Solver parameters

Selecting the Options button in the Solver Parameters dialog brings up the Solver Options dialog box shown in Figure 7.5. The current Solver version does not determine automatically if the problem is linear or nonlinear. To inform Solver that... 

Select the Show Iteration Results box, click OK in the Solver Options dialog, then click Solve on the Solver Parameter dialog. This causes the simplex solver to stop after each iteration. Because an initial feasible basis is not provided, the simplex method begins with an infeasible solution in phase 1 and proceeds to reduce the sum of infeasibilities sinf in Equation (7.40) as described in Section 7.3. Observe this by selecting Continue after each iteration. The first feasible solution found is shown in Figure 7.6. It has a cost of 3210, with most shipments made from the cheapest source, but with other sources used when the cheapest one runs out of supply. Can you see a way to improve this solution ... 

An evolutionary algorithm is included in the current release of Frontline Systems Premium Excel Solver (for current information, see www.frontsys.com). It is invoked by choosing Standard Evolutionary from the Solver dropdown list in the Solver Parameters Dialog Box. The other nonlinear solver is Standard GRG Nonlinear, which is the GRG2 solver described in Section 8.7. As discussed there, GRG2 is a gradient-based local solver, which will find the nearest local solution to its starting point. The evolutionary solver is much less likely to stop at a local minimum, as we illustrate shortly. 

The extensive options allow the user to tune the performance of each algorithm. Some of the frequently used options are (i) the incorporation of integer cuts, (ii) the solution of continuous relaxation problems, (iii) alternative feasibility problems, (iv) an automatic initialization procedure, (v) a tightening of bounds procedure, and (vi) solvers parameter changes. 

To use the Solver, choose Solver... from the Formula menu. First you may see displayed the message box shown in Figure 12-2. This is only an advisory message, not an error message. Press OK. The Solver Parameters dialog box (Figure 12-3) will then be displayed. 

There are some additional controls in the Solver Parameters dialog box ... 

The Options button in the Solver Parameters dialog box activates the Solver Options dialog box (Figure 12-7) and allows you to control the way Solver attempts to reach a solution. The default values of the options are shown in the dialog box. 

Roe PL (1981) Approximate Riemann solvers, parameter vectors and difference schemes. J Comput Phys 43 357-372... 

Step 1 Go to Solver Parameters and choose Parametric nonlinear. Fill in the window as shown in Figure 9.6 to have a go from 0 to 20 in steps of (2). 

One handy way to get all the solutions for several pressure drops (and avoid convergence problems) is to use the Parametric Nonlinear option in the Solver Parameters. Call the variable presdropx and set its value to 0 1 7. Then in the Physics/Subdomain Settings, where you put the Ap, replace it with lO presdropx. The program FEMLAB... 

Step 7 Then choose the Solve/Solver Parameters menu. Change the solution method to Time Dependent. The default times listed are 0 0.1 1. This means a solution will be available for plotting at f = 0, 0.1, 0.2, 0.3,..., 1.0. Press OK, then click the = to solve the problem. 

Step 5 How long do you need to compute You can set that in Solve/Solver Parameters by clicking the Time-dependent Solver. The time is in seconds, and you think the flow will come to steady state within 10 s. Therefore, put Times as [0 0.1 1 2 3 4 5 6 7]. 

Now call in the troops, with Tools => Solver. In the Solver Parameter dialog box, enter E1 in the top window, push the radio button with Min, and enter B1 B2 in the window belowit, so that you can read the box as SetTargetCellEl Equal to Min By Changing Cells B1 B2 . Then push the Solve button. 

There are many other possible pitfalls in using Solver. For example, in the Solver Parameters dialog box you may have noticed the Options button. Push it, and you get... 

Click on Tools => Solver to get the Solver Parameters dialog box. There, Set Target Cell to where you display the value of SRR, Equal to Min Value, By Changing Cells to where you display the values of Caa, Kaa> then select Options. This opens the Solver Options dialogbox, in which you select Show Iteration Results, then push OK to bringyouback to the earlier dialogbox, where you now press Solve. 

Invoke Solver with Tools O Solver, and in the Solver Parameters dialog box instruct the computer to Set Target Cell to the address of SRR, Equal to Min, By Changing Cells B1 B5 (if that is where you put the five Ca s). 

Depress the Add button, and repeat for Ca2, etc. until all five concentrations have been constrained to positive values. Then depress the OK button, which will get you back to the Solver Parameters box. 

Select the computed Solver parameter PI or parameters Dim myRangel As Range... 

The parameters determined by Solver are located in ", Title ="SolverAid InputBox 1 Solver parameters". Type =8) myRangel.Select Dim rP As Integer... 

Answer = MsgBox ("There are data in the cells to the right of the" Chr(13) "Solver parameters. Can they be overwritten ", vbYesNo, "Overwrite ")... 

The Solver program is generally found under Tools in the Excel spreadsheet. If you do not see it there, it is probably an Add-In, which you have to activate by checking the Solver Add-In box. Once you locate Solver, click on it and you will open the Solver Parameters dialogue box. The filled-in Solver dialogue box for Example 6.1 is shown here ... 

Subtract the = 3 equation from the = 4 equation and from the = 5 equation to obtain two equations in two unknowns. Then combine these equations to eliminate A. To solve the remaining equation for B, put all terms on one side of the equation and use the Excel Solver to find B. Then find the other two unknowns, (b) Now use the = 3,4,5, and 6 energies and the Excel Solver to find the values of the three parameters in (15.23) that minimize 2n=3( (15.23) cc-pVnz) - Take the initial guesses for the parameters as the results from part (a). In Excel 2010, he sure and uncheck the Make Unconstrained Variables Non-Negative box in the Solver Parameters box. 

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