Shape Optimization of Intz Tank Using Genetic Algorithm and Sequential Quadratic Programming

In the past, design of water tanks was based on the recommendations of codes and designer's experience. Nowadays, the designs are optimized using linear and dynamic programming methods and evolutionary algorithms. Classical optimization methods not only are time consuming but also are not capable to produce more than one answer because of the complexity of imposed constraints [1]. In order to investigate the efficiency and accuracy of the modern optimization methods in comparison with classical methods, an elevated Intz tank is primarily designed based on the recommendations of Indian IS: 3370 code [2] and then optimized using genetic algorithm and sequential quadratic programming. Tanks of various sizes are optimized and effective parameters are extracted, finally the key ratios of optimum design are compared to the initial design assumptions. Genetic algorithms and their variations are based on the mechanisms of natural selection. Unlike the conventional optimization which search approaches based on gradients, the genetic algorithm (GA) works on a population of possible solutions, attempting to find a solution set that either maximizes or minimizes the value of a function of those solution values. This function is called the objective function. In GA, key tools are generation method and its associated operators. The operator will determine the rate of convergence and accuracy of genetic methods. Genetic algorithms are randomized general-purpose search techniques used for finding the best values ofthe parameters or decision-variables of existing models. Some populations of solutions may improve the value of the objective function, others may not. The ones that improve its value play a greater role in the generation of new populations of solutions than those that do not. The flowchart of GA optimization is shown in Fig. 1 [3]. The Convergence of cost function using GA and SQP methods are shown in Figs. 3 and 4, respectively. The optimal solution was achieved after seven generations and nineteen times trial and error process for the GA and SQPmethods, respectively. The SQP method provides concrete placement volume of 130 m3which in comparison with the initial volume of 230 m3 shows a 46% reduction and represents approximately 26% decrease in the formwork. On the other hand, the GA method results in 44% and 21% reduction in volume of concrete placement andformwork, respectively. It is noteworthy that the internal stresses are significantly close to their maximum values while the conditions of code regulation are satisfied in both methods. The results indicated that the GA and SQP methods are agree well in the optimized design and slightly difference, 4 percent in volume and 5 percent in area ofconcrete work, is obtained. Efficiency and accuracy of the both evolutionary optimization methods is concluded. Intz tank with 850 m3 volumes was optimized by the GA method and compared with the results of the sequential quadratic programming (SQP) method in order to indicate the efficiency and accuracy of evolutionary methods. In this study the concrete volume of the body and surface of the tank is considered as an objective function. Design constraints are divided into some groups including the behavior, geometric and stability constraints. All constraints were satisfied and the stresses and stability constraints were in acceptable ranges. Considerable amount of decreasing in objective function, 46% and 44% for GA and SQP respectively was obtained. Based on the results, both methods, GA and SQP, were reliable and flexible methods in optimizing the Intz tank.