Metaheuristic–Boltzmannian optimization model: A new methodology for convergence using the Jensen–Shannon metric in continuous optimization problems

Abstract

We present a new methodology called J–SIGMA to infer state change information using the minimum Jensen–Shannon distance to describe a continuous optimization problem as a Boltzmannian system, as well as its applications to population-based metaheuristics. In general, a Boltzmannian system describes a macrostate from the statistics of the constituent microstate where the minimum energy is the most probable. If we model an optimization problem as a Boltzmann process, the global optimum would be the most probable state. To achieve this, we propose an analytical derivation of the minimum distance to the Boltzmann distribution using the parameters μ and σ 2 to fit this model. As a case study, we implemented the J–SIGMA methodology on three families of population-based metaheuristics: Swarm, Evolutionary, and Estimation of Distribution, and used a set of continuous optimization functions from CEC’17 to evaluate their performance against other metaheuristics of each family. Finally, from a statistical analysis of the convergence performance, the evidence is shown to affirm that the J–SIGMA methodology can significantly improve the convergence performance of the algorithms, regardless of the metaheuristic family to which it belongs.