A methodology for solving facility layout problem considering barriers: genetic algorithm coupled with A* search

This work proposes a new methodology and mathematical formulation to address the facility layout problem. The goal is to minimise the total material handling cost subjected to production-derived constraints. This cost is a function of the distance that the products should cover within the facility. The first idea is to use the A∗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\text{A}}^{ *} $$\end{document} algorithm to identify the distances between workstations in a more realistic way. A∗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\text{A}}^{ *} $$\end{document} determines the shortest path within the facility that contains obstacles and transportation routes. The second idea is to combine a genetic algorithm and the A∗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\text{A}}^{ *} $$\end{document} algorithm with a homogenous methodology to improve the quality of the facility layouts. In an iterative way, the layout solution space is explored using the genetic algorithm. We study the impacts of the appropriate crossover and mutation operators and the values of the parameters used in this algorithm on the cost of the proposed arrangements. These operators and parameter values are fine-tuned using Monte Carlo simulations. The facility arrangements are all compared and discussed based on their material handling cost associated with the Euclidean distance, rectilinear distance, and A∗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\text{A}}^{ *} $$\end{document} algorithm. Finally, we present a set of conclusions regarding the suggested methodology and discuss our future research goals.