Professor Visvesvaraya National Institute of Technology Nagpur
The primary focus in the design of a water distribution network (WDN) is on minimizing the network cost. However, the diameters obtained solely through cost optimization may not ensure redundancy or reliability in the network. Incorporating reliability directly into the design proves challenging due to the requirement of consideration of actual performance under various emergency conditions. To address this issue, researchers have explored alternative approaches by using reliability surrogate measures, which are easier to implement. A WDN will have higher reliability if the capacity of alternate paths connected at node have similar capacity. In such a case, the impact of disruption of flow in one path will have lesser affect due to availability of alternate path of same capacity as compared to a condition when the alternative path is of lesser capacity. Defining a measure to achieve equality in flow capacities of different paths at different nodes is challenging. Therefore, the problem solution is approached in simpler ways by achieving equality in pipe flows in the network using flow-entropy or minimum variance of pipe flows. The minimum variance signifies the maximum uniformity in the pipe flow and observed to provide design with maximum demand satisfaction ratio when failure of individual pipe is considered. A two-phase methodology for the optimal design of network based on minimum variance was used earlier, in which, in the first phase the variance of flow series was minimized using Genetic Algorithm (GA) and the optimal design for the obtained flows was implemented in the second phase using linear programming (LP). In the present work a single phase methodology is developed for the optimal network design corresponding to the minimum variance. A normalized objective function including both network cost and variance of pipe flow series is developed and optimized. Both objective functions are connected with the help of weights assigned to them. Different weights (w1– for network cost & w2 – for variance) are used to obtain different solutions lying on the pareto front such that the addition of w1and w2 is always equal to one. Jaya, which is a parameter-less evolutionary algorithm is used for the present work. When the weight for the cost is reduced to zero, it is observed that the present methodology was able to locate the minimum variance value, which is found to be very close to the global minimum obtained earlier by solving problem of minimizing the variance of pipe-flows. It is found that the algorithm converges to the near optimum value in fewer iterations. The optimal cost corresponding to the minimum variance is also obtained for all the different combinations of weights. It also found that the solution corresponding to the minimum variance has the maximum value of reliability for 1-pipe failure scenario. Highlights: 1. Present work incorporates the variance of flow series as surrogate for the optimal design of WDNs. 2. A single phase methodology is developed for the optimal network design corresponding to the minimum variance. 3. By varying the weights of the objective function, more feasible solutions lying on a pareto front can be obtained. 4. Parameter-less algorithm is applied which minimizes the computational efforts required for tuning the constants.
