A Pareto frontier for node survivable computer network design problem
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A Pareto frontier for node survivable computer network design problem Ali Hadian1 · Mehri Bagherian2
© Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract In a survivable network design problem in cloud computing, one important goal is minimizing the network building costs, and the other important goal is maximizing the technical capability of the network. The literature investigation shows that the previous studies for computer network design proposed models only considering one of the above-mentioned goals and neglected the other. In this paper, a new model is developed in which the node survivable network design problem is formulated as a two-objective optimization problem considering both goals. To solve the formulated problem, several twoobjective optimization procedures are adopted and the results are discussed. Finally, numerical simulations are performed for two real examples and the obtained results are discussed. Keywords Mathematical optimization · Survivable network design problem · Two-objective optimization
1 Introduction One of the basic issues in the area of cloud computing is the network design problem (NDP). The general form of the NDP is defined as follows.
1.1 NDP general form Given an undirected graph G (V , E) with weights c : E → R+ and connectivity requirement ri j ≥ 0 for each pair of nodes i and j, the goal is to find a minimum weight spanning sub graph G of G such that for each i, j ∈ V there exist at least ri j edge-disjoint paths from i to j in G . In telecommunication networks, the stability is achieved by insertion of additional paths between each pair of nodes. In other words, the more paths lead to more stability. The difference between the NDP problem and the minimum cost flow problem (MCF) is that in MCF, ci j is the cost
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Mehri Bagherian [email protected] Ali Hadian [email protected]
1
Department of Applied Mathematics, University Campus 2, University of Guilan, Rasht, Iran
2
Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran
of sending unit flow on link (i, j) ∈ E, while in the NDP case, ci j is the cost of inserting the link (i, j) ∈ E, and the amount of flow is unimportant, i.e. the total cost does not change with the amount of flow. In the area of cloud computing, the concept of the transfer layer or the data exchange layer can be modeled as a graph [1]. For example, in connection-oriented networks, packets of information, frames, and bits are considered as network flows, which are transmitted from a source node to a destination node. The total amount of data sending and receiving power in a telecommunication line or bandwidth depends on different physical equipment. Generally speaking, in the physical layer of computer networks, there are three types of hardware with different bandwidth capabilities. These bandwidths are created by electrical waves on copper wires (such as ATM, Cat6, Leased lines, etc.), radio waves (such as Wi-Fi, 5G), optical waves (such as WDM, DWDM, CW
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