Dilation Functions in Global Optimization

Complex tasks in Computer Science can be reformulated as optimization problems, in which the global optimum of a given function must be identified. Such problems are typically noisy, multi-modal, non-convex and non-separable, and they require the application of population-based global search metaheuristics to effectively explore the search space. In this work, we address the issue of manipulating the search space of these complex optimization problems to the aim of improving the exploration and exploitation capabilities of metaheuristics. In particular, we show that the implicit assumption in global optimization problems, i.e., that candidate solutions are represented by vectors of values whose meaning has a straightforward interpretation, is not always adequate and that the semantics of parameters can be modified by re-mapping their values in the search space by means of user-defined Dilation Functions. Dilation Functions are general purpose transformations that can be applied to any metaheuristics and optimization problem to "compress" or "dilate" some regions of the search space, allowing to improve the quality of the initial population and the exploitation of promising areas, especially in the case of Swarm Intelligence algorithms. The advantages given by the application of Dilation Functions have been observed by running experiments with Fuzzy Self-Tuning Particle Swarm Optimization and Covariance Matrix Adaptation Evolution Strategies, for the optimization of the Ackley benchmark function and for the parameter estimation of a "synthetic" model of a biochemical system.