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We propose a new method based on discrete Fourier analysis to analyze the time evolutionary algorithms spend on plateaus. This immediately gives a concise proof of the classic estimate of the expected runtime of the $(1+1)$ evolutionary…
We give a detailed analysis of the cost used by the (1+1)-evolutionary algorithm. The problem has been approached in the evolutionary algorithm literature under various views, formulation and degree of rigor. Our asymptotic approximations…
Convolutional highways are deep networks based on multiple stacked convolutional layers for feature preprocessing. We introduce an evolutionary algorithm (EA) for optimization of the structure and hyperparameters of convolutional highways…
We consider the evolutionary trajectories traced out by an infinite population undergoing mutation-selection dynamics in static, uncorrelated random fitness landscapes. Starting from the population that consists of a single genotype, the…
An important question in evolutionary computation is how good solutions evolutionary algorithms can produce. This paper aims to provide an analytic analysis of solution quality in terms of the relative approximation error, which is defined…
The $(1+(\lambda,\lambda))$ genetic algorithm is a bright example of an evolutionary algorithm which was developed based on the insights from theoretical findings. This algorithm uses crossover, and it was shown to asymptotically outperform…
In evolution theory the concept of a fitness landscape has played an important role, evolution itself being portrayed as a hill-climbing process on a rugged landscape. In this article it is shown that in general, in the presence of other…
When a problem instance is perturbed by a small modification, one would hope to find a good solution for the new instance by building on a known good solution for the previous one. Via a rigorous mathematical analysis, we show that…
We consider the evolution of large but finite populations on arbitrary fitness landscapes. We describe the evolutionary process by a Markov, Moran process. We show that to $\mathcal O(1/N)$, the time-averaged fitness is lower for the finite…
In this paper, the monotone submodular maximization problem (SM) is studied. SM is to find a subset of size $\kappa$ from a universe of size $n$ that maximizes a monotone submodular objective function $f$. We show using a novel analysis…
How fast does a population evolve from one fitness peak to another? We study the dynamics of evolving, asexually reproducing populations in which a certain number of mutations jointly confer a fitness advantage. We consider the time until a…
We investigate the evolutionary dynamics of a finite population of sequences adapting to NK fitness landscapes. We find that, unlike in the case of an infinite population, the average fitness in a finite population is maximized at a small…
One of the first and easy to use techniques for proving run time bounds for evolutionary algorithms is the so-called method of fitness levels by Wegener. It uses a partition of the search space into a sequence of levels which are traversed…
Functional effects of different mutations are known to combine to the total effect in highly nontrivial ways. For the trait under evolutionary selection (`fitness'), measured values over all possible combinations of a set of mutations yield…
We present the first parameterized analysis of a standard (1+1) Evolutionary Algorithm on a distribution of vertex cover problems. We show that if the planted cover is at most logarithmic, restarting the (1+1) EA every $O(n \log n)$ steps…
Optimization problem, nowadays, have more application in all major but they have problem in computation. Calculation of the optimum point in the spaces with the above dimensions is very time consuming. In this paper, there is presented a…
We introduce a new parameter to discuss the behavior of a genetic algorithm. This parameter is the mean number of exact copies of the best fit chromosomes from one generation to the next. We argue that the genetic algorithm should operate…
We analyse the performance of well-known evolutionary algorithms (1+1)EA and (1+$\lambda$)EA in the prior noise model, where in each fitness evaluation the search point is altered before evaluation with probability $p$. We present refined…
The $(1 + (\lambda,\lambda))$ genetic algorithm is a younger evolutionary algorithm trying to profit also from inferior solutions. Rigorous runtime analyses on unimodal fitness functions showed that it can indeed be faster than classical…
Evolutionary algorithms are well suited for solving the knapsack problem. Some empirical studies claim that evolutionary algorithms can produce good solutions to the 0-1 knapsack problem. Nonetheless, few rigorous investigations address the…