Solver options

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A number of improvements that can be made to the branching rules will accelerate the convergence of this method. A comprehensive discussion of all these options can be found in Nemhauser and Wolsey (1988). Also, a number of efficient MILP codes have recently been developed, including CPLEX, OSL, XPRESS, and ZOOM. All these serve as excellent large-scale optimization codes as well. A detailed description and availability of these and other MILP solvere... 

Currently, a good LP solver running on a fast (> 500 mHz) PC with substantial memory, solves a small LP in less than a second, a medium-size LP in minutes to tens of minutes, and a large LP in an hour or so. These codes hardly ever fail, even if the LP is badly formulated or scaled. They include preprocessing procedures that detect and remove redundant constraints, fixed variables, variables that must be at bounds in any optimal solution, and so on. Preprocessors produce an equivalent LP, usually of reduced size. A postprocessor then determines values of any removed variables and Lagrange multipliers for removed constraints. Automatic scaling of variables and constraints is also an option. Armed with such tools, an analyst can solve virtually any LP that can be formulated. 

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 ... 

C8 G10>=0 Number to ship must be greater than or equal toO. You can solve this problem faster by selecting the Assume linear model check box in the Solver Options dialog box before clicking Solve. A problem of this type has an optimum solution at which amounts to ship are integers, if all of the supply and demand constraints are integers. ... 

GRG2. This code is presently the most widely distributed for the generalized reduced gradient and its operation is explained in Section 8.7. In addition to its use as a stand-alone system, it is the optimizer employed by the Solver optimization options within the spreadsheet programs Microsoft Excel, Novell s Quattro Pro, Lotus 1-2-3, and the GINO interactive solver. 

We now ask the reader to start Excel, either construct or open this model, and solve it after checking the Show Iteration Results box in the Solver Options dialog (see Figure E9.2d). The sequence of solutions produced is the same as is shown in the BB tree of Figure E9.2b. The initial solution displayed has all four variables equal to zero, indicating the start of the LP solution at node 1. After a few iterations, the optimal node 1 solution is obtained. The solver then creates and solves the node 2 subproblem and displays its solution after a few simplex iterations. Finally, the node 3 subproblem is created and solved, after which an optimality message is shown. 

Options dialog for the evolutionary solver. Permission by Microsoft. 

Note also that the Newton-Gauss algorithm for function optimisation is the standard option in Excel s solver. 

Equilibria and 3.3.4 Solmng Non-Linear Equations. The Solver includes optimisation as one of the options. Its main application, within this chapter on data analysis, is data fitting, based on the minimisation of sum of squares. 

Sometimes SOLVER cannot find a solution if Precision is set too small in the Options window. You can make the Precision larger and see if SOLVER can find a solution. You can also try a different initial guess for pH. 

Each row of the spreadsheet must be dealt with separately. For example, in row 10. the pH was set to 0 in cell A10 and the initial guessed value of [F ] in cell CIO was 0.000 1 M. Before executing SOLVER, Precision was set to le-16 in SOLVER Options. In SOLVER, Set Target Cell DIP Equal to Value of 0 By Changing Cells CIO. SOLVER changes the value of [F-] in cell CIO to 3.517E-5 to satisfy the mass balance in cell D10. With the correct value of [F ] in cell CIO, the concentrations of [Ca2+1, [CaOH+], [CaF+], [HF], and [OH ] in columns E through I must be correct. 

E. feU (a) Using the ion-pair equilibrium constant in Appendix J, with activity coefficients = 1, find the concentrations of species in 0.025 M MgS()4. Hydrolysis of the cation and anion near neutral pH is negligible. Only consider ion-pair formation. You can solve this problem exactly with a quadratic equation. Alternatively, if you use SOLVER, set Precision to le-6 (not le-16) in the SOLVER Options. If Precision is much smaller. SOLVER does not find a satisfactory solution. The success of SOLVER in this problem depends on how close your initial guess is to the correct answer. 

We solve Equation A for [HT] by using solver in the spreadsheet, with an initial guess of pH = 10 in cell H10. In the tools menu, select solver and choose Options. Set Precision to le-16 and click OK. In the solver window, Set Target Cell E12 Equal To Value of 0 By Changing Cells HIP. Oick Solve and solver finds pH = 10.33 in cell H10. giving a net charge near 0 in cell E12. 

Open solver from the tools menu. Select solver Options and set Precision = le-6. Click OK. In the solver window, Set Target Cell F14 Equal To Value of 169.8 By Changing Cells Bll, solver finds [Mg2+] = 0.009 54 M and p = 0.038 2 M. 

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. 

The lines that follow the initial % MATLAB comment lines in fixedbedreact.m set up default values for the seven optional parameters. Then we prepare for the MATLAB IVP solver ode.. . that solves our problem by using the function dydt to evaluate the right-hand side of our IVP (4.22). Having solved (4.22) we plot two curves of the solution to the two joint DEs. 

MATLAB allows the user to choose the IVP integrator, such as ode23 or ode45 etc, and to select a stiff or nonstiff integrator, each as warranted by the specific problem. Moreover, each of the MATLAB s ODE solvers ode... allows us to specify certain options , as done in fluidbed.m in the fourth MATLAB command line options = odeset( RelTol ,10 -6, AbsTol ,10 -8, Vectorized , on ) for example. 

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