Application and comparison of single-objective (GA) and multi-objective (NSGA-II) optimization methods in optimal design of pressurized network

Proper design of technical and hydraulic parameters plays an essential role in the success of a pressurized irrigation or urban water distribution project and its economy. Therefore, engineers should be able to select the best solution in different stages in terms of design, construction, maintenance and operation according to the existing limitations and make the necessary decisions.The ultimate objective of such decisions is to minimize costs or maximize benefits by considering limitations.The objectives defined for each system may be different but it is certain that in today's engineering world, one-sided objectives are never defined.Today, meta-exploration optimization methods for the optimal design of irrigation and water supply networks have been considered.It is not possible to compare one-objective and two-objective methods in appearance. But in the two-objective method, one of the objectives is defined in such a way that it eventually goes to zero this comparison is possible.

Hence in the present study, the optimal design of a pressurized network with one-objective binary genetic algorithm and two- objective NSGAII has been done.Genetic algorithm is a method that evaluates different designs through trial and error with analogy criteria and maintains the best designs and eventually achieves the proper design. Multi-objective optimization is a sub-branch of the MCDM multi-criteria decision-making set that takes place among an unlimited set of possible solutions. In such cases unlike single-objective optimization problems, due to the existence of several conflicting goals, a set of answers is obtained instead of just one answer. In order to compare the two methods in terms of accuracy of results and speed of calculations the second objective function in NSGA-II was defined as the sum of the pressure deficiencies in the network. Observance of minimum pressure constraints in the network causes the value of this objective function to reach zero and the results of the two methods are comparable. In order to analyze the network and obtain the pipe flow and pressure in the system nodes, the matrix shape of the gradient method was used. Computer code was developed for single-objective (GA) and multi-objective (NSGAII) optimization methods in VB programming environment. Also, the simulation code according to the matrix shape of the gradient method was prepared in this programming environment. Finally, All the codes were linked to each other.

In order to validate the NSGA-II developed cod, its ability to solve several constrained and none- constrained multi-objective mathematical problems was proposed. The results showed that there is a very good agreement between the results of the present model and the results presented by previous researchers. In order to validate the genetic algorithm model, the model was used to solve the linear and nonlinear constrained optimizations problems that have analytical solutions. it has been shown that the results obtained from the model are exactly equal to the results of analytical solutions. After verifying the prepared codes from a programming point of view, a proposed two-loop network consisting of 7 pipes and 8 nodes whit one earth reservoir was designed with both GA and NSGA-II algorithms. The result showed, estimated cost of implementing the studied network by tow method was the same and with a difference of less than 1%, while the cost of calculations in NSGA-II method was estimated to be about 2% of the genetic algorithm method. That is, the time to reach the optimal answer in NSGA-II method is 50 times faster than GA method.

Given that the cost of calculations in the NSGA-II method is much lower than the GA method, the use of this method to optimal design of water presuurized network is recommended, Provided that in this method the second objective function is defined in such a way that if all the constraints are observed, its value will be close to zero. For this purpose, the objective function of the sum of pressure deficiencies Was deemed appropriate.