hw2e.rar - Obtain the solution using analytical method, i.e., conditions of optimality d. Obtain the solution using Steepest Descent Method e. Obtain the solution using Netwon’s method f. Obtain the solution using Marquart’s method g. Compare convergence speeds/efficiencies of the algorithms in (d), (e) and (f) h. Use different parameter value set (other than the ones suggested below) with the numerical methods to see how the performance of the methods would change under different parameter values and makes some comments on parameter sensitivity of the methods,2016-01-17 16:07:39,下载2次
hw2a.rar - where E is Young’s modulus, A is the cross-sectional area of each member, l is the span of the truss, s is the length of each member, h is the height of the truss, P is the applied load, is the angle at which the load is applied, x1 and x2 are the horizontal and vertical displacement of the free node, respectively.
Find the values of x1 and x2 that minimize the potential energy when E = 207x109 Pa, A = 10-5 m2, l =1.5 m, h = 4.0 m, P = 104 N and ,2016-01-17 16:06:00,下载1次
hw2d.rar - Obtain the solution using graphical method c. Obtain the solution using analytical method, i.e., conditions of optimality d. Obtain the solution using Steepest Descent Method e. Obtain the solution using Netwon’s method f. Obtain the solution using Marquart’s method g. Compare convergence speeds/efficiencies of the algorithms in (d), (e) and (f) h. Use different parameter value set (other than the ones suggested below) with the numerical methods to see how the performance of the methods would change under different parameter values and makes some comments on parameter sensitivity of the methods.
Notes,2016-01-17 16:04:48,下载1次
hw2f.rar - For numerical calculations of partial differentiations in parts (d), (e) and (f), use Newton’s central difference method with disturbance parameter =0.01xi 2. For parts (d), (e) and (f), initialize the algorithms with the following parameter vales: starting solution x(0) = (0.1, 0.01), maximum iteration number M=200, termination parameter =10-5 3. For part (f), set the initial value of parameter to 103. 4. For parts (d) and (e), use interval halving method with [0,1] and iterate the method until the search interval for is small, say less than 10-4. 5. For parts (d), (e) and (f), show the iteration of the algorithm on a 2D design space that you have drawn in part (a) 6. Attach your written codes to your assignment and submit them electronically as ,2016-01-17 16:02:51,下载1次
trans_f.rar - By comparing elapsed times one can say that Hooke and Jeeves methods converge faster than other methods and the slowest one seems to be Nelder and Mead Simplex Method.
In this part of the assignment we are going to reach the solution by using Nelder and Mead Simplex method. Note that the starting simplex points are given. We also have reflection, contraction, expansion and scaling parameters.
Inspecting the results given in Table 1 one can say that the elapsed time is low (the code is working smoothly) and iteration number is acceptable. Both step sizes and their norm is in the allowed range. Final or optimized R, t and weight values are really close to the results that we have obtained in Homework III. As a results we can deduct that we accomplished a good optimization problem solution by using Hooke and Jeeves method.,2016-01-17 15:54:34,下载2次
Nelder.rar - We can now compare the convergence speeds and iteration numbers of the methods. Since Lagrange Multiplier Method and Sequential Linear Programming Method include manual calculations elapsed time comparison is not applicable for them.
There is also another important point. In Nelder and Mead Method although the code output for iteration number is 2 it is different in reality. We used while function in the code this repeats the calculations and does not affect the iteration number. On the other hand elapsed time of codes give us enough information to compare the codes.
,2016-01-17 15:53:09,下载3次
Hooke.rar - The elapsed time of Nelder and Mead simplex method seems to be larger than Hooke and Jeeves method but, it reached the solution in just 2 iterations which is remarkably less than the previous method. From Tables 1 and 2 it can be said that the optimized R, t and weight values are same in both methods.
Results of Part (a) and Part (b) are also parallel with the results of Homework III. Sequential Linear Programming methods seems to be closest method to Hooke and Jeeves method and Nelder and Mead simplex method. Yet all the differences between the final values are less than our termination parameter as a result, it can be said that all results have converged to the similar values. Thus the current solutions also gave us reliable results for the problem.,2016-01-17 15:51:08,下载1次