Phase Transitions and Symmetry Breaking in Genetic Algorithms with Crossover

In this paper, we consider the role of the crossover operator in genetic algorithms. Specifically, we study optimisation problems that exhibit many local optima and consider how crossover affects the rate at which the population breaks the symmetry of the problem. As an example of such a problem, we consider the subset sum problem. In so doing, we demonstrate a previously unobserved phenomenon, whereby the genetic algorithm with crossover exhibits a critical mutation rate, at which its performance sharply diverges from that of the genetic algorithm without crossover. At this critical mutation rate, the genetic algorithm with crossover exhibits a rapid increase in population diversity. We calculate the details of this phenomenon on a simple instance of the subset sum problem and show that it is a classic phase transition between ordered and disordered populations. Finally, we show that this critical mutation rate corresponds to the transition between the genetic algorithm accelerating or preventing symmetry breaking and that the critical mutation rate represents an optimum in terms of the balance of exploration and exploitation within the algorithm

The effect of missing values using genetic programming on evolvable diagnosis

Medical databases usually contain missing values due the policy of reducing stress and harm to the patient. In practice missing values has been a problem mainly due to the necessity to evaluate mathematical equations obtained by genetic programming. The solution to this problem is to use fill in methods to estimate the missing values. This paper analyses three fill in methods: (1) attribute means, (2) conditional means, and (3) random number generation. The methods are evaluated using sensitivity, specificity, and entropy to explain the exchange in knowledge of the results. The results are illustrated based on the breast cancer database. Conditional means produced the best fill in experimental results

Studying Parallel Evolutionary Algorithms: The cellular Programming Case

Parallel evolutionary algorithms, studied to some extent over the past few years, have proven empirically worthwhile—though there seems to be lacking a better understanding of their workings. In this paper we concentrate on cellular (fine-grained) models, presenting a number of statistical measures, both at the genotypic and phenotypic levels. We demonstrate the application and utility of these measures on a specific example, that of the cellular programming evolutionary algorithm, when used to evolve solutions to a hard problem in the cellular-automata domain, known as synchronization

Dynamical transitions in the evolution of learning algorithms by selection

We study the evolution of artificial learning systems by means of selection. Genetic programming is used to generate a sequence of populations of algorithms which can be used by neural networks for supervised learning of a rule that generates examples. In opposition to concentrating on final results, which would be the natural aim while designing good learning algorithms, we study the evolution process and pay particular attention to the temporal order of appearance of functional structures responsible for the improvements in the learning process, as measured by the generalization capabilities of the resulting algorithms. The effect of such appearances can be described as dynamical phase transitions. The concepts of phenotypic and genotypic entropies, which serve to describe the distribution of fitness in the population and the distribution of symbols respectively, are used to monitor the dynamics. In different runs the phase transitions might be present or not, with the system finding out good solutions, or staying in poor regions of algorithm space. Whenever phase transitions occur, the sequence of appearances are the same. We identify combinations of variables and operators which are useful in measuring experience or performance in rule extraction and can thus implement useful annealing of the learning schedule.Comment: 11 pages, 11 figures, 2 table

Taxonomic evidence applying intelligent information algorithm and the principle of maximum entropy: the case of asteroids families

The Numeric Taxonomy aims to group operational taxonomic units in clusters (OTUs or taxons or taxa), using the denominated structure analysis by means of numeric methods. These clusters that constitute families are the purpose of this series of projects and they emerge of the structural analysis, of their phenotypical characteristic, exhibiting the relationships in terms of grades of similarity of the OTUs, employing tools such as i) the Euclidean distance and ii) nearest neighbor techniques. Thus taxonomic evidence is gathered so as to quantify the similarity for each pair of OTUs (pair-group method) obtained from the basic data matrix and in this way the significant concept of spectrum of the OTUs is introduced, being based the same one on the state of their characters. A new taxonomic criterion is thereby formulated and a new approach to Computational Taxonomy is presented, that has been already employed with reference to Data Mining, when apply of Machine Learning techniques, in particular to the C4.5 algorithms, created by Quinlan, the degree of efficiency achieved by the TDIDT family´s algorithms when are generating valid models of the data in classification problems with the Gain of Entropy through Maximum Entropy Principle.Fil: Perichinsky, Gregorio. Universidad de Buenos Aires. Facultad de Ingeniería; ArgentinaFil: Jiménez Rey, Elizabeth Miriam. Universidad de Buenos Aires. Facultad de Ingeniería; ArgentinaFil: Grossi, María Delia. Universidad de Buenos Aires. Facultad de Ingeniería; ArgentinaFil: Vallejos, Félix Anibal. Universidad de Buenos Aires. Facultad de Ingeniería; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Astronómicas y Geofísicas; ArgentinaFil: Servetto, Arturo Carlos. Universidad de Buenos Aires. Facultad de Ingeniería; ArgentinaFil: Orellana, Rosa Beatriz. Universidad Nacional de La Plata. Facultad de Ciencias Astronómicas y Geofísicas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Plastino, Ángel Luis. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Física; Argentin

Genetic Transfer or Population Diversification? Deciphering the Secret Ingredients of Evolutionary Multitask Optimization

Evolutionary multitasking has recently emerged as a novel paradigm that enables the similarities and/or latent complementarities (if present) between distinct optimization tasks to be exploited in an autonomous manner simply by solving them together with a unified solution representation scheme. An important matter underpinning future algorithmic advancements is to develop a better understanding of the driving force behind successful multitask problem-solving. In this regard, two (seemingly disparate) ideas have been put forward, namely, (a) implicit genetic transfer as the key ingredient facilitating the exchange of high-quality genetic material across tasks, and (b) population diversification resulting in effective global search of the unified search space encompassing all tasks. In this paper, we present some empirical results that provide a clearer picture of the relationship between the two aforementioned propositions. For the numerical experiments we make use of Sudoku puzzles as case studies, mainly because of their feature that outwardly unlike puzzle statements can often have nearly identical final solutions. The experiments reveal that while on many occasions genetic transfer and population diversity may be viewed as two sides of the same coin, the wider implication of genetic transfer, as shall be shown herein, captures the true essence of evolutionary multitasking to the fullest.Comment: 7 pages, 6 figure