Edit Optimization Options

The settings in the Optimization Options dialog box are algorithm-specific.

If you edit the settings and want to reset to the defaults, select Optimization > Reset Options. If you add parameters to user-defined optimization scripts, you might need to use this reset option to make all new parameters appear in the dialog box.

fmincon Optimization Parameters

The fmincon optimization algorithm in CAGE uses the fmincon function in the Optimization Toolbox™. In CAGE, the fmincon algorithm wraps up the fmincon function so that you can use the function for maximizing and minimizing. See fmincon and options.

Parameter	Description
Constrained optimization algorithm	fmincon function algorithms: Try sqp or interior-point with sum optimizations that are slow or have problems converging. sqp (default) — Option for sum optimizations that are slow active-set interior-point — Default option for sum optimizations that have problems converging and optimizations with a large number of constraints
Display	Determines the level of diagnostic information displayed in the workspace. none (default) — No information displayed during optimization iter — Displays statistical information every iteration final — Displays statistical information at the end of the optimization
Maximum iterations	Maximum number of iterations allowed.
Maximum function evaluations	Maximum number of function evaluations allowed.
Function tolerance	Termination tolerance on the function value.
Variable tolerance	Termination tolerance on the optimization variables.
Constraint tolerance	Termination tolerance on the constraint violation.
Sub algorithm	Select ldl-factorization or cg to determine how the iteration step is calculated. Note The Sub algorithm parameter only applies if the interior-point algorithm is used.
Barrier update method	Select predictor-corrector (default) or monotone to specify the algorithm to update the barrier parameter for optimizations. predictor-corrector can provide improved performance for sum optimizations. Note The Barrier update method parameter only applies if the interior-point algorithm is used.
Number of start points	Positive integer, N. Optimization generates (N-1) start points per run in addition to the starting value specified in the Input Variable Values pane. The optimization runs from each of the N start points and chooses the best solution. To generate the N-1 extra start points: Generate a 10,000-point Halton set design, D, over the optimization variables. Evaluate the objectives and constraints over D. Return the N-1 feasible points with the lowest objective value. If there are not N-1 feasible points, fill the remaining starting values with the points with the lowest maximum constraint violation. If the specified initial value does not satisfy the constraints, CAGE uses the 10,000 search points. Note For point optimization problems, set Number of start points to 1 or 2.
Run from feasible start points only	Select this option to terminate all runs that start with an initial value that does not satisfy the constraints. In the Solution Information pane of the Optimization Output view, the Output message reports the termination.
Soft constraints weighting	Weighting factor that the optimization uses for soft constraints. By default, the value is 1. Increasing the value forces the optimization to find feasible solutions while satisfying the hard constraints and minimizing the slack for soft constraints. If you set the value to inf, the optimization considers all constraints hard constraints. If you set the value to 0, the optimization does not try to satisfy any soft constraints.
Make table gradient constraints feasible	Select this option to make constraints feasible for sum optimizations with table gradient constraints on the optimization variables. Consider clearing this option if the table gradient constraints are soft.

ga Optimization Parameters

The ga optimization algorithm in CAGE uses the ga function in the Global Optimization Toolbox. In CAGE, the ga algorithm wraps up the ga function so that you can use the function for maximizing and minimizing. See ga (Global Optimization Toolbox) and options (Global Optimization Toolbox).

Parameter	Description
Generations	Algorithm stops when the number of generations exceeds specified value.
Population size	Number of population members that the algorithm uses. For guidelines on setting the populating size, see options (Global Optimization Toolbox).
Display	Determines the level of diagnostic information displayed in the workspace. none (default) — No information displayed during optimization iter — Displays statistical information every iteration final — Displays statistical information at the end of the optimization
Crossover function	Function that generates new population members from the existing GA population by crossover. For more information on each function, see options (Global Optimization Toolbox). Do not to use a heuristic crossover function for nonlinearly constrained problems.
Crossover fraction	Fraction of the next generation, other than elite children, produced by crossover.
Mutation function	Function that generates new population members from the existing GA population by mutation. The fraction of the next generation, other than elite children, produced by mutation is one minus the value of Crossover fraction. For nonlinearly constrained problems, select adaptfeasible.
Selection function	Function that selects the population members that are the parents for the crossover and selection functions.
Hybrid function	Optimization function that runs after the GA termination to try to improve the value of the objective function. If the algorithm has nonlinear constraints, the hybrid function cannot be fminunc or fminsearch. If either of these algorithms are specified for nonlinear constraints, the hybrid algorithm switches to fmincon.
Stall generations	Algorithm stops when the weighted average change in the objective function over the value of Stall generations is less than the value of Function tolerance.
Stall time limit	Algorithm stops if there is no improvement in the objective function during the specified time stall time limit, in sec.
Function tolerance	Algorithm runs until the weighted average change in the fitness function value over the value of Stall generations is less than the value of Function tolerance.
Constraint tolerance	Tolerance that determines whether a population member is feasible with respect to the nonlinear constraints.
Time limit	Time to stop the algorithm.
Soft constraints weighting	Weighting factor that the optimization uses for soft constraints.

patternsearch Optimization Parameters

The patternsearch optimization algorithm in CAGE uses the patternsearch function in the Global Optimization Toolbox. In CAGE, the patternsearch algorithm wraps up the patternsearch function so that you can use the function for maximizing and minimizing. See patternsearch (Global Optimization Toolbox) and options (Global Optimization Toolbox).

Parameter	Description
Display	Determines the level of diagnostic information displayed in the workspace. none (default) — No information displayed during optimization iter — Displays statistical information every iteration final — Displays statistical information at the end of the optimization
Time limit	Time to stop the algorithm.
Maximum number of iterations	Maximum number of algorithm iterations.
Maximum function evaluations	Algorithm stops if the number of function evaluations reaches this value.
Variable tolerance	Algorithm stops if the distance between two consecutive optimization variable values is less than the variable tolerance.
Function tolerance	Algorithm stops if the distance between two consecutive objective function values and the mesh size are both less than the value of Function tolerance.
Constraint tolerance	Determine feasibility with respect to the nonlinear constraints.
Mesh tolerance	Algorithm stops if the mesh size is smaller than this value.
Initial mesh size	Sets the initial size of the mesh for the pattern search algorithm. Setting this value too small can lead to the algorithm getting trapped in local optima.
Poll method	Sets the polling strategy that used by the pattern search algorithm. Generally, the GPSPositiveBasis2N and MADSPositiveBasis2N methods are slower than the GPSPositiveBasisNp1 and MADSPositiveBasisNp1 methods. However, the former methods perform a more thorough search. For more information on these methods, see options (Global Optimization Toolbox).
Search method	Select the function that performs a search, in addition to that performed by the pattern search algorithm. For automotive problems, searchlhs tends to perform well. For details on possible search methods, see options (Global Optimization Toolbox).
Soft constraints weighting	Weighting factor that the optimization uses for soft constraints.

MultiStart Optimization Parameters

The MultiStart optimization algorithm in CAGE uses the MultiStart function in the Global Optimization Toolbox. The MultiStart algorithm tries to identify multiple optimal solutions for each operating point. You can set a subset of the algorithm options in CAGE.

In CAGE, the MultiStart algorithm generates Sobol design points and chooses the best one to start the optimization. You can specify the number of start points and other options in the Optimization Parameters dialog box.

To change the number of start points to run:

1. In the Optimization view, select Optimization > Optimization Options, or click the Set up optimization toolbar button.

   The Optimization Options dialog box opens.

2. Change the value of Number of start points. This setting determines how many optimizations to run for each point.

3. Click OK.

Parameter	Description
Number of start points	Number of start points per operating point (default is 10).
Start point set type	Choose Sobol Set (space-filling start points) or Random (random start points).
Start points to run	Choose all or bounds-ineqs. Use bounds-ineqs to run only feasible start points that meet constraints.
Run start points in parallel	Choose never or always to run each start point in parallel. Check that the Distribute Runs optimization option is turned off for the start points to run in parallel.
Tolerance for separate objective values	Specify how far apart objective values must be to qualify as separate local optima.
Tolerance for separate solutions	Specify how far apart solution-optimization variable values must be to qualify as separate solutions.
Local optimization solver	Specify fmincon options.

NBI Optimization Parameters

Use the NBI algorithm for multiobjective optimizations.

Parameter	Description
Tradeoff points per objective pair, Np	Specify how many tradeoff solutions you want the optimization to find per run. To determine the number of tradeoff solutions between the objectives, Npts, the optimization uses this formula: Np — Number of points per objective pair n — Number of objective functions Note For problems with two objectives (n = 2), For problems with three objectives (n = 3),
Shadow minima options and NBI subproblem options	The NBI algorithm uses the fmincon function to solve the shadow minima problem and the NBI subproblems. The options available are similar to those for the fmincon function.

gamultiobj Optimization Parameters

The gamultiobj algorithm uses the gamultiobj function in the Global Optimization Toolbox. This algorithm is recommended for multiobjective optimizations.

Use a point optimization to find feasible start points for a sum optimization, and then select Solution > Create Sum Optimization. CAGE sets a default population size of 200 for the gamultiobj sum optimization. If CAGE does not find a feasible solution, try increasing the population size in the Optimization Parameters dialog box. Larger populations increase the chance of finding feasible points but take longer to compute. See gamultiobj (Global Optimization Toolbox) and options (Global Optimization Toolbox).

paretosearch Optimization Parameters

The paretosearch algorithm uses the paretosearch function in the Global Optimization Toolbox.

Use the paretosearch algorithm to find the optimal tradeoffs between competing objective functions. See paretosearch (Global Optimization Toolbox) and options (Global Optimization Toolbox).

Modal optimization Parameters

Use the Modal optimization algorithm with a composite model to select the best operating mode for each operating point. The algorithm uses the fmincon algorithm to optimize an objective for each operating mode and select the best solution.

Modal optimization has the same parameters as fmincon, plus two additional parameters.

Parameter	Description
Mode variable index	Specify mode variable. The Optimization Quick Start Tool sets up the mode variable as the first optimization variable.
Objective to determine best mode (index)	(Optional) If you have multiple CAGE objectives, choose which objective to use to select best mode. The default is 1, so CAGE uses the optimized values of the first objective to select the best mode.

For more information, see Set Up Modal Optimizations.

Scale Optimization

The Optimization menu contains the option to Scale Optimization Items — Select this to toggle scaling on and off. When you select scaling on, objective and constraint evaluations are (approximately) scaled onto the range [-1 1]. With scaling off, when you run the optimization the objective and constraint evaluations return their raw numbers.

This setting is not recommended. Instead, try running your optimization with scaling turned off to see whether the optimization converges to a satisfactory solution. Check the output flags and the contour view for confirmation. If your optimization solution is unsatisfactory, check to see if the objective and constraint functions have different scales. In this case, try turning on scaling.

The output view always shows the solutions in raw, unscaled values, whether or not you use scaling to evaluate the problem.