A. Ashlock

Graph based evolutionary algorithms (GBEAs) are a novel evolutionary optimization technique that utilize population graphing to impose a topology or geography on the evolving solution set. In many cases in nature, the ability of a particular member of a population to mate and reproduce is limited. The factors creating these limits vary widely and include geographical distance, mating rituals, and others. The effect of these factors is to limit the mating pool, reducing the rate of spread of genetic characteristics, and increased diversity within the population. GBEAs mimic these factors resulting in increased diversity within the solution population. When properly tuned to the problem and the size of the population set, GBEAs can result in improved convergence times and a more diverse number of viable solutions. This paper examines the impact of the fitness landscape, population size, and choice of graph on the evolutionary process. In general, it was found that there was an optimal population size and graph combination for each problem. This optimal graph/population was problem dependent.


2020 ◽  
Author(s):  
Arsen Korpetayev

Selection shadow has been the conventional theory of evolution of ageing for decades. I argue that selection shadow is merely a phenomenon by which deleterious mutation will be inevitably passed on if they manifest only after mating. However, to explain prevalence of ageing, the authors of the conventional theory erroneously equated passing on and persistence by interpreting selection shadow as if “selection pressure is decreased after mating” and for the same reason assumed that ageing is deleterious1,2. In their conventional framework, although ageing is assumed to be deleterious, it is immune to natural selection, due to happening after mating i.e. being in the selection shadow. In reality selection pressure still remains after mating in form of the need to feed offspring and so also in form of inter- and intraspecies competition and predation avoidance etc. I show that the conventional selection shadow theory is therefore inconsistent, since shadowed counteracting “positive” mutations will inevitably pass with “negative” mutations, resulting in individuals that do not age. And so, since ageing is assumed to be deleterious in this conventional framework, inevitable non-ageing individuals will outcompete ageing ones in intra- and interspecies competition for similar ecological niches. This way the inconsistency of the conventional theory of selection shadow predicts that non-ageing organisms will prevail, which is not what we observe. Recently, some articles incline towards adaptive theory of ageing i.e. ageing as an advantageous mechanism. However, the ground of such inclination has mostly been reduced competition for food and space between parents and offsprings3,4. I show that ageing allows for increased reproduction rate, while maintaining optimal population size. As a result of promoted reproduction rate, rate of introduced germline mutations is increased, which means faster adaptation. Faster adapting ageing individuals outcompete non-ageing slower adapting individuals that occupy similar ecological niches, inter and intraspecies. Therefore, since ageing is obviously advantageous, this means that all experimental evidence that supported selection shadow theory of ageing5–9, also support the proposed adaptive theory of faster adaptation, the difference is interpretation: investigated pleiotropic muta-tions are not antagonistic after all, and mutation accumulation actually accumulates positive germline ageing mutations. Based on genome analysis10 of the longest living mammal – bowhead whale, I also propose that mutations in DNA repair proteins are a mechanism to tune ageing by natural selection when optimal population size is changed by long lasting shifts in ecosystem, such as new food source. I suggest that DNA repair complexes are purposely of lowered fidelity to allow for somatic mutations to accumulate and so to increase deathrate by ageing leading to faster adaptation.


Author(s):  
Thomas Bäck

So far, the basic knowledge about setting up the parameters of Evolutionary Algorithms stems from a lot of empirical work and few theoretical results. The standard guidelines for parameters such as crossover rate, mutation probability, and population size as well as the standard settings of the recombination operator and selection mechanism were presented in chapter 2 for the Evolutionary Algorithms. In the case of Evolution Strategies and Evolutionary Programming, the self-adaptation mechanism for strategy parameters solves this parameterization problem in an elegant way, while for Genetic Algorithms no such technique is employed. Chapter 6 served to identify a reasonable choice of the mutation rate, but no theoretically confirmed knowledge about the choice of the crossover rate and the crossover operator is available. With respect to the optimal population size for Genetic Algorithms, Goldberg presented some theoretical arguments based on maximizing the number of schemata processed by the algorithm within fixed time, arriving at an optimal size λ* = 3 for serial implementations and extremely small string length [Gol89b]. However, as indicated in section 2.3.7 and chapter 6, it is by no means clear whether the schema processing point of view is appropriately preferred to the convergence velocity investigations presented in section 2.1.7 and chapter 6. As pointed out several times, we prefer the point of view which concentrates on a convergence velocity analysis. Consequently, the search for useful parameter settings of a Genetic Algorithm constitutes an optimization problem by itself, leading to the idea of using an Evolutionary Algorithm on a higher level to evolve optimal parameter settings of Genetic Algorithms. Due to the existence of two logically different levels in such an approach, it is reasonable to call it a meta-evolutionary algorithm. By concentrating on meta-evolution in this chapter, we will radically deviate from the biological model, where no two-level evolution process is to be observed but the self-adaptation principle can well be identified (as argued in chapter 2). However, there are several reasons why meta-evolution promises to yield some helpful insight into the working principles of Evolutionary Algorithms: First, meta-evolution provides the possibility to test whether the basic heuristic and the theoretical knowledge about parameterizations of Genetic Algorithms is also evolvable by the experimental approach, thus allowing us to confirm the heuristics or to point at alternatives.


2017 ◽  
Vol 25 (2) ◽  
pp. 237-274 ◽  
Author(s):  
Dirk Sudholt

We reinvestigate a fundamental question: How effective is crossover in genetic algorithms in combining building blocks of good solutions? Although this has been discussed controversially for decades, we are still lacking a rigorous and intuitive answer. We provide such answers for royal road functions and OneMax, where every bit is a building block. For the latter, we show that using crossover makes every ([Formula: see text]+[Formula: see text]) genetic algorithm at least twice as fast as the fastest evolutionary algorithm using only standard bit mutation, up to small-order terms and for moderate [Formula: see text] and [Formula: see text]. Crossover is beneficial because it can capitalize on mutations that have both beneficial and disruptive effects on building blocks: crossover is able to repair the disruptive effects of mutation in later generations. Compared to mutation-based evolutionary algorithms, this makes multibit mutations more useful. Introducing crossover changes the optimal mutation rate on OneMax from [Formula: see text] to [Formula: see text]. This holds both for uniform crossover and k-point crossover. Experiments and statistical tests confirm that our findings apply to a broad class of building block functions.


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