Solver options

Here are all the options that can be used in SHOT compiled. Note that the default value is normally a good starting point, so do not change options unless you have a good reason.

Dual strategy

These settings control the various functionality of the dual strategy in SHOT, i.e., the polyhedral outer approximation utilizing the ESH or ECP algorithms.

Name and description

Valid values

Default value

Dual.CutStrategy Dual cut strategy 0: ESH 1: ECP

{0.0,1.0}

0

Extended supporting hyperplane method

These settings control various aspects of the ESH implementation, including the strategy to obtain the interior point.

Name and description

Valid values

Default value

Dual.ESH.InteriorPoint.CuttingPlane.ConstraintSelectionFactor The fraction of violated constraints to generate cutting planes for

[0.0,1.0]

0.25

Dual.ESH.InteriorPoint.CuttingPlane.IterationLimit Iteration limit for minimax cutting plane solver

{1.0,...,∞}

100

Dual.ESH.InteriorPoint.CuttingPlane.IterationLimitSubsolver Iteration limit for minimization subsolver

{0.0,...,∞}

100

Dual.ESH.InteriorPoint.CuttingPlane.Reuse Reuse valid cutting planes in main dual model

true/false

false

Dual.ESH.InteriorPoint.CuttingPlane.TerminationToleranceAbs Absolute termination tolerance between LP and linesearch objective

[0.0,∞]

1.0

Dual.ESH.InteriorPoint.CuttingPlane.TerminationToleranceRel Relative termination tolerance between LP and linesearch objective

[0.0,∞]

1.0

Dual.ESH.InteriorPoint.CuttingPlane.TimeLimit Time limit for minimax solver

[0.0,∞]

10.0

Dual.ESH.InteriorPoint.MinimaxObjectiveLowerBound Lower bound for minimax objective variable

[-∞,0.0]

-1e12

Dual.ESH.InteriorPoint.MinimaxObjectiveUpperBound Upper bound for minimax objective variable

[-∞,∞]

0.1

Dual.ESH.InteriorPoint.UsePrimalSolution Utilize primal solution as interior point 0: No 1: Add as new 2: Replace old 3: Use avarage

{0.0,...,3.0}

1

Dual.ESH.Rootsearch.ConstraintTolerance Constraint tolerance for when not to add individual hyperplanes

[0.0,∞]

1e-08

Dual.ESH.Rootsearch.UniqueConstraints Allow only one hyperplane per constraint per iteration

true/false

false

Generated hyperplane cuts

These settings control how the cutting planes or supporting hyperplanes are generated.

Name and description

Valid values

Default value

Dual.HyperplaneCuts.ConstraintSelectionFactor The fraction of violated constraints to generate supporting hyperplanes / cutting planes for

[0.0,1.0]

0.5

Dual.HyperplaneCuts.Delay Add hyperplane cuts to model only after optimal MIP solution

true/false

true

Dual.HyperplaneCuts.MaxConstraintFactor Rootsearch performed on constraints with values larger than this factor times the maximum value

[1e-06,1.0]

0.1

Dual.HyperplaneCuts.MaxPerIteration Maximal number of hyperplanes to add per iteration

{0.0,...,∞}

200

Dual.HyperplaneCuts.ObjectiveRootSearch When to use the objective root search 0: Always 1: IfConvex 2: Never

{0.0,...,2.0}

1

Dual.HyperplaneCuts.UseIntegerCuts Add integer cuts for infeasible integer-combinations for binary problems

true/false

false

MIP solver

These settings control the general functionality of the MIP solver in the dual strategy. Note that solver-specific settings for Cplex, Gurobi and Cbc are available under the "Subsolver" category.

Name and description

Valid values

Default value

Dual.MIP.CutOff.InitialValue Initial cutoff value to use

[-∞,∞]

1.798e+308

Dual.MIP.CutOff.Tolerance An extra tolerance for the objective cutoff value (to prevent infeasible subproblems)

[-∞,∞]

1e-05

Dual.MIP.CutOff.UseInitialValue Use the initial cutoff value

true/false

false

Dual.MIP.InfeasibilityRepair.IntegerCuts Allow feasibility repair of integer cuts

true/false

true

Dual.MIP.InfeasibilityRepair.IterationLimit Max number of infeasible problems repaired without primal objective value improvement

{0.0,...,∞}

100

Dual.MIP.InfeasibilityRepair.TimeLimit Time limit when reparing infeasible problem

[0.0,∞]

10.0

Dual.MIP.NodeLimit Node limit to use for MIP solver in single-tree strategy

[0.0,∞]

1.798e+308

Dual.MIP.NumberOfThreads Number of threads to use in MIP solver: 0: Automatic

{0.0,...,999.0}

0

Dual.MIP.OptimalityTolerance The reduced-cost tolerance for optimality in the MIP solver

[1e-09,0.01]

1e-06

Dual.MIP.Presolve.Frequency When to call the MIP presolve 0: Never 1: Once 2: Always

{0.0,...,2.0}

1

Dual.MIP.Presolve.RemoveRedundantConstraints Remove redundant constraints (as determined by presolve)

true/false

false

Dual.MIP.Presolve.UpdateObtainedBounds Update bounds (from presolve) to the MIP model

true/false

true

Dual.MIP.SolutionLimit.ForceOptimal.Iteration Iterations without dual bound updates for forcing optimal MIP solution

{0.0,...,∞}

10000

Dual.MIP.SolutionLimit.ForceOptimal.Time Time (s) without dual bound updates for forcing optimal MIP solution

[0.0,∞]

1000.0

Dual.MIP.SolutionLimit.IncreaseIterations Max number of iterations between MIP solution limit increases

{0.0,...,∞}

50

Dual.MIP.SolutionLimit.Initial Initial MIP solution limit

{1.0,...,∞}

1

Dual.MIP.SolutionLimit.UpdateTolerance The constraint tolerance for when to update MIP solution limit

[0.0,∞]

0.001

Dual.MIP.SolutionPool.Capacity The maximum number of solutions in the solution pool

{0.0,...,∞}

100

Dual.MIP.Solver Which MIP solver to use 0: Cplex 1: Gurobi 2: Cbc

{0.0,...,2.0}

0

Dual.MIP.UpdateObjectiveBounds Update nonlinear objective variable bounds to primal/dual bounds

true/false

false

Dual reduction cut

These settings control the added dual reduction cuts from the primal solution that will try to force a better primal solution. This functionality is only used if SHOT cannot deduce that the problem is nonconvex .

Name and description

Valid values

Default value

Dual.ReductionCut.MaxIterations Max number of primal cut reduction without primal improvement

{0.0,...,∞}

5

Dual.ReductionCut.ReductionFactor The factor used to reduce the cutoff value

[0.0,1.0]

0.001

Relaxation strategies

These settings contorl various aspects regarding integer-relaxation of the dual problem.

Name and description

Valid values

Default value

Dual.Relaxation.Frequency The frequency to solve an LP problem: 0: Disable

{0.0,...,∞}

0

Dual.Relaxation.IterationLimit The max number of relaxed LP problems to solve initially

{0.0,...,∞}

200

Dual.Relaxation.MaxLazyConstraints Max number of lazy constraints to add in relaxed solutions in single-tree strategy

{0.0,...,∞}

0

Dual.Relaxation.TerminationTolerance Time limit (s) when solving LP problems initially

[-∞,∞]

0.5

Dual.Relaxation.TimeLimit Time limit (s) when solving LP problems initially

[0.0,∞]

30.0

Dual.Relaxation.Use Initially solve continuous dual relaxations

true/false

true

Tree strategy

The single-tree strategy is normally more efficient than the multi-tree one. However, not all MIP solvers support the required lazy constraint callbacks. These settings selects this strategy and controls its behaviour.

Name and description

Valid values

Default value

Dual.TreeStrategy The main strategy to use 0: Multi-tree 1: Single-tree

{0.0,1.0}

1

Optimization model

These settings control various aspects of SHOT's representation for and handling of the provided optimization model.

Bound tightening

SHOT performs bound tightening to strengthen the internal representation of the problem. These settings control how and when bound tightening is performed.

Name and description

Valid values

Default value

Model.BoundTightening.FeasibilityBased.MaxIterations Maximal number of bound tightening iterations

{0.0,...,∞}

5

Model.BoundTightening.FeasibilityBased.TimeLimit Time limit for bound tightening

[0.0,∞]

5.0

Model.BoundTightening.FeasibilityBased.Use Peform feasibility-based bound tightening

true/false

true

Model.BoundTightening.FeasibilityBased.UseNonlinear Peform feasibility-based bound tightening on nonlinear expressions

true/false

true

Convexity

These settings control the convexity detection functionality.

Name and description

Valid values

Default value

Model.Convexity.AssumeConvex Assume that the problem is convex.

true/false

false

Model.Convexity.Quadratics.EigenValueTolerance Convexity tolerance for the eigenvalues of the Hessian matrix for quadratic terms

[0.0,∞]

1e-05

Automatic reformulations

These settings control the automatic reformulations performed in SHOT.

Name and description

Valid values

Default value

Model.Reformulation.Bilinear.AddConvexEnvelope Add convex envelopes (subject to original bounds) to bilinear terms

true/false

false

Model.Reformulation.Bilinear.IntegerFormulation How to reformulate integer bilinear terms 0: None 1: 1D 2: 2D

{0.0,...,2.0}

1

Model.Reformulation.Bilinear.IntegerFormulation.MaxDomain Do not reformulate integer variables in bilinear terms which can assume more than this number of discrete values

{2.0,...,∞}

100

Model.Reformulation.Constraint.PartitionNonlinearTerms When to partition nonlinear sums in objective function 0: Always 1: If convex 2: Never

{0.0,...,2.0}

1

Model.Reformulation.Constraint.PartitionQuadraticTerms When to partition quadratic sums in objective function 0: Always 1: If convex 2: Never

{0.0,...,2.0}

1

Model.Reformulation.Monomials.Extract Extract monomial terms from nonlinear expressions

true/false

true

Model.Reformulation.Monomials.Formulation How to reformulate binary monomials 0: None 1: Simple 2: Costa and Liberti

{0.0,...,2.0}

1

Model.Reformulation.ObjectiveFunction.Epigraph.Use Reformulates a nonlinear objective as an auxiliary constraint

true/false

false

Model.Reformulation.ObjectiveFunction.PartitionNonlinearTerms When to partition nonlinear sums in objective function 0: Always 1: If convex 2: Never

{0.0,...,2.0}

1

Model.Reformulation.ObjectiveFunction.PartitionQuadraticTerms When to partition quadratic sums in objective function 0: Always 1: If convex 2: Never

{0.0,...,2.0}

1

Model.Reformulation.Quadratics.ExtractStrategy How to extract quadratic terms from nonlinear expressions 0: Do not extract 1: Extract to same objective or constraint 2: Extract to quadratic equality constraint if nonconvex 3: Extract to quadratic equality constraint even if convex

{0.0,...,3.0}

1

Model.Reformulation.Quadratics.Strategy How to treat quadratic functions 0: All nonlinear 1: Use quadratic objective 2: Use convex quadratic objective and constraints 3: Use nonconvex quadratic objective and constraints

{0.0,...,3.0}

2

Model.Reformulation.Signomials.Extract Extract signomial terms from nonlinear expressions

true/false

true

Variables

These settings control the maximum variable bounds allowed in SHOT. Projection will be performed onto these intervals. Note that the MIP solvers may have stricter requirements, in which case those may be used.

Name and description

Valid values

Default value

Model.Variables.Continuous.MaximumUpperBound Maximum upper bound for continuous variables

[-∞,∞]

1e+50

Model.Variables.Continuous.MinimumLowerBound Minimum lower bound for continuous variables

[-∞,∞]

-1e+50

Model.Variables.Integer.MaximumUpperBound Maximum upper bound for integer variables

[-∞,∞]

2e9

Model.Variables.Integer.MinimumLowerBound Minimum lower bound for integer variables

[-∞,∞]

-2e9

Model.Variables.NonlinearObjectiveVariable.Bound Max absolute bound for the auxiliary nonlinear objective variable

[-∞,∞]

1e12

Solver output

These settings control how much and what output is shown to the user from the solver.

Name and description

Valid values

Default value

Output.Console.DualSolver.Show Show output from dual solver on console

true/false

false

Output.Console.Iteration.Detail When should the fixed strategy be used 0: Full 1: On objective gap update 2: On objective gap update and all primal NLP calls

{0.0,...,2.0}

1

Output.Console.LogLevel Log level for console output 0: Trace 1: Debug 2: Info 3: Warning 4: Error 5: Critical 6: Off

{0.0,...,6.0}

2

Output.Console.PrimalSolver.Show Show output from primal solver on console

true/false

false

Output.Debug.Enable Use debug functionality

true/false

false

Output.Debug.Path The folder where to save the debug information

string

Output.File.LogLevel Log level for file output 0: Trace 1: Debug 2: Info 3: Warning 4: Error 5: Critical 6: Off

{0.0,...,6.0}

2

Output.OutputDirectory Where to save the output files 0: Problem directory 1: Program directory

{0.0,1.0}

1

Output.SaveNumberOfSolutions Save this number of primal solutions to OSrL file

{0.0,...,∞}

1

Primal heuristics

These settings control the primal heuristics used in SHOT.

Fixed-integer (NLP) strategy

The main primal strategy in SHOT is to solve integer-fixed NLP problems. These settings control, e.g., how often NLP problems are solved.

Name and description

Valid values

Default value

Primal.FixedInteger.CallStrategy When should the fixed strategy be used 0: Use each iteration 1: Based on iteration or time 2: Based on iteration or time, and for all feasible MIP solutions

{0.0,...,2.0}

2

Primal.FixedInteger.CreateInfeasibilityCut Create a cut from an infeasible solution point

true/false

false

Primal.FixedInteger.DualPointGap.Relative If the objective gap between the MIP point and dual solution is less than this the fixed strategy is activated

[0.0,∞]

0.001

Primal.FixedInteger.Frequency.Dynamic Dynamically update the call frequency based on success

true/false

true

Primal.FixedInteger.Frequency.Iteration Max number of iterations between calls

{0.0,...,∞}

10

Primal.FixedInteger.Frequency.Time Max duration (s) between calls

[0.0,∞]

5.0

Primal.FixedInteger.IterationLimit Max number of iterations per call

{0.0,...,∞}

10000000

Primal.FixedInteger.OnlyUniqueIntegerCombinations Whether to resolve with the same integer combination, e.g. for nonconvex problems with different continuous variable starting points

true/false

true

Primal.FixedInteger.Solver NLP solver to use 0: Ipopt 1: GAMS

{0.0,1.0}

0

Primal.FixedInteger.Source Source of fixed MIP solution point 0: All 1: First 2: All feasible 3: First and all feasible 4: With smallest constraint deviation

{0.0,...,4.0}

3

Primal.FixedInteger.SourceProblem Which problem formulation to use for NLP problem 0: Original problem 1: Reformulated problem 2: Both

{0.0,...,2.0}

0

Primal.FixedInteger.TimeLimit Time limit (s) per NLP problem

[0.0,∞]

10.0

Primal.FixedInteger.Use Use the fixed integer primal strategy

true/false

true

Primal.FixedInteger.Warmstart Warm start the NLP solver

true/false

true

SHOT can utilize root searches between the dual solution point and an integer-fixed interior point. This setting controls whether this strategy is used.

Name and description

Valid values

Default value

Primal.Rootsearch.Use Use a rootsearch to find primal solutions

true/false

true

Primal.Tolerance.Integer Integer tolerance for accepting primal solutions

[-∞,∞]

1e-05

Primal.Tolerance.LinearConstraint Linear constraint tolerance for accepting primal solutions

[-∞,∞]

1e-06

Primal.Tolerance.NonlinearConstraint Nonlinear constraint tolerance for accepting primal solutions

[-∞,∞]

1e-05

Primal.Tolerance.TrustLinearConstraintValues Trust that subsolvers (NLP, MIP) give primal solutions that respect linear constraints

true/false

true

Strategy

Overall strategy parameters used in SHOT.

Name and description

Valid values

Default value

Strategy.UseRecommendedSettings Modifies some settings to their recommended values based on the strategy

true/false

true

Subsolver functionality

These settings allow for more direct control of the different subsolvers utilized in SHOT.

Cbc

Name and description

Valid values

Default value

Subsolver.Cbc.AutoScale Whether to scale objective, rhs and bounds of problem if they look odd (experimental)

true/false

false

Subsolver.Cbc.DeterministicParallelMode Run Cbc with multiple threads in deterministic mode

true/false

false

Subsolver.Cbc.NodeStrategy Node strategy 0: depth 1: downdepth 2: downfewest 3: fewest 4: hybrid 5: updepth 6: upfewest

{0.0,...,6.0}

4

Subsolver.Cbc.Scaling Whether to scale problem 0: automatic 1: dynamic 2: equilibrium 3: geometric 4: off 5: rowsonly

{0.0,...,5.0}

0

Subsolver.Cbc.Strategy This turns on newer features 0: easy problems 1: default 2: aggressive

{0.0,...,2.0}

1

Cplex

Name and description

Valid values

Default value

Subsolver.Cplex.AddRelaxedLazyConstraintsAsLocal Whether to add lazy constraints generated in relaxed points as local or global

true/false

false

Subsolver.Cplex.FeasOptMode Strategy to use for the feasibility repair 0: Minimize the sum of all required relaxations in first phase only 1: Minimize the sum of all required relaxations in first phase and execute second phase to find optimum among minimal relaxations 2: Minimize the number of constraints and bounds requiring relaxation in first phase only 3: Minimize the sum of squares of required relaxations in first phase only 4: Minimize the sum of squares of required relaxations in first phase and execute second phase to find optimum among minimal relaxations

{0.0,...,4.0}

0

Subsolver.Cplex.MIPEmphasis Sets the MIP emphasis 0: Balanced 1: Feasibility 2: Optimality 3: Best bound 4: Hidden feasible

{0.0,...,4.0}

1

Subsolver.Cplex.MemoryEmphasis Try to conserve memory when possible

{0.0,1.0}

0

Subsolver.Cplex.NodeFile Where to store the node file 0: No file 1: Compressed in memory 2: On disk 3: Compressed on disk

{0.0,...,3.0}

1

Subsolver.Cplex.NumericalEmphasis Emphasis on numerical stability

{0.0,1.0}

0

Subsolver.Cplex.OptimalityTarget Specifies how CPLEX treats nonconvex quadratics 0: Automatic 1: Searches for a globally optimal solution to a convex model 2: Searches for a solution that satisfies first-order optimality conditions, but is not necessarily globally optimal 3: Searches for a globally optimal solution to a nonconvex model

{0.0,...,3.0}

0

Subsolver.Cplex.ParallelMode Controls how much time and memory should be used when filling the solution pool -1: Opportunistic 0: Automatic 1: Deterministic

{-1.0,...,1.0}

0

Subsolver.Cplex.Probe Sets the MIP probing level -1: No probing 0: Automatic 1: Moderate 2: Aggressive 3: Very aggressive

{-1.0,...,3.0}

0

Subsolver.Cplex.SolutionPoolGap Sets the relative gap filter on objective values in the solution pool

[0.0,∞]

1e+75

Subsolver.Cplex.SolutionPoolIntensity Controls how much time and memory should be used when filling the solution pool 0: Automatic 1: Mild 2: Moderate 3: Aggressive 4: Very aggressive

{0.0,...,4.0}

0

Subsolver.Cplex.SolutionPoolReplace How to replace solutions in the solution pool when full 0: Replace oldest 1: Replace worst 2: Find diverse

{0.0,...,2.0}

0

Subsolver.Cplex.UseGenericCallback Use the new generic callback in the single-tree strategy

true/false

false

Subsolver.Cplex.WorkDirectory Directory for swap file

string

Subsolver.Cplex.WorkMemory Memory limit for when to start swapping to disk

[0.0,∞]

0.0

GAMS

Settings for the GAMS NLP solvers.

Name and description

Valid values

Default value

Subsolver.GAMS.NLP.OptionsFilename Options file for the NLP solver in GAMS

string

Subsolver.GAMS.NLP.Solver NLP solver to use in GAMS (auto: SHOT chooses)

string

auto

Gurobi

Name and description

Valid values

Default value

Subsolver.Gurobi.Heuristics The relative amount of time spent in MIP heuristics.

[0.0,1.0]

0.05

Subsolver.Gurobi.MIPFocus MIP focus 0: Automatic 1: Feasibility 2: Optimality 3: Best bound

{0.0,...,3.0}

0

Subsolver.Gurobi.NumericFocus MIP focus 0: Automatic 1: Mild 2: Moderate 3: Aggressive

{0.0,...,3.0}

2

Subsolver.Gurobi.PoolSearchMode Finds extra solutions 0: No extra effort 1: Try to find solutions 2: Find n best solutions

{0.0,...,2.0}

0

Subsolver.Gurobi.PoolSolutions Determines how many MIP solutions are stored

{1.0,...,2000000000.0}

1

Subsolver.Gurobi.ScaleFlag Controls model scaling -1: Automatic 0: Off 1: Mild 2: Moderate 3: Aggressive

{-1.0,...,3.0}

-1

Ipopt

Name and description

Valid values

Default value

Subsolver.Ipopt.ConstraintViolationTolerance Constraint violation tolerance in Ipopt

[-∞,∞]

1e-08

Subsolver.Ipopt.LinearSolver Ipopt linear subsolver 0: Default 1: MA27 2: MA57 3: MA86 4: MA97 5: MUMPS

{0.0,...,5.0}

0

Subsolver.Ipopt.MaxIterations Maximum number of iterations

{0.0,...,∞}

1000

Subsolver.Ipopt.RelativeConvergenceTolerance Relative convergence tolerance

[-∞,∞]

1e-08

Root search solver

Settings for the Boost rootsearch functionality.

Name and description

Valid values

Default value

Subsolver.Rootsearch.ActiveConstraintTolerance Epsilon constraint tolerance for root search

[0.0,∞]

0.0

Subsolver.Rootsearch.MaxIterations Maximal root search iterations

{0.0,...,∞}

100

Subsolver.Rootsearch.Method Root search method to use 0: TOMS748 1: Bisection

{0.0,1.0}

0

Subsolver.Rootsearch.TerminationTolerance Epsilon lambda tolerance for root search

[0.0,∞]

1e-16

Termination

These settings control when SHOT will terminate the solution process.

Name and description

Valid values

Default value

Termination.ConstraintTolerance Termination tolerance for nonlinear constraints

[0.0,∞]

1e-08

Termination.DualStagnation.ConstraintTolerance Min absolute difference between max nonlinear constraint errors in subsequent iterations for termination

[0.0,∞]

1e-06

Termination.DualStagnation.IterationLimit Max number of iterations without significant dual objective value improvement

{0.0,...,∞}

50

Termination.IterationLimit Iteration limit for main strategy

{1.0,...,∞}

200000

Termination.ObjectiveConstraintTolerance Termination tolerance for the nonlinear objective constraint

[0.0,∞]

1e-08

Termination.ObjectiveGap.Absolute Absolute gap termination tolerance for objective function

[0.0,∞]

0.001

Termination.ObjectiveGap.Relative Relative gap termination tolerance for objective function

[0.0,∞]

0.001

Termination.PrimalStagnation.IterationLimit Max number of iterations without significant primal objective value improvement

{0.0,...,∞}

50

Termination.TimeLimit Time limit (s) for solver

[0.0,∞]

1.798e+308