Heuristic and genetic algorithms for solving survivability problem in the design of last mile communication networks

Given a connected, undirected and weighted graph G=(V,E)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$G = (V, E)$$\end{document}, a set of infrastructure nodes J\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$J$$\end{document} and a set of customers C\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C$$\end{document} include two customer types whereby customers C1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C_{1}$$\end{document} require a single connection (type-1) and customers C2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C_{2}$$\end{document} need to be redundantly connected (type-2). Survivable network design problem (SNDP) seeks a sub-graph of G\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$G$$\end{document} with the smallest weight in which all customers are connected to infrastructure nodes. SNDP has applications in the design of the last mile of the real-world communication networks. SNDP is NP-hard so heuristic approaches are normally adopted to solve this problem, especially for large-scale networks. This paper proposes a new heuristic algorithm and a new genetic algorithm for solving SNDP. The proposed algorithms are experimented on real-world instances and random instances. Results of computational experiments show that the proposed heuristic algorithm is much more efficient than the other heuristics in running time, and the proposed genetic algorithm is much more efficient than the other heuristics in terms of minimizing the network cost.