Maximization of a dissimilarity measure for multimodal optimization

Abstract

Many practical problems are described by an objective-function with the intent to optimize a single goal. This leads to the important research topic of nonlinear optimization, that seeks to create algorithms and computational methods that are capable of finding a global optimum of such functions. But, many functions are multimodal, having many different global optima. Also, given the impossibility to create an exact model of a real-world problem, not every global (or local) optima is feaseable to be conceived. As such, it is interesting to find as many alternative optima in order to find one that is feaseable given unmodelled constraints. This paper proposes a methodology that, given a local optimum, it finds nearby local optima with similar objective-function values. This is performed by maximizing the approximation error of a Linear Interpolation of the function. The experiments show promising results regarding the number of detected peaks when compared to the state-of-the-art, though requiring a higher number of function evaluations on average.