Entropy maximizing evolutionary design optimization of water distribution networks under multiple operating conditions

Abstract

The informational entropy model for flow networks was formulated over 30 years ago by Tanyimboh and Templeman (University of Liverpool, UK) for a single discrete operating condition that typically comprises the maximum daily demands and was undefined for water distribution networks (WDNs) under multiple operating conditions. Its extension to include multiple independent discrete operating conditions was investigated experimentally herein considering the relationships between flow entropy and hydraulic capacity reliability and redundancy. A novel penalty-free multi-objective genetic algorithm was developed to minimize the initial construction cost and maximize the flow entropy subject to the design constraints. Furthermore, optimized designs derived from the maximum daily demands as a single discrete operating condition were compared to those derived from a combination of discrete operating conditions. Optimized designs from a combination of discrete operating conditions outperformed those from a single operating condition in terms of performance and initial construction cost. The best results overall were achieved by maximizing the sum of the flow entropies of the discrete operating conditions. The logical inference from the results is that the flow entropy of multiple discrete operating conditions is the sum of their respective entropies. In addition, a crucial property of the resulting flow entropy model is that it is bias free with respect to the individual operating conditions; hitherto a fundamental weakness concerning the practical application of the flow entropy model to WDNs is thus addressed.