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The problem of broadcasting a message through a network is considered. The objective is to minimize the number of time steps necessary to complete the broadcast. This problem is known as the Minimum Broadcast Time Problem or the Local Broadcasting Problem. Finding an optimal broadcast using a local broadcasting scheme is known to be NP-Complete. A genetic algorithm (GA) is used as a heuristic technique to find near optimal solutions to this problem. The GA is compared to a variant of a recent heuristic technique presented in the literature.

In this paper we investigate genetic algorithms (GA) as a .heuristic technique for obtaining near optimal solutions to the probabilistic minimum spanning tree (PMST) problem. The PMST problem is a natural generalization of the classical minimum spanning tree (MST) problem and is frequently a more realistic model. The PMST problem addresses the circumstances that arise when not all nodes are deterministically present but, rather, nodes are present with known probabilities. Although there are some special cases that are solvable in polynomial time, it is known that the PMST problem is NP-complete.

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This paper explores the application of genetic algorithms (GA) to the problem of scheduling product movement in a multi-product, fungible, liquids pipeline. The storage of, and demand for product at multiple terminal facilities are modeled as well as the one way transfer of products between the pipeline terminals. The GA is driven to its optimal or nearoptimal solution by a table-based set of product volume goals for each terminal and by penalties for nonfeasible solutions that do not represent a valid pipeline schedule. Our model was tested with great success. The significance of this research is (1) this problem, to the authors' knowledge, has not been solved before using evolutionary computation methods or any other method other than brute force or by applying previous experience, and (2) our GA model for constructing the chromosome and applying rules as we step through the pipeline can (in theory) be scaled up for a more complicated (industrial size) pipeline network which includes more products, terminals, edges and links.