This paper presents an exhaustive study of the Simple Genetic Algorithm (SGA), Steady State Genetic Algorithm (SSGA) and Replacement Genetic Algorithm (RGA). The performance of each method is analyzed in relation to several operators types of crossover, selection and mutation, as well as in relation to the probabilities of crossover and mutation with and without dynamic change of its values during the optimization process. In addition, the space reduction of the design variables and global elitism are analyzed. All GAs are effective when used with its best operations and values of parameters. For each GA, both sets of best operation types and parameters are found. The dynamic change of crossover and mutation probabilities, the space reduction and the global elitism during the evolution process show that great improvement can be achieved for all GA types. These GAs are applied to TEAM benchmark problem 22.

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Irregularly shaped spatial disease clusters occur commonly in epidemiological studies, but their geographic delineation is poorly defined. Most current spatial scan software usually displays only one of the many possible cluster solutions with different shapes, from the most compact round cluster to the most irregularly shaped one, corresponding to varying degrees of penalization parameters imposed on the freedom of shape. Even when a fairly complete set of solutions is available, the choice of the most appropriate parameter setting is left to the practitioner, whose decision is often subjective. We propose quantitative criteria for choosing the best cluster solution, through multiobjective optimization, by finding the Pareto-set in the solution space. Two competing objectives are involved in the search: regularity of shape and scan statistic value. Instead of running sequentially a cluster-finding algorithm with varying degrees of penalization, the complete set of solutions is found in parallel, employing a genetic algorithm. The cluster significance concept is extended for this set in a natural and unbiased way, being employed as a decision criterion for choosing the optimal solution. The Gumbel distribution is used to approximate the empirical scan statistic distribution, speeding up the significance estimation. The multiobjective methodology is compared with the genetic mono-objective algorithm. The method is fast, with good power of detection. We discuss an application to breast cancer cluster detection. The introduction of the concept of Pareto-set in this problem, followed by the choice of the most significant solution, is shown to allow a rigorous statement about what is a "best solution," without the need of any arbitrary parameter.

This paper is concerned with the problem of evaluating genetic algorithm (GA) operator combinations. Each GA operator, like crossover or mutation, can be implemented according to several different formulations. This paper shows that: 1) the performances of different operators are not independent and 2) different merit figures for measuring a GA performance are conflicting. In order to account for this problem structure, a multiobjective analysis methodology is proposed. This methodology is employed for the evaluation of a new crossover operator (real-biased crossover) that is shown to bring a performance enhancement. A GA that was found by the proposed methodology is applied in an electromagnetic (EM) benchmark problem.

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