Hybrid of exact and genetic algorithms for graph optimal problems with application to survivable network design
Abstract
Many combinatorial problems which are (NP) hard on general graphs yield to polynomial algorithms when restricted to k-trees which are graphs that can be reduced to the k-complete graph by repeatedly removing degree k vertices having completely connected neighbors. Such algorithms have limited domain and fail when the underlying graph is not a k-tree (for example a complete graph). Among the (NP) hard are survivable network problems. Survivability of a network is a measure of its connectivity (or restoration capability) in case of node or link failure. We present a hybrid method for finding approximate optimal solutions for these problems. In particular: We give linear time algorithms for survivable network design problems with low connectivity constraints on a class of graphs known as 3-trees. We present a genetic algorithm which seeks a heuristic optimum solution by generating an evolving population of k-tree subgraphs, thereby extending the domain of k-tree restricted algorithms. We validate our algorithm by testing it on the problem of finding a minimum total cost 3-tree subgraph of a complete graph. We present a hybrid method for solving survivable network problems on complete graphs. In this method, we combine our genetic algorithm which generates "good" 3-tree subgraphs of the underlying network with our exact algorithms that find the optimal survivable network on those 3-trees. Here goodness is measured relative to the exact optimal survivable subgraph of the given 3-tree. The best such subgraph is taken as an approximate optimum for the full problem.
Degree
Ph.D.
Advisors
Rardin, Purdue University.
Subject Area
Industrial engineering
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