Optimal multivariate mixture: a genetic algorithm approach.

The Optimal Multivariate Mixture Problem (OMMP) consists of finding an optimal mixture which, starting from a set of elements (items) described by a set of variables (features), is as close as possible to an ideal solution. This problem has numerous applications spanning various fields, including food science, agriculture, chemistry, materials science, medicine, and pharmaceuticals. The OMMP is a class of optimization problems that can be addressed using traditional Operations Research (OR) approaches. However, it can also be effectively tackled using meta-heuristic techniques within Artificial Intelligence (AI). This paper aims to present an Artificial Intelligence perspective. It proposes a Genetic Algorithm (GA) for Optimal Multivariate Mixture (GA-OMM), a novel improved version of a GA whose modified genetic operators prove to improve the exploration efficiency. Here, the algorithm is described in its general framework, and a test case 8-items 5-features is conducted to evaluate efficiency by exploring various combinations of hyperparameters. Test cases are also set up for the previous version, as well as a linear programming (LP) approach. The data experiments indicate that the proposed GA is efficient, converges towards the global optimum, consistently outperforms its predecessor, and delivers highly competitive results. In particular, GA-OMM shows an average fitness of GA-OMMP/LP and standard deviation with an order of magnitude ranging between 10-8\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$10^{-8}$$\end{document} to 10-4\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$10^{-4}$$\end{document}. Moreover, it consistently outperforms its predecessor, which exhibits similar values around 10-3\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$10^{-3}$$\end{document} [ABSTRACT FROM AUTHOR]