Theory Of Evolutionary Algorithms Research Articles

Theory of (1+1) ES on SPHERE Revisited

The theory of evolutionary algorithms on continuous space gravitates around the evolution strategy with one individual, adaptive mutation and elitist selection, optimizing the symmetric, quadratic SPHERE function. The classic, normal mutation theory consists of three main building-blocks: i) a two-term formula for the local (constant mutation) expected progress; ii) an exponential formula for the global behavior of the (adaptive mutation) algorithm; iii) linear convergence time with respect to both space dimension n and (logarithm of) initial distance to optimum. We show that the three main results still hold if we replace the normal mutation with uniform inside the sphere and also with the sum of two uniforms. That makes the case for an important conclusion: the linear convergence time of the algorithm is not a consequence of the normal mutation, but of the elitist selection and 1/5 success rule. A simplified version of the 1/5-rule allows also for an intuitive representation of the algorithm, as a sequence of constant-mutation, independent and identical (expected) length cycles.

A Survey on Recent Progress in the Theory of Evolutionary Algorithms for Discrete Optimization

The theory of evolutionary computation for discrete search spaces has made significant progress since the early 2010s. This survey summarizes some of the most important recent results in this research area. It discusses fine-grained models of runtime analysis of evolutionary algorithms, highlights recent theoretical insights on parameter tuning and parameter control, and summarizes the latest advances for stochastic and dynamic problems. We regard how evolutionary algorithms optimize submodular functions, and we give an overview over the large body of recent results on estimation of distribution algorithms. Finally, we present the state of the art of drift analysis, one of the most powerful analysis technique developed in this field.

Modeling SELEX for regulatory regions using Royal Road and Royal Staircase fitness functions

The field of evolutionary algorithms (EAs) emerged in the area of computer science due to transfer of ideas from biology and developed independently for several decades, enriched with techniques from probability theory, complexity theory and optimization methods. In this paper, we consider some recent results form the EAs theory transferred back into biology. The well-known biotechnological procedure SELEX (Systematic Evolution of Ligands by EXponential enrichment) is viewed as an experimental implementation of an evolutionary algorithm. Theoretical bounds on EAs runtime are applied to model SELEX search for a regulatory region consisting of promoter and enhancer sequences. A comparison of theoretical bounds to the results of computational simulation indicates some cases where the theoretical bounds give favorable prediction, while simulation requires prohibitive computational resource.

A Tight Runtime Analysis for the $${(\mu + \lambda )}$$ EA

Despite significant progress in the theory of evolutionary algorithms, the theoretical understanding of evolutionary algorithms which use non-trivial populations remains challenging and only few rigorous results exist. Already for the most basic problem, the determination of the asymptotic runtime of the $(\mu+\lambda)$ evolutionary algorithm on the simple OneMax benchmark function, only the special cases $\mu=1$ and $\lambda=1$ have been solved. In this work, we analyze this long-standing problem and show the asymptotically tight result that the runtime $T$, the number of iterations until the optimum is found, satisfies \[E[T] = \Theta\bigg(\frac{n\log n}{\lambda}+\frac{n}{\lambda / \mu} + \frac{n\log^+\log^+ \lambda/ \mu}{\log^+ \lambda / \mu}\bigg),\] where $\log^+ x := \max\{1, \log x\}$ for all $x > 0$. The same methods allow to improve the previous-best $O(\frac{n \log n}{\lambda} + n \log \lambda)$ runtime guarantee for the $(\lambda+\lambda)$~EA with fair parent selection to a tight $\Theta(\frac{n \log n}{\lambda} + n)$ runtime result.

A spatially explicit evolutionary algorithm for the spatial partitioning problem

Spatial optimization seeks optimal allocation or arrangement of spatial units under constraints such as distance, adjacency, contiguity, and pattern. Evolutionary Algorithms (EAs) are well-known optimization heuristics. However, classic EAs, based on a binary problem encoding and bit-operation-based offspring operators, are spatially unaware and do not capture topological and geometric relationships. Unsurprisingly when spatial characteristics are not explicitly considered in the design of EA operators, that EA becomes ineffective because satisfying spatial constraints is computationally expensive. We design and develop novel spatially explicit EA recombination operators, inspired by the path relinking and ejection chain heuristic strategies, that implement crossover and mutation using intelligently guided strategies in a spatially constrained decision space. Our spatial EA approach is general and slots well into the foundational theory of evolutionary algorithms for spatial optimization. We demonstrate improved solution quality and computational performance with a large-scale spatial partitioning application.

Spatiotemporal Subpixel Geographical Evolution Mapping

In recent decades, spatiotemporal subpixel mapping (SSM) approaches have been extensively developed to deal with the mixed-pixel problem by incorporating fine spatial resolution images with the same field of view from different acquisition times. This is an alternative to the conventional subpixel mapping (SPM) method, which is based on only monotemporal images. SSM has become one of the state-of-the-art SPM approaches, and has been widely applied in urban management and ecological monitoring. However, in the traditional SSM methods, the spatial correlation within the multitemporal images is insufficiently exploited and is ignored in the spatiotemporal model construction. In addition, the contribution of the land covers' spatial distribution in the multitemporal images is incompletely considered, and the geographic variation during the time interval is ignored, which underutilizes the spatiotemporal information. In this paper, an SSM algorithm based on a geographically weighted regression (GWR) model and evolutionary algorithm theory, called spatiotemporal subpixel geographical evolution mapping (STGEM), is proposed for multitemporal remote sensing images. The proposed algorithm considers the spatiotemporal dependence not only between the current subpixel and the corresponding fine pixel, but also with the neighboring fine distribution patterns within the fine image. Moreover, the potential temporal information of the geospatial variation is fully realized by considering not only the time interval between the bitemporal images, but also the ratio of changed area between them, based on the GWR model. Two synthetic-image experiments with bitemporal Landsat 8 images and bitemporal QuickBird images were carried out to validate the proposed algorithm. Furthermore, a real-image experiment using a bitemporal pair of Gaofen-2 images and a Landsat 8 image was also undertaken. A comparison was made with several traditional SPM methods, as well as the state-of-the-art SSM approaches, and the experimental results confirmed the superiority of the proposed STGEM algorithm. The proposed STGEM achieves a fine spatial and temporal resolution thematic map, both qualitatively and quantitatively, and has great potential for fine-scale and frequent time-series observation and monitoring.

Estimates from evolutionary algorithms theory applied to gene design

Estimates from evolutionary algorithms theory applied to gene design

Review of "Special Issue on Theory of Evolutionary Algorithms"

Review of "Special Issue on Theory of Evolutionary Algorithms"

Models of Performance of Evolutionary Program Induction Algorithms Based on Indicators of Problem Difficulty

Modeling the behavior of algorithms is the realm of evolutionary algorithm theory. From a practitioner's point of view, theory must provide some guidelines regarding which algorithm/parameters to use in order to solve a particular problem. Unfortunately, most theoretical models of evolutionary algorithms are difficult to apply to realistic situations. However, in recent work (Graff and Poli, 2008, 2010), where we developed a method to practically estimate the performance of evolutionary program-induction algorithms (EPAs), we started addressing this issue. The method was quite general; however, it suffered from some limitations: it required the identification of a set of reference problems, it required hand picking a distance measure in each particular domain, and the resulting models were opaque, typically being linear combinations of 100 features or more. In this paper, we propose a significant improvement of this technique that overcomes the three limitations of our previous method. We achieve this through the use of a novel set of features for assessing problem difficulty for EPAs which are very general, essentially based on the notion of finite difference. To show the capabilities or our technique and to compare it with our previous performance models, we create models for the same two important classes of problems-symbolic regression on rational functions and Boolean function induction-used in our previous work. We model a variety of EPAs. The comparison showed that for the majority of the algorithms and problem classes, the new method produced much simpler and more accurate models than before. To further illustrate the practicality of the technique and its generality (beyond EPAs), we have also used it to predict the performance of both autoregressive models and EPAs on the problem of wind speed forecasting, obtaining simpler and more accurate models that outperform in all cases our previous performance models.

Cellular Harmony Search for Optimization Problems

Structured population in evolutionary algorithms (EAs) is an important research track where an individual only interacts with its neighboring individuals in the breeding step. The main rationale behind this is to provide a high level of diversity to overcome the genetic drift. Cellular automata concepts have been embedded to the process of EA in order to provide a decentralized method in order to preserve the population structure. Harmony search (HS) is a recent EA that considers the whole individuals in the breeding step. In this paper, the cellular automata concepts are embedded into the HS algorithm to come up with a new version called cellular harmony search (cHS). In cHS, the population is arranged as a two-dimensional toroidal grid, where each individual in the grid is a cell and only interacts with its neighbors. The memory consideration and population update are modified according to cellular EA theory. The experimental results using benchmark functions show that embedding the cellular automata concepts with HS processes directly affects the performance. Finally, a parameter sensitivity analysis of the cHS variation is analyzed and a comparative evaluation shows the success of cHS.

Analysis Method of Crack Propagation Data by Genetic Algorithms

A practice for analyzing some raw data from fatigue crack growth tests, carried out on specimens obtained from a railway component (wheel), is presented. Despite the data sample is small, it allows to identify the material parameters of the “threshold” propagation model that make this latter amazingly realistic for the examined material. The proposed analysis method is based on the Evolutionary Algorithms theory and uses raw data obtained from C(T) specimens instrumented with crack gauges.

Theory of Evolutionary Computation

Evolutionary algorithms are general-purpose randomized search heuristics. They have been successfully applied to many different kinds of search and optimization problems. They are popular in practice since they are easy to implement and easy to apply, and yet often find good solutions in reasonable time. This lead to an increased interest in gaining a thorough understanding of their strengths (and limitations). In the past decades, the theory of evolutionary algorithms has become an important and accepted field of research. This special issue Theory of Evolutionary Computation of Algorithmica contains expanded research from the theory track of the Genetic and Evolutionary Computation Conference and the International Conference on Parallel Problem Solving From Nature. All papers have been enhanced, extended, and undergone a critical journal reviewing process. The result is a collection of seven papers that all deal with theoretical aspects of evolutionary computation in a rigorous and accessible way. It contributes to the development of a better understanding of evolutionary algorithms, paving the way for a more informed application of these algorithms. Ten years after the first publication of a run-time analysis of the most simple evolutionary algorithm, the (1 + 1) evolutionary algorithm, Jens Jagerskupper reconsiders the result. By using the drift analysis method introduced by He and Yao in a sophisticated way, he obtains much more precise bounds on the expected optimization time. Drift analysis is also the topic of Pietro S. Oliveto’s and Carsten Witt’s article. They present a theorem that yields exponential lower bounds on the expected op-

Drift analysis and average time complexity of evolutionary algorithms

The computational time complexity is an important topic in the theory of evolutionary algorithms (EAs). This paper reports some new results on the average time complexity of EAs. Based on drift analysis, some useful drift conditions for deriving the time complexity of EAs are studied, including conditions under which an EA will take no more than polynomial time (in problem size) to solve a problem and conditions under which an EA will take at least exponential time (in problem size) to solve a problem. The paper first presents the general results, and then uses several problems as examples to illustrate how these general results can be applied to concrete problems in analyzing the average time complexity of EAs. While previous work only considered (1+1) EAs without any crossover, the EAs considered in this paper are fairly general, which use a finite population, crossover, mutation, and selection.

Theory of evolutionary algorithms: a bird's eye view

In this paper we consider the most important questions, research topics and technical tools used in various branches of evolutionary algorithms. The road map we give is to facilitate the readers’ orientation in evolutionary computation theory. In the meanwhile, this survey provides key references for further study and evidence that the field of evolutionary computation is maturing rapidly, having many important results and even more interesting challenges.

Some Comments on Evolutionary Algorithm Theory

The development of a sound theory that predicts and verifies existing evolutionary algorithms (EA) is one of the most important research issues in the field today. In mathematical proofs, the assumption of spherical symmetry is probably one of the most widely used simplifications. This paper discusses the extent to which spherical symmetry is appropriate for certain EAs. It turns out that spherical symmetry leads to simplifications in (self-adaptive) EAs but seems inappropriate for certain genetic algorithm variants, since small mutation rates bias a search algorithm toward the coordinate axes. This paper also argues that current test suites are weak in that they do not provide problems with significant epistasis that describes the interaction between different parameters. Consequently, when using an empirical test for pushing existing theory beyond its limits, benchmark functions should include more epistatic interaction or at least should use coordinate rotations.