Optimization of parameters for binary genetic algorithms.

In the GA framework, a species or population is a collection of individuals or chromosomes, usually initially generated randomly. A predefined fitness function guides selection while operators like crossover and mutation are used probabilistically in order to emulate reproduction.Genetic Algorithms (GAs) belong to the field of evolutionary computation which is inspired by biological evolution. From an engineering perspective, a GA is an heuristic tool that can approximately solve problems in which the search space is huge in the sense that an exhaustive search is not tractable. The appeal of GAs is that they can be parallelized and can give us "good" solutions to hard problems.One of the difficulties in working with GAs is choosing the parameters---the population size, the crossover and mutation probabilities, the number of generations, the selection mechanism, the fitness function---appropriate to solve a particular problem. Besides the difficulty of the application problem to be solved, an additional difficulty arises because the quality of the solution found, or the sum total of computational resources required to find it, depends on the selection of the parameters of the GA; that is, finding a correct fitness function and appropriate operators and other parameters to solve a problem with GAs is itself a difficult problem. The contributions of this dissertation, then, are: to show that there is not a linear correlation between diversity in the initial population and the performance of GAs; to show that fitness functions that use information from the problem itself are better than fitness functions that need external tuning; and to propose a relationship between selection pressure and the probabilities of crossover and mutation that improve the performance of GAs in the context of of two extreme schema: small schema, where the building block in consideration is small (each bit individually can be considered as part of the general solution), and long schema, where the building block in consideration is long (a set of interrelated bits conform part of the general solution).Theoretical and practical problems like the one-max problem and the intrusion detection problem (considered as problems with small schema) and the snake-in-the-box problem (considered as a problem with long schema) are tested under the specific hypotheses of the Dissertation.The Dissertation proposes three general hypotheses. The first one, in an attempt to measure the impact of the input over the output, study that there is not a linear correlation between diversity in the initial population and performance of GAs. The second one, proposes the use of parameters that belong to the problem itself to joint objective and constraint in fitness functions, and the third one use Holland's Schema Theorem for finding an interrelation between selection pressure and the probabilities of crossover and mutation that, if obeyed, is expected to result in better performance of the GA in terms of the solution quality found within a given number of generations and/or the number of generations to find a solution of a given quality than if the interrelation is not obeyed

Phenotype Operators for Improved Performance of Heuristic Encoding Within Genetic Algorithms

Many approaches to applying Genetic Algorithms (GAs) to Nondeterministic Polynomial time Complete (NPC) problems involve population members encoded directly from the problem solution space. While this technique enables trivial mapping of the population members to solutions, it can cause complex problems for GA operators as they attempt to direct the evolution of the population toward more promising areas of the solution space. These operators, using inspiration from genetics and evolution in the biological world, combine and manipulate the current population to produce a new population that, it is hoped, will eventually converge toward better solutions to the original problem. However, many problems, especially graph-space problems, cannot be so easily manipulated when GA members consist of direct encodings. In such cases, GA operators must perform awkward transformations to convert the progeny into viable solutions. Here is where heuristic encoding comes into play, in that any combination of genes will produce a viable solution. However, this additional level of abstraction does cause other problems and tends to weaken the guiding effects of traditional GA operators. Thus, I have designed custom GA operators that mitigate these problems by using the solutions produced by the heuristic encoded members to better guide the manipulation when producing the next generation. This dissertation shows that heuristic encoding is an effective technique for the representation of solutions to graph-space problems. It also shows that, when using heuristic encoding, GAs with traditional operators perform well compared to more direct encoding techniques. Finally it shows the combination of heuristic encoding and GA operators designed to work with them increases GA performance and can be competitive with other techniques. I believe that these techniques will also work well for other types of problems for which GAs are commonly applied

Evidence for divergent patterns of local selection driving venom variation in Mojave Rattlesnakes (\u3ci\u3eCrotalus scutulatus\u3c/i\u3e)

Snake venoms represent an enriched system for investigating the evolutionary processes that lead to complex and dynamic trophic adaptations. It has long been hypothesized that natural selection may drive geographic variation in venom composition, yet previous studies have lacked the population genetic context to examine these patterns. We leverage range-wide sampling of Mojave Rattlesnakes (Crotalus scutulatus) and use a combination of venom, morphological, phylogenetic, population genetic, and environmental data to characterize the striking dichotomy of neurotoxic (Type A) and hemorrhagic (Type B) venoms throughout the range of this species. We find that three of the four previously identified major lineages within C. scutulatus possess a combination of Type A, Type B, and a ‘mixed’ Type A + B venom phenotypes, and that fixation of the two main venom phenotypes occurs on a more fine geographic scale than previously appreciated. We also find that Type A + B individuals occur in regions of inferred introgression, and that this mixed phenotype is comparatively rare. Our results support strong directional local selection leading to fixation of alternative venom phenotypes on a fine geographic scale, and are inconsistent with balancing selection to maintain both phenotypes within a single population. Our comparisons to biotic and abiotic factors further indicate that venom phenotype correlates with fang morphology and climatic variables. We hypothesize that links to fang morphology may be indicative of co-evolution of venom and other trophic adaptations, and that climatic variables may be linked to prey distributions and/or physiology, which in turn impose selection pressures on snake venoms