Evaluating a Solution Found by the Evolutionary Solving Method

Once you have a solution from the Evolutionary method, what can you do with it? Here are some ideas:

1. Keep the resulting solution, restart the Evolutionary method from that solution, and see if it is able to find an even better solution in a reasonable length of time.

2. Tighten the Convergence value, increase the Maximum Subproblems and Maximum Feasible Solutions values, and restart the Evolutionary method. This will take more time, but will allow Solver to explore more possibilities.

3. Increase the Population Size and/or the Mutation Rate, and restart the Evolutionary method. This will also take more time, but will tend to increase the diversity of the population and the portion of the search space that is explored.

4. Keep the resulting solution, switch to the GRG Solving method and start it from that solution, and see if it finds the same or a better solution. If the GRG method displays the message “Solver found a solution,” you may have found at least a locally optimal point (but remember that this test depends on smoothness of the problem functions).

5. Select and examine the Population Report. If the Best Values are similar from run to run of the Evolutionary method, and if the Standard Deviations are small, this may be reason for confidence that your solution is close to the global optimum. Since optimization tends to drive the variable values to extremes, if the solution is feasible and the Best Values are close to the Maximum or Minimum Values listed in the Population Report, this may indicate that you have found an optimal solution.

As you work with the Evolutionary method, you will appreciate its ability to find “good” solutions to previously intractable optimization problems, but you will also come to appreciate its limitations. The Evolutionary method allows you to spend less time analyzing the mathematical properties of your model, and still obtain “good” solutions – but it is not a panacea.

Create Solver reports

1. Define and solve a problem. A list of reports appears in theReports box of the Solver Results dialog box. If the solving process stopped prematurely when you pressed ESC or selected Stop when a Solving limit was reached, no reports are available.

2. Click to select one or more reports. Select the Outline Reports check box if you would like Solver to use Excel’s outlining feature in the reports. Outlining groups the variables and constraints in the reports into “blocks,” just as you entered them in the Solver Parameters dialog; you can expand or collapse the groups to see only the information you want.

3. Select any other options you want in the Solver Results dialog box, and click OK. The reports you selected appear as new worksheets, inserted into your Excel workbook just to the left of the worksheet containing the Solver model.

Reports available when Solver finds a solution

 In almost all cases where Solver finds an optimal solution, Solver converges to the current solution, or Solver cannot improve the current solution, the Answer Reportis available. When the Evolutionary Solving method is used, itsPopulation Reportis also available. If Solver finds a (locally or globally) optimal solution, and there are no integer constraints, two additional reports are available: theSensitivity Reportand theLimits Report.

Reports available when Solver encounters a problem

 If you receive the message “The linearity conditions required by this LP Solver are not satisfied,” and the problem has no integer constraints, the Linearity Reportis available. This report can help you find cell formulas in your model that make the problem nonlinear (possibly by mistake). If your model is intentionally nonlinear, you should select the GRG Nonlinear Solving method are re-solve the problem.

 If you receive the message “Solver could not find a feasible solution,” and the problem has no integer constraints, two variants of a diagnostic report, the Feasibility ReportandFeasibility-Bounds Report, are available. One of these reports (there’s never a reason to select both of them) can help you find certain constraints that are impossible to satisfy – possibly because you mistakenly used >= instead of <=, for example. If the constraints are correct, and the business situation you are modeling has no feasible solution, these reports can help you understand why.