Dynamic Compartmental Models for Large Multi-objective Landscapes and Performance Estimation

Dynamic Compartmental Models are linear models inspired by epidemiology models to study Multi- and Many-Objective Evolutionary Algorithms dynamics. So far they have been tested on small MNK-Landscapes problems with 20 variables and used as a tool for algorithm analysis, algorithm comparison, and algorithm configuration assuming that the Pareto optimal set is known. In this paper, we introduce a new set of features based only on when non-dominated solutions are found in the population, relaxing the assumption that the Pareto optimal set is known in order to use Dynamic Compartment Models on larger problems. We also propose an auxiliary model to estimate the hypervolume from the features of population dynamics that measures the changes of new non-dominated solutions in the population. The new features are tested by studying the population changes on the Adaptive \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\epsilon $$\end{document}-Sampling \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\epsilon $$\end{document}-Hood while solving 30 instances of a 3 objective, 100 variables MNK-landscape problem. We also discuss the behavior of the auxiliary model and the quality of its hypervolume estimations.