WHAT ARE GENETIC ALGORITHMS in Software

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WHAT ARE GENETIC ALGORITHMS
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A genetic algorithm solves a problem using a process similar to biological evolution. It works by the recombination and mutation of gene sequences. Recombination and 257
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mutation are genetic operators; i.e., they manipulate genes. A gene is a string of codes (the genotype) that is decoded to yield a functional organism with specific characteristics (the phenotype). A chromosome is a string of genes. In the case of genetic optimization, as caxried out on such problems as those being addressed here, the string of codes usually takes the form of a series of numbers. During the simulated evolutionary process, a GA engages in mating and selecting the members of the population (the chromosomes). Mating involves crossover and mutation. In crossover, the elements that comprise the genes of different chromosomes (members of the population or solutions) are combined to form new chromosomes. Mutation involves the introduction of random alterations to these elements. This provides additional variation in the sets of chromosomes being generated. As with the process of biological selection (where less-fit members of the population leave fewer progenies), the less-fit solutions are weeded out so the more-fit solutions can proliferate, yielding another generution that may contain some better solutions than the previous one. The process of recombination, random mutation, and selection has been shown to be an extremely powerful problem-solving mechanism. EVOLVING RULE-BASED ENTRY MODELS What would happen if a GA were allowed to search, not merely for the best parameters (the more common way a GA is applied by traders), but also for the best rules In this chapter, the consequences of using a GA to evolve a complete entry model, by discovering both the rules and the optimal parameters for those rules, will be explored. Although somewhat complex, this methodology proved to be effective in our first investigation (Katz and McCormick, February 1997). How can a GA be used to discover great trading rules The garden variety GA just juggles numbers. It is necessary to find a way to map sets of numbers in a one-to-one fashion to sets of rules. There are many ways this can be accomplished. A simple and effective method involves the construction of a set of rule templates. A rule template is a partial specification for a rule, one that contains blanks that need to be filled in. For example, if some of the rules in previous chapters were regarded as rule templates, the blanks to be filled in would be the values for the look-backs, thresholds, and other parameters. Using rule templates, as defined in this manner, a one-to-one mapping of sets of numbers to fully specified rules can easily be achieved. The first number (properly scaled) of any set is used as an index into a table of rule templates. The remaining numbers of the set are then used to fill in the blanks, with the result being a fully specified rule. The code below contains a C+ + function (Rules) that implements this mapping strategy; it will be discussed later. Although C+ + was used in the current study, this method can also be implemented in TradeStation using the TS-EVOLVE software from Scientific Consultant Services (516-696-3333).
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The term genetic search applies to the use of a genetic algorithm to search through an incredibly large set of potential solutions to find those that are best, i.e., that have the greatest fitness. In the current application, the intention is to use the evolutionary process to discover sets of numbers (genotypes) that translate to rulebased entry models (phenotypes) with the greatest degree of fitness (defined in terms of desirable trading behavior). In short, we are going to attempt to engage in the selective breeding of rule-based entry methods! Instead of beginning with a particular principle on which to base a model (e.g., seasonal@, breakouts, etc.), the starting point is an assortment of ideas that might contribute to the development of a profitable entry. Instead of testing these ideas one by one or in combinations to determine what works, something very unusual will be done: The genetic process of evolution will be allowed to breed the best possible entry model from the raw ideas. The GA will search an extremely broad space of possibilities to find the best rule-based entry model that can be achieved given the constraints imposed by the rule templates, the data, and the limitation of restricting the models to a specified number of rules (to prevent curve-fitting). To accomplish this, it is necessary to find the best sets of numbers (those that map to the best sets of rule-based entry models) from an exceedingly large universe of possibilities. The kind of massive search for solutions would be almost impossible-certainly impractical, in any realistic sense-to accomplish without the use of genetic algorithms. There are alternatives to GAS, e.g., brute force searching may be used, but we do not have thousands of years to wait for the results. Another alternative might be through the process of rule induction, i.e., where an attempt is made to infer rules from a set of observations; however, this approach would not necessarily allow a complex function, such as that of the risk-to-reward ratio of a trading model, to be maximized. Genetic algorithms provide an efticient way to accomplish very large searches, especially when there are no simple problem-solving heuristics or techniques that may otherwise be used.
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