In designing Water Distribution Networks(WDN) against emergency situation, efforts must be exercised for optimization with two objectives-maximizing reliability and minimizing cost. For such optimization, it is necessary first to quantify the reliability of WDN using a surrogate measure. In this paper, connectivity is introduced as a surrogate measure of reliability. The mechanical connection between sources and nodes does not guarantee reliability to WDN unless required flow at adequate pressure is provided at the nodes. But, if it could guarantee such quantity and pressure requirements, connectivity can be a good measure of WDN reliability. This paper develops ways of providing such conditions using the Genetic Algorithm (GA). In addition, an optimization method has been developed to get a minimum cost design satisfying given reliability constraints in terms of connectivity and the connectivity in the model is called Hydraulic Connectivity. Hydraulic-Connectivity is selected as a surrogate measure that indicates a probability that every demand node in the network is connected to at least one supply source with required flow at adequate pressure. When emergency situations break out, the most important necessary condition for water supply is that the demand nodes must remain as being connected at some positive pressure to one of the sources. In this sense, therefore, maximizing the hydraulic-connectivity can be a good way of increasing reliability against emergency situations. For the calculation of this measure, water distribution systems are often be modeled as networks of supply and demand nodes, connected by links. The nodes are modeled as being perfectly reliable. Each link i is said to have a probability pi of functioning at any point in time and a probability qi (= 1-pi )of failing. At any point in time, the system can assume one of a large number of configurations, with some links functioning and other links failed. The probability of any one configuration occurring can be calculated as the product of the p is for the operative links times the product of the q is of the failed links. For connectivity calculation, each configuration corresponds to either a connected system, where every demand node is connected via functioning links to some sources, or a disconnected system. In order to calculate Hydraulic-Connectivity of a network, the "reliability preserving reduction" and the "K-terminal reliability" method for connectivity and GA for quantity and pressure requirements has been used in this paper. For simplicity of optimization, this study considers pipes only even if a network consists of many components such as pipes, tanks, pumps and valves. To simulate the emergency situations, each pipe ''i'' is assigned a probability of failure, qi, which is a function of diameter. By using the probability and diameters of individual pipes and the network configuration, connectivity is calculated.
Just for illustration, the optimization model is applied to the New York City water supply tunnel. And, we conducted the optimal design of WDN with multi-sources as well as single source. The yielded optimal design is found to be superior to the least cost design obtained from the different methods when the hydraulic-connectivity is 0.9781 in single source. To demonstrate this Model capability of handling connectivity, a number of optimizations are conducted with varying connectivity in multi-source as well as in single source. the connectivity is increased from 0.9781 to 0.982 in the cases of single source, and 0.9956 to 0.999 in the cases of multi-source. As expected, the cost increases as the connectivity increases, and the connectivity of the multi-source is much more reliable than that of the single source.
The application results also demonstrate that the tradeoff between cost and hydraulic connectivity can be explored and thus designers can design WDN based on more quantitative information regarding cost and reliability.
