Rational behavior design using multi-selective generation

This paper extends a technique that solves a generalization of the standard global optimization problem: instead of generating the optimizer, the technique produces, on the search space, a probability density function referred to as the behavior. The generalized solution depends on a parameter, the level of selectivity, such that as this parameter tends to infinity, the behavior becomes a delta function at the location of the optimizer. The motivation for this generalization is that traditional off-line global optimization is unresponsive to perturbations of the objective function. Although the original technique achieves responsive optimization, a large number of iterations may be required. In most instances, the extended technique of this paper, which is known as multi-selective generation, averages fewer iterations to achieve responsive optimization. Multi-selective generation is formulated here to generalize the canonical genetic algorithm with fitness proportional selection. Necessary and sufficient conditions that are required by multi-selective generation to achieve so-called rational behavior are specified. Rational behavior is desirable because it can lead to both efficient search and responsive optimization. However, the conditions for the extended technique to behave rationally are highly restrictive. The implication is that the original technique, which behaves rationally, is preferable for efficient search and responsive optimization.