Comparison of strategies for solving global optimization problems using speculation and interval computations

Many real-life situations require that a match between quantities, behaviors, etc. be found. That is the case, for instance, when scientists try to find a fit between two sets of data, or a set of observations and a given model. Often such situations require that the minimum (or maximum) of a computed difference be found. These situations can be modeled as optimization problems. There exist multiple flavors of optimization problems: constrained and unconstrained (whether we are looking for the minimum - or maximum - of a function over the entire search space or only within the subspace of elements that satisfy some given constraints); local and global (whether we are looking solutions for the minimum within a neighborhood or among the whole search space); continuous, discrete, and mixed (whether the parameters of the problem at hand take their values all in discrete domains, all in continuous domains, or in a mix of these). In this article, we focus on continuous unconstrained global optimization and algorithms to solve such problems. Without loss of generality, we will discuss minimization. There exist many algorithms to address such problems. Most are based on interval computations for they provide a way to conduct a fully covering search in continuous domains where enumeration of alternatives is impossible. In this article, we propose to look at a specific type of algorithm: known as speculation, which consists in betting on which value is going to be the minimum we are looking for. More specifically, we propose to improve our speculative approach using different strategies. We present and discuss the results of a series of experiments comparing the performance of the speculative algorithm with the proposed strategies.