The Cross Entropy Method: A Unified Approach To Combinatorial Optimization, Monte-carlo Simulation (Information Science and Statistics)
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This paper describes the methodology and application of Cross Entropy (CE) to the optimal design problem of a water distribution system (WDS). The CE method is a new powerful evolutionary iterative technique based on the concept of rare events (or the Kullback-Leibler distance measure of information). The optimal design problem of a WDS is to find its component characteristics (e.g., pipe diameters, pump heads and maximum power) which minimize its capital and operational costs such that the system hydraulic laws are maintained (i.e., Kirchoff's Laws No. 1 and 2), and constraints on quantities and pressures at the consumer nodes are fulfilled. The CE methodology is demonstrated using a well known bench-mark problem reported in the WDSs research literature, reaching the best solution already obtained and suppressing the computational effort required to achieving it.