Using a hybrid of exact and genetic algorithms to design survivable networks

Abstract Wide-band technology has the capability to carry many services such as voice, video and other web-site technology on one link. Therefore these networks differ significantly from traditional dense copper-based networks. These networks are sparse and tree-like, and there are few disjoint paths (links) between a pair of nodes (space and/or terrestrial stations). Therefore connectivity has become a very important issue for survivability of these networks. Survivable networks are ones which can remain suitably connected after the incapacitation of a node or a link. Finding subgraphs that meet survivability requirements is ( NP ) hard on general graphs. However there are polynomial time algorithms available when these problems are solved on special graphs, including ones known as k -trees. We present a hybrid method for finding approximate optimal solutions for survivable network problems on complete graphs that takes advantage of k -tree solvability. A genetic algorithm generates “good” 3-tree subgraphs of the underlying network, where goodness is measured by the exact optimal survivable subgraph of the given 3-tree. The best such subgraph is taken as an approximate optimum for the full problem. Sufficient conditions for existence of a partial 3-tree optimal solution to the full survivable network problem validate the approach, and some computational experience is reported. Scope and purpose Wide-band technology has the capability to carry many services such as voice, video and other web-site technology on one link. Corresponding networks thus differ significantly from traditionally dense copper-based networks. Wide-band networks are sparse and tree-like, with few disjoint paths between any pair of nodes (space and/or terrestrial stations). Therefore connectivity has become a very important issue for survivability of these networks. We propose and report computational results for a procedure to choose approximately optimal networks in this context where designs are considered survivable if they will remain suitably connected after the incapacitation of a single node or link. The algorithm is hybrid in the sense that it combines efficient algorithms for special cases with a randomized search through a sequence of such cases until a satisfactory design is obtained.