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Simulated evolution and simulated annealing algorithms for solving multi-objective open shortest path first weight setting problem

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Abstract

Optimal utilization of resources in present-day communication networks is a challenging task. Routing plays an important role in achieving optimal resource utilization. The open shortest path first (OSPF) routing protocol is widely used for routing packets from a source node to a destination node. This protocol assigns weights (or costs) to the links of a network. These weights are used to determine the shortest path between all sources to all destination nodes. Assignment of these weights to the links is classified as an NP-hard problem. This paper formulates the OSPF weight setting problem as a multi-objective optimization problem, with maximum utilization, number of congested links, and number of unused links as the optimization objectives. Since the objectives are conflicting in nature, an efficient approach is needed to balance the trade-off between these objectives. Fuzzy logic has been shown to efficiently solve multi-objective optimization problems. A fuzzy cost function for the OSPF weight setting problem is developed in this paper based on the Unified And-OR (UAO) operator. Two iterative heuristics, namely, simulated annealing (SA) and simulated evolution (SimE) have been implemented to solve the multi-objective OSPF weight setting problem using a fuzzy cost function. Results are compared with that found using other cost functions proposed in the literature (Sqalli et al. in Network Operations and Management Symposium, NOMS, 2006). Results suggest that, overall, the fuzzy cost function performs better than existing cost functions, with respect to both SA and SimE. Furthermore, SimE shows superior performance compared to SA. In addition, a comparison of SimE with NSGA-II shows that, overall, SimE demonstrates slightly better performance in terms of quality of solutions.

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Notes

  1. Waxman graphs are frequently chosen in simulations as topologies resembling communications networks. Waxman graphs are named after Bernard M. Waxman.

  2. A hot spot is a network point or router having heavy incoming and outgoing traffic.

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of Pretoria, Pretoria, 0002, South Africa

    Mohammed A. Mohiuddin, Salman A. Khan & Andries P. Engelbrecht

  2. Department of Computer Engineering, College of Information Technology, University of Bahrain, Sakhir, Bahrain

    Salman A. Khan

Authors
  1. Mohammed A. Mohiuddin
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  2. Salman A. Khan
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  3. Andries P. Engelbrecht
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Corresponding author

Correspondence to Mohammed A. Mohiuddin.

Appendix

Appendix

1.1 A.1 Nomenclature

G :

Graph

N :

Set of nodes

n :

A single element in set N

A :

Set of arcs

A t :

Set of arcs representing shortest paths from all sources to destination node t

a :

A single element in set A. It can also be represented as (i,j)

s :

Source node

v :

Intermediate node

t :

Destination node

D :

Demand matrix

D[s,t]:

An element in the demand matrix that specifies the demand from source node s to destination node t; It can also be specified as d st

w ij :

Weight on arc (i,j); if a=(i,j), then it can also be represented as w a

c ij :

Capacity on arc (i,j); if a=(i,j), then it can also be represented as c a

Φ :

Cost function

Φ i,j :

Cost associated with arc (i,j); if a=(i,j), then it can also be represented as Φ a

\(\delta_{u}^{t}\) :

Outdegree of node u when destination node is t

δ +(u):

Outdegree of node u

δ −(u):

Indegree of node u

\(l_{a}^{t}\) :

Load on arc a when destination node is t

l a :

Total traffic load on arc a

\(f^{(s,t)}_{a}\) :

Traffic flow from node s to t over arc a

SetCA :

Set of congested arcs

1.2 A.2 Terminology

  1. 1.

    A single element in the set N is called a “Node”. It is represented as n.

  2. 2.

    A single element in the set A is called an “Arc” or “Link”. It is represented as a.

  3. 3.

    A set G=(N,A) is a graph defined as a finite nonempty set N of nodes and a collection A of pairs of distinct nodes from N.

  4. 4.

    A “directed graph” or “digraph” G=(N,A) is a finite nonempty set N of nodes and a collection A of ordered pairs of distinct nodes from N; each ordered pair of nodes in A is called a “directed arc”.

  5. 5.

    A digraph is “strongly connected” if for each pair of nodes i and j there is a directed path (i=n 1,n 2,…,n l =j) from i to j. A given graph G must be strongly connected for this problem.

  6. 6.

    A “demand matrix” is a matrix that specifies the traffic flow between s and t, for each pair (s,t)∈N×N.

  7. 7.

    (n 1,n 2,…,n l ) is a “directed walk” in a digraph G if (n i ,n i+1) is a directed arc in G for 1≤i≤l−1.

  8. 8.

    A “directed path” is a directed walk with no repeated nodes.

  9. 9.

    Given any directed path p=(i,j,k,…,l,m), the “length” of p is defined as w ij +w jk +⋯+w lm .

  10. 10.

    The “outdegree” of a node u is a set of arcs leaving node u i.e., {(u,v):(u,v)∈A}.

  11. 11.

    The “indegree” of a node u is a set of arcs entering node u i.e., {(v,u):(v,u)∈A}.

  12. 12.

    The input to the problem will be a graph G, a demand matrix D, and capacities of each arc.

  13. 13.

    The term MU refers to the maximum utilization. It is the highest load/capacity ratio of the network.

  14. 14.

    The term NOC refers to the number of congested links.

  15. 15.

    The term NUL refers to the number of unused links.

  16. 16.

    The term E refers to the total number of links in the network.

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Mohiuddin, M.A., Khan, S.A. & Engelbrecht, A.P. Simulated evolution and simulated annealing algorithms for solving multi-objective open shortest path first weight setting problem. Appl Intell 41, 348–365 (2014). https://doi.org/10.1007/s10489-014-0523-3

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