Interpreting the Answer Report

The Answer Report, which is available whenever a solution has been found, provides basic information about the decision variables and constraints in the model. It also gives you a quick way to determine which constraints are “binding” or satisfied with equality at the solution, and which constraints have slack. The Answer Report records the message that appeared in the Solver Results dialog, the Solving method used to solve the problem, Solver Option settings, and statistics such as the time, iterations and subproblems required to solve the problem.

First shown are the objective function and decision variables, with their original value and final values. Next are the constraints, with their final cell values; a formula representing the constraint; a “status” column showing whether the constraint was binding or non-binding at the solution; and the slack value – the difference between the final value and the lower or upper bound imposed by that constraint.

When creating a report, Solver constructs the entries in the Name column by searching for the first text cell to the left and the first text cell above each variable (changing) cell and each constraint cell. If you lay out your Solver model in tabular form, with text labels in the leftmost column and topmost row, these entries will be most useful. The formatting for the Original Value, Final Value and Cell Value is “inherited” from the formatting of the corresponding cell in the Solver model.

Interpreting the Population Report

The Population Report gives you summary information about the entire population of candidate solutions maintained by the Evolutionary Solving method at the end of the solution process. The Population Report can give you insight into the performance of the Evolutionary method as well as the characteristics of your model, and help you decide whether additional runs of the Evolutionary method are likely to yield even better solutions.

For each variable and constraint, the Population Report shows the best value found by the Evolutionary method, and the mean (average) value, standard deviation, maximum value, and minimum value of that variable or constraint across the entire population of candidate solutions at the end of the solution process. These values will give you an idea of the diversity of solutions represented by the population.

How you interpret the Population Report depends in part on your knowledge of the problem, and past experience solving it with the Evolutionary method or with other Solving methods. For example, if the Best Values are similar from run to run, and if the Standard Deviations are small, this may be reason for confidence that your solution is close to the global optimum. However, if the Best Values vary from run to run, small Standard Deviations might indicate a lack of diversity in the population, suggesting that you should increase the Mutation Rate and run Solver again.

Interpreting the Sensitivity Report

The Sensitivity Report provides classical sensitivity analysis information for both linear and nonlinear programming problems, including dual values (in both cases) and range information (for linear problems only). The dual values for (nonbasic) variables are called Reduced Costs in the case of linear programming problems, and Reduced Gradients for nonlinear problems. The dual values for binding constraints are called Shadow Prices for linear programming problems, and Lagrange Multipliers for nonlinear problems.

Constraints which are simple upper and lower bounds on the variables, that you enter in the Constraints section of the Solver Parameters dialog, are handled specially (for efficiency reasons) by both the linear and nonlinear Solver algorithms, and will not appear in the Constraints section of the Sensitivity report. When an upper or lower bound on a variable is binding at the solution, a nonzero Reduced Cost or Reduced Gradient for that variable will appear in the “Decision Variable Cells” section of the report; this is normally the same as a Lagrange Multiplier or Shadow Price for the upper or lower bound.