Optimizer control settings

Analytica Optimizer GuideOptimizer control settings

This chapter shows you how to specify Optimizer engine settings in DefineOptimization(), determine the available settings, defaults and possible range for each optimization engine, determine size capacities for installed engines, control termination criteria during optimization, select search algorithms, and specify numeric precision.

Sections

Controlling the search

The optimization engine exposes several settings that you can change to influence how the search for the optimum proceeds and when it terminates. The specific collection of available settings is a function of which engine is used to solve the optimization, so that if you install and use an add-on engine, other than the engine that comes standard with Analytica Optimizer, the possible settings might be different. The OptInfo() function can be used to view current values for a problem.

To see this, define a variable as:

   OptInfo(Opt, "Settings")

Where Opt identifies the variable containing the DefineOptimization() function.

Settings can be changed for a particular problem by specifying values for the SettingName and SettingValue parameters to DefineOptimization(). The first subsection below describes how you specify and view settings, while the subsequent sub-sections detail particular settings used by engines the come standard with Analytica Optimizer.

Selecting the optimization engine

Four optimization engines come standard with Analytica Optimizer:

LP/Quadratic - uses a dual simplex method combined with branch-and bound for mixed-integer constraints, with a variety of integer cut-set procedures. This is generally the engine of choice for LPs and mixed-integer LPs. For hard mixed-integer LPs, however, the Evolutionary engine uses a very different approach and might be worth trying.

SOCP Barrier - uses interior point methods designed specifically for quadratically constrained convex problems. The GRG Nonlinear engine is often a good alternative for thi type of problem, especially if the constraints end up being non-convex.

GRG Nonlinear - The Generalized Reduced Gradient solver is suitable for smooth non-linear problems. If gradients and Jacobians can be analytically determined, the speed of this method will be dramatically faster.

Evolutionary - Best suited for non-smooth problems the evolutionary engine creates a population of potential solutions and keeps the best ones.. By default, the Evolutionary engine does not use gradient information. However, if the LocalSearch setting is on, then it optimizes sample points before adding them to the population using various techniques including gradient-based search.

The following matrix shows engine compatibility for each problem type:

		LP/Quadratic	SOCP Barrier	GRG Nonlinear	Evolutionary
LP	Linear Program	*	*	*	*
QP	Quadratic Program (linearly constrained)	*	*	*	*
QCP	Quadratically Constrained Program		*^[1]	*	*
CQCP	Convex QCP		*	*	*
NCQCP	Non-Convex QCP			*	*
NLP	Non-Linear Program (smooth)			*	*
NSP	Non-Smooth Program			*	*

If you have purchased other add-on engines, other options might also be available to you. You can obtain a full list of installed engines and the problem types supported by each by evaluating the following Analytica expression.

   OptEngineInfo("All","ProblemTypes")

To explicitly select the engine to be used, include the Engine parameter to DefineOptimization().

   Engine : Optional Text

For example:

   DefineOptimization( ..., Engine: "Evolutionary" )

If you do not specify the engine, Analytica selects an appropriate engine based on the properties of the problem that you specified. However, if the engine does not perform satisfactorily on that problem, you might obtain better results with a different engine.

To determine what engine is actually used on a problem, evaluate this Analytica expression.

   OptInfo(Opt, "Engine")

Where Opt is the object returned by DefineOptimization().

Examining engine capabilities

Information about the limits on the maximum number of variables or constraints allowed by each installed engine can be accessed using this expression:

 OptEngineInfo( "All",["MaxVars","MaxIntVars","MaxConstraints"])

This returns a table indexed by .ProblemType, .Engine and the limit type, e.g.:

The problem types displayed include are:

Element	Description
LP	linear program
QP	quadratic objective, linear constraints
QCP	quadratic with convex quadratic constraints (solvers designed specifically for quadratics treat this as if the problem is convex)
NLP	smooth nonlinear
NSP	non-smooth nonlinear

Specifying settings

If you want to change the value for a single control setting, you can specify values for two optional parameters, settingName and settingValue, to DefineOptimization(), providing the text name of the setting to settingName, and the numeric value to settingValue. For example, if you want to set the Scaling parameter to 1, you would modify your call to DefineOptimization() as follows.

   DefineOptimization( .., settingName: "Scaling", settingValue: 1 )

To alter more than one control setting, you need to supply arrays to these parameters. The arrays passed to settingName and settingValue should have a single common index. If the index of the array passed to settingValue is a list of labels, where the index labels contain the name of each control setting, then you only need to include the settingValue parameter.

It is often convenient to specify control settings in a self-indexed edit table. The following steps illustrate this:

Drag a variable node to your diagram, title it Opt Settings.
In the definition pane, set the definition type to Table.
In the Index Chooser box, select Opt Settings (Self) as the table index.
Click the row heading cell, and change Item 1 to Scaling.
With the row header still selected, press down-arrow to add a row.
Change the second row header cell to MaxTime.
Enter 1 into the first table body cell.
Enter 30 into the second body table cell.

In your call to DefineOptimization(), insert a settng parameter as follows.

     DefineOptimization( ..., settingValue: Opt_Settings )

The Optimizer scales parameters and terminates after 30 seconds if the optimum has not been found. A self-indexed table set up in this fashion makes it easy to adjust multiple control settings if the need arises.

Examining available settings

The following function returns the set of control settings used for a problem.

   OptInfo(opt, "Setting")

Replace opt with the name of the variable holding the result from DefineOptimization().

You can also access the range of allowed values for each setting, as well as the default value, using OptInfo() or OptEngineInfo(). OptInfo() is used when you have a problem instance, OptEngineInfo() is defined when you know the name of the engine but don’t have a problem instance.

The range (min/max) of possible values for each setting, and the default value, can be obtained using these — first case using an existing problem instance, second case using the engine name:

   OptInfo( opt,["MinSetting","MaxSetting","Defaults"])
   OptEngineInfo("LP/Quadratic",["MinSetting","MaxSetting","Defaults"])

Termination controls

Iterations

Specifies the maximum number of iterations (pivots) by the simplex algorithm during the optimization. If this is exceeded, OptStatusNum() returns 3 (Iterates limit reached. Indicates an early exit of the algorithm.). Maximum number of generations in Evolutionary solver. Maximum number of gradient descent steps by GRG Nonlinear. If the problem has integer or grouped integer domains, it is preferred to use the MaxSubproblems setting instead of Iterations.

Default: no limit

MaxSubproblems

Applies only to problems with integer or grouped integer domains. Places a limit on the number of sub-problems that the Branch & Bound algorithm explores before pausing and prompting the user to stop or continue.

Default: no limit

MaxIntegerSols

Applies only to problems with integer or grouped integer domains. Places a limit on the number of integer solutions the Branch & Bound algorithm explores before pausing and prompting the user to stop or continue.

Default: no limit

MaxTime

Maximum number of seconds the Optimizer spends on the problem. If exceeded, OptStatusNum() is 10 (Time out status. Returned when the maximum allowed time has been exceeded. Indicates an early exit of the algorithm.).

Default: no limit

MaxTimeNoImp

The maximum number of seconds that the Optimizer continues without finding any improvement in the best solution.

Default: 30 seconds

Allowed range: positive

IntTolerance

In a MIP optimization, if the branch-and-bound algorithm can determine that the best solution found so far is within this relative tolerance of the true optimal, it terminates the search and return the best solution found so far. The bound is relative, meaning a value of 10% guarantees a solution within 10% of the optimal. Often, the branch-and-bound algorithm quickly locates a nearly optimal solution, but then spends a large amount of refining its best solution to the true optimum. Specifying a non-zero gap tolerance can eliminate this additional search, thus in some cases drastically reducing computation time. The gap is computed as the absolute value of the difference between the best solution so far, and the best bound on the optimum, divided by the best bound on the optimum. With zero gap (default), the search continues until the entire search space is eliminated so that the global optimum is reached.

Default: 0%

Allowed range: 0 to 1

Convergence

The evolutionary solver stops with status “Solver has converged to the current solution” when nearly all members in the current population have very similar fitness values. This stopping criteria is satisfied when 99% of the population members all have fitness values within Convergence tolerance of each other.

The fitness value is a combination of the objective function value and a penalty for constraints still violated. If you think the evolutionary solver is terminating too quickly, you can make this tolerance smaller, but you might also want to increase MutationRate or PopulationSize in order to increase the diversity of trial solutions.

Default: 10^-4

Allowed range: 0 to 1

Tolerance

If the relative (i.e., percentage) improvement observed during the previous MaxTimeNoImp seconds does not exceed this value, then Evolutionary solver terminates. See MaxTimeNoImp.

Default: 0

Allowed range: 0 to 1

MaxTimeNoImp

Controls the amount of time (in seconds) that the evolutionary solver is willing to spend without making any significant progress. If the relative improvement during this time has not exceeded the setting specified by Tolerance, it terminates with status set to either Solver cannot improve the current solution or Solver could not find a feasible solution.

Default: 10-5

Allowed range: 10-9 to 10-4

MaxFeasibleSolutions

The maximum number of feasible solutions found by the Evolutionary algorithm before terminating.

Default: no limit

Allowed range: positive

↑ You may not know whether your QCP is convex when you formulate it, and DefineOptimization’s quadratic analysis does not determine convexity. Testing for convexity can be more computationally intensive than solving the problem, so if you think SOCP Barrier is the preferred engine, you can attempt to solve it using SOCP Barrier. During the solution, it may succeed, or it may detect the non-convexity and terminate without a feasible solution. Always check OptStatusText().

[1] You may not know whether your QCP is convex when you formulate it, and DefineOptimization’s quadratic analysis does not determine convexity. Testing for convexity can be more computationally intensive than solving the problem, so if you think SOCP Barrier is the preferred engine, you can attempt to solve it using SOCP Barrier. During the solution, it may succeed, or it may detect the non-convexity and terminate without a feasible solution. Always check OptStatusText().

[1]