Solve Advanced Settings

Automatically select the best method to use, given the basic settings.

Use to resolve linear problems.

The Simplex LP Solver Pro finds optimal solutions to problems where the objective and constraints are all linear functions of the variables. Since all linear functions are convex, the Solver can normally find the globally optimal solution, if one exists. Because a linear function (a straight line) can always be increased or decreased without limit, the optimal solution is always determined by the constraints.

Use to resolve smooth nonlinear problems.

The nonlinear GRG Solver finds optimal solutions to problems where the objective and constraints are all smooth (convex or nonconvex) functions of the variables. (You can imagine a graph – whether straight or curved – that contains no “breaks.”) For non-convex problems, the Solver normally can find a locally optimal solution, if one exists – but this may or may not be the globally optimal solution. A nonlinear objective function can have a natural “peak” or “valley,” but in most problems the optimal solution is partly or wholly determined by the constraints. The nonlinear GRG can be used on problems with all-linear functions, but it is much less effective and efficient than the LP Solver on such problems. If you use multi start methods for global optimization with the nonlinear GRG, you will have a better chance (but not a guarantee) of finding the globally optimal solution. The idea behind multi start methods is to automatically start the Solver from a variety of starting points, to find the best of the locally optimal solutions – ideally the globally optimal solution.

The required degree of precision. For a constraint to be considered satisfied, the relationship between the Cell Reference and the Constraint value cannot be violated by more than this amount.

The smaller the number, the higher the precision.

Internally rescale the values of variables, constraints, and the objective to similar magnitudes.

This reduces the impact of extremely large or small values on the accuracy of the solution process, and is enabled by default.

Solving with Integer Constraints

Ignore the integer, binary, and all different constraints when you run Solve.

Note: This is called solving the relaxation of the integer programming problem.

The maximum percentage difference between the objective value of the best integer solution and the best known bound-on true optimal objective value that Solve should accept before stopping. The default value is 1%. Set to 0% to ensure a proven optimal solution is found.

Note: The Integer Optimality percentage is sometimes called the (relative) "MIP gap".

Solving Limits

The maximum time, in seconds, that Solve runs for before it stops.

The maximum number of iterations that Solve may perform on one problem. Iterations are "pivots" for the Simplex method, or "major iterations" for the GRG method.

The limit on the number of sub-problems explored by the Branch & Bound algorithm before Solve stops.

The amount of relative change allowed in the last five iterations before Solve stops with the message Solve converged to the current solution.

Note: Providing smaller values typically means that Solve will take more time but stop at a point closer to the optimal solution.

Select the mechanism to use to estimate derivatives:

• Select Forward (default) to use forward differencing.
• Select Central to use central differencing. Central differencing yields more accurate derivatives but requires twice as many calculations of the worksheet at each new trial solution.

Multi Start

Use the multi start method for global optimization. If this option is selected when you run Solve, the GRG Nonlinear method is run repeatedly, starting from different (automatically chosen) starting value for the decision variables. This process may find a better solution, but will take more computing time than a single run of the GRG Nonlinear method.

The number of different starting points (values for the decision variables) for the multi start method to consider.

Notes:

• The minimum population size is 10.
• If you supply a value that is less than 10, or leave the field empty, it is set to 10 times the number of decision variables up to a maximum population size of 200.

The random seed for the random number generator used when creating candidate starting points for the GRG Nonlinear method.

The seed number entered here is used as a fixed starting point for the random number generator:

• If you enter a number, that number is used as the starting point by the random seed generator each time you run Solve.
• If you do not enter a number, the random number generator uses a different seed each time you run Solve. This may yield a different (better or worse) solution each time.

The maximum percentage difference in objective values for the top 99% of the population that Solve should allow before it stops with the message Solve converged to the current solution.

Note: Providing smaller values typically means that Solve will take more time but stop at a point closer to the optimal solution.

A number between 0 and 1 that indicates the relative frequency with which some member of the population will be altered or "mutate" to create a new trial solution during each generation or sub-problem considered by the Evolutionary method.

A higher Mutation Rate increases the diversity of the population and the chance that a new, better solution, will be found; but may also increase the total solution time.

The number of different points (values for the decision variables) for the Evolutionary method to maintain at any given time in its population of candidate solutions.

Notes:

• The minimum population size is 10.
• If you supply a value that is less than 10, or leave the field empty, it is set to 10 times the number of decision variables up to a maximum population size of 200.

The random seed for the Evolutionary method, which is used when making a variety of random choices.

The seed number entered here is used as a fixed starting point for the random number generator:If you enter a number, that number is used as the starting point by the random seed generator each time you run Solve. If you do not enter a number, the random number generator uses a different seed each time you run Solve. This may yield a different (better or worse) solution each time.

The maximum number of seconds you want the Evolutionary method to continue without a meaningful improvement in the objective value of the best solution in the population. After this time, it will stop with the message Solve cannot improve the current solution.