LINDO Global Optimization Parameter Options

List of Options

Option Name MPL Name Solver Param ParamNr Type Default Min Max
Minimal box width GOPTolMinWidthBox GOP_BoxTol 402 real 1e-6 0 MAXREAL
Maximum box width GOPTolMaxWidthBox GOP_WidTol 403 real 1e-4 0 MAXREAL
Delta convexification tolerance GOPTolDelta GOP_DeltaTol 404 real -1 -1 MAXINT
Certify global optimality GOPCertifyGlobalOpt GOP_OptChkMd 407 real 1e-4 0 MAXREAL
Use maximum width GOPMaxWidthFlag GOP_MaxWidMd 409 flag 0 0 1
GOP branching strategy GOPBranching GOP_BranchMd 408 list 5 0 5
GOP presolve level GOPPresolve GOP_PreLevel 410 list 1022 0 1022
GOP post-solving level GOPPostSolving GOP_PostLevel 411 int 6 0 6
GOP node selection GOPNodeSelection GOP_BBSrchMd 412 list 1 0 1
GOP decomposition GOPDecompositionRule GOP_DecompPtMd 413 list 1 0 1
GOP Algebraic reformulation GOPAlgebraicReform GOP_AlgReformMd 414 list 18 0 30
GOP Rounding GOPReliableRounding GOP_RelBrndMd 415 list 0 0 6
GOP Use bound limits GOPUseBoundLimit GOP_UseBndLim 417 list 1 0 2
GOP branch and bound GOPBandBStrategy GOP_CoreLevel 419 list 30 0 32
GOP Optimization mode GOPOptimizationMode GOP_Opt_Mode 420 list 1 0 2
GOP Heuristic mode GOPHeuristicMode GOP_Heu_Mode 421 flag 0 0 1
GOP new solution branching limit GOPNewSolBranchLimit GOP_LSolBranLim 424 int -1 -1 MAXINT
Use global optimizer UseGlobalOptimizer flag 0 0 1


Description of Options

Minimal box width

This value specifies the minimal width of variable intervals in a box allowed to branch. The default value is 1.0e-6.

Maximum box width

This value specifies the maximal width of variable intervals for a box to be considered as an incumbent box containing an incumbent solution.

Delta convexification tolerance

This value is the delta tolerance in the GOP convexification. It is a measure of how closely the additional constraints added as part of convexification should be satisfied. The default value is 1e-7.

Certify global optimality

This specifies the criterion used to certify the global optimality. When this value is 0, the absolute deviation of objective lower and upper bounds should be smaller than GOP optimality tolerance at the global optimum. When its value is 1, the relative deviation of objective lower and upper bounds should be smaller than GOP optimality tolerance at the global optimum. The default value is 2, which means both absolute and relative tolerances are satisfied at global optimum.

Use maximum width

This is the maximum width flag for the global solution. The GOP branch and bound may continue contracting a box with an incumbent solution until its maximum width is smaller than maximum box width. The possible value of 1 means the maximum width criterion is performed and 0 means the maximum width criterion is suppressed. The default value is 0.

GOP branching strategy

This specifies the direction to branch first when branching on a variable. The branch variable is selected as the one that holds the largest magnitude in the measure. Possible values are:

Absolute width (0) Uses absolute width.
Locally relative width (1) Uses locally relative width.
Globally relative width (2) Uses globally relative width.
Globally relative distance (3) Uses globally relative distance from the convex minimum to the bounds.
Absolute violation (4) Absolute violation between the function and its convex envelope at the convex minimum.
Relative violation (5) Relative violation between the function and its convex envelope at the convex minimum.

GOP presolve level

This controls the amount and type of GOP pre-solving. Possible options are:

Initial local optimization (2)
Initial linear constraint propagation (4)
Recursive linear constraint propagation (8)
Recursive nonlinear constraint propagation (16)
Search for good near feasible solutions (32)
Check for unboundedness (64)
Alter derivative methods (128)
MIP pre-optimizations (256)
NLP pre-optimizations (512)

GOP post-solving level

This controls the amount and type of GOP post-solving. The default value is 6 which will reoptimize variable bounds.

GOP node selection

This specifies the node selection rule for choosing between all active nodes in the GOP branch-and-bound tree when solving global optimization programs. Possible selections are:

Depth first search (0) Uses depth first approach during the branch and bound phase.
Worst bound (1) Selects node with the worst bound.

GOP decomposition

This specifies the decomposition point selection rule. In the branch step of GOP branch-and-bound, a branch point M is selected to decompose the selected variable interval [Lb, Ub] into two subintervals, [Lb, M] and [M, Ub]. Possible options are:

Mid-point (0) Uses selection rule based on mid-points.
Convex minimum (1) Based on local or convex minimum.

GOP Algebraic reformulation

This controls the algebraic reformulation rule for a GOP. The algebraic reformulation and analysis is very crucial in building a tight convex envelope to enclose the nonlinear/nonconvex functions. A lower degree of overestimation on convex envelopes helps increase the convergence rate to the global optimum. Possible options are:

Rearrange (2) Rearranges and collects terms.
Full expansion (4) Expands all parentheses
Retain (8) Retains nonlinear functions.
Selective expansion (16) Selectively expands parentheses.

GOP Rounding

This controls the reliable rounding rule in the GOP branch-and-bound. The global solver applies many sub optimizations to estimate the lower and upper bounds on the global optimum. A rounding error or numerical instability could unintentionally cut off a good solution. A variety of reliable approaches are available to improve the precision. Thought the default setting does not use any of these routines.

Small tolerances (2) Use smaller optimality/feasibility tolerances and appropriate presolving options.
Interval arithmetic (4) Apply interval arithmetic to verify the solution feasibility.

GOP Use bound limits

This value is a flag for the parameter GOP bound limit". Possible values are:

Not used (0) Does not use the bound limit on the variables.
In start (1) Use the bound limit right at the beginning of global optimization.
After start (2) Use the bound limit after the initial local optimization, if selected. This properly sets the bound limit for each variable to include the initial solution, if any, within the range.

GOP branch and bound

This controls the strategy of GOP branch-and-bound procedure. Possible options are:

LP convex (2) Uses LP convex relaxations.
Honor NLP solutions (4) Honors NLP solutions.
Box branching (8) Uses box branching.
Honor IPM solutions (16) Honors IPM solutions.

GOP Optimization mode

This specifies the mode for global search. Possible values are

Feasible solution (0) Does global search for a feasible solution.
Optimal solution (1) Does global search for an optimal solution.
Unboundedness (2) Does global search for an unbounded solution.

GOP Heuristic mode

This flag specifies if the heuristic is used in the global solver to find good solution. The default is off.

GOP new solution branching limit

This value controls the branch limit until finding a new nonlinear solution since the last nonlinear solution is found. The default value is -1, which means no branch limit is imposed.

Use global optimizer

Boolean option that determines whether one wants the solve the NLP model with LINDO's global solver. The default is set to off.


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