Reference · 2.0 development

Solver settings

All settings of SHOT, including those of the MIP and NLP solvers and of GAMS. These only have an effect if SHOT is built with them, as noted in the descriptions; a build without them warns when they are changed. Some settings have another default for nonconvex problems, applied unless Strategy.UseRecommendedSettings is false, and the default MIP solver depends on the build.

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 2: Only external (through callback)	{0,…,2}	0
Dual.TreeStrategy The main strategy to use 0: Multi-tree 1: Single-tree	{0,1}	1

Convex Bounding

These settings control the convex bounding strategy that solves a MIP problem with all hyperplane cuts generated for convex constraints so far and ignoring those generated for nonconvex constraints. This will give a dual bound for the nonconvex problem.

Name and description	Valid values	Default value
Dual.ConvexBounding.IdleIterations How many iterations with new hyperplanes the convex bounding strategy is skipped before it is performed again: 0 = Every iteration with new hyperplanes, 1 = Every second such iteration, etc.	{0,…,∞}	10
Dual.ConvexBounding.Use Enable the convex bounding strategy for nonconvex problems	true/false	true

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 Max number of violated nonlinear constraints, the most violated first, to generate cutting planes for in the interior point search, as a fraction of the number of nonlinear constraints	[0,1]	0.25
Dual.ESH.InteriorPoint.CuttingPlane.IterationLimit Iteration limit for minimax cutting plane solver Nonconvex default: 50	{1,…,∞}	100
Dual.ESH.InteriorPoint.CuttingPlane.IterationLimitSubsolver Iteration limit for minimization subsolver	{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,∞]	1
Dual.ESH.InteriorPoint.CuttingPlane.TerminationToleranceRel Relative termination tolerance between LP and linesearch objective	[0,∞]	1
Dual.ESH.InteriorPoint.CuttingPlane.TimeLimit Time limit for minimax solver	[0,∞]	10
Dual.ESH.InteriorPoint.MinimaxObjectiveLowerBound Lower bound for minimax objective variable	[-∞,0]	-1000000000000
Dual.ESH.InteriorPoint.MinimaxObjectiveUpperBound Upper bound for minimax objective variable	[-∞,∞]	0.1
Dual.ESH.InteriorPoint.Strategy Strategy for finding ESH interior points 0: Use internal strategy 1: Only external (through callback)	{0,1}	0
Dual.ESH.InteriorPoint.UsePrimalSolution Utilize primal solution as interior point 0: Only if there is no interior point 1: Add as new 2: Replace old 3: Use average	{0,…,3}	1
Dual.ESH.Rootsearch.ConstraintTolerance Constraint tolerance for when not to add individual hyperplanes	[0,∞]	1e-08
Dual.ESH.Rootsearch.UseMaxFunction Perform rootsearch on max function, otherwise on individual constraints	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 Max number of violated nonlinear constraints, the most violated first, to generate hyperplanes for in each solution point, as a fraction of the number of nonlinear constraints Nonconvex default: 1	[0,1]	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]	0.1
Dual.HyperplaneCuts.MaxPerIteration Maximal number of hyperplanes to add per iteration	{0,…,∞}	200
Dual.HyperplaneCuts.NonfinitePointRetreatFactor The smallest fraction of the distance to a point where the constraint is finite that the point a hyperplane is generated in is moved, when the constraint is not finite in it	[1e-12,0.5]	0.001
Dual.HyperplaneCuts.ObjectiveRootSearch When to use the objective root search 0: Always 1: IfConvex 2: Never	{0,…,2}	1
Dual.HyperplaneCuts.UniqueConstraints Allow only one hyperplane per constraint per iteration	true/false	false
Dual.HyperplaneCuts.UseIntegerCuts Add integer cuts for infeasible integer-combinations for binary problems Nonconvex default: true	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	[-∞,∞]	1.7976931348623157e+308
Dual.MIP.CutOff.Tolerance An extra tolerance for the objective cutoff value (to prevent infeasible subproblems)	[0,∞]	1e-05
Dual.MIP.CutOff.UseInitialValue Use the initial cutoff value	true/false	false
Dual.MIP.InfeasibilityRepair.CutResetLimit Max number of times the cuts of nonconvex constraints are removed without primal objective value improvement when the infeasibility repair loops	{0,…,∞}	3
Dual.MIP.InfeasibilityRepair.IntegerCuts Allow feasibility repair of integer cuts	true/false	false
Dual.MIP.InfeasibilityRepair.IterationLimit Max number of infeasible problems repaired without primal objective value improvement	{0,…,∞}	100
Dual.MIP.InfeasibilityRepair.RelaxCutsViolatedByPrimal Relax the cuts of nonconvex constraints that cut off a known primal solution	true/false	true
Dual.MIP.InfeasibilityRepair.TimeLimit Time limit when repairing infeasible problem	[0,∞]	10
Dual.MIP.InfeasibilityRepair.Use Enable the infeasibility repair strategy for nonconvex problems	true/false	true
Dual.MIP.NodeLimit Node limit for each solve of the MIP solver: 0: No limit	{0,…,∞}	0
Dual.MIP.NumberOfThreads Number of threads to use in MIP solver: 0: Automatic	{0,…,999}	0
Dual.MIP.OptimalityTolerance The reduced-cost tolerance for optimality in the MIP solver	[1e-09,0.01]	1e-06
Dual.MIP.RandomSeed Random seed for the pseudorandom choices in the MIP solver: 0: The default of the solver used	{0,…,∞}	0
Dual.MIP.SolutionLimit.ForceOptimal.Iteration Iterations without dual bound updates for forcing optimal MIP solution (multi-tree)	{0,…,∞}	10000
Dual.MIP.SolutionLimit.ForceOptimal.Time Time (s) without dual bound updates for forcing optimal MIP solution (multi-tree)	[0,∞]	1000
Dual.MIP.SolutionLimit.IncreaseFactor Factor the MIP solution limit is multiplied by when increased: 1: Increase by one	[1,∞]	2
Dual.MIP.SolutionLimit.IncreaseIterations Max number of iterations between MIP solution limit increases	{0,…,∞}	50
Dual.MIP.SolutionLimit.Initial Initial MIP solution limit Nonconvex default: ∞	{1,…,∞}	1
Dual.MIP.SolutionLimit.UpdateTolerance The constraint tolerance for when to update MIP solution limit	[0,∞]	0.001
Dual.MIP.SolutionPool.Capacity The maximum number of solutions in the solution pool of the MIP solver	{1,…,∞}	100
Dual.MIP.Solver Which MIP solver to use. Default: the first available of Gurobi, Cplex, Highs and Cbc 0: Cplex 1: Gurobi 2: Cbc 3: Highs	{0,…,3}	3
Dual.MIP.UpdateObjectiveBounds Update nonlinear objective variable bounds to primal/dual bounds	true/false	false
Dual.MIP.UseDualSolutionStart Give the discrete values of the previous MIP solution as a partial MIP start in the multi-tree strategy; Cplex and Gurobi get it in addition to the primal solution, HiGHS and Cbc instead of it Nonconvex default: false	true/false	true

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 convex.

Name and description	Valid values	Default value
Dual.ReductionCut.MaxIterations Maximum number of reduction cuts without primal improvement before terminating	{0,…,∞}	20
Dual.ReductionCut.ReductionFactor Reduction of the cutoff per reduction cut, relative to max(1,	cutoff	), in the Fraction strategy when the relative gap is at most 0.1 or above 1
Dual.ReductionCut.Strategy The reduction cut strategy to use 0: Fraction 1: GoldenRatio	{0,1}	0
Dual.ReductionCut.Use Enable the dual reduction cut strategy for nonconvex problems	true/false	true

Relaxation strategies

These settings control 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, if Dual.Relaxation.Use is true (by default not for nonconvex problems): 0: Disable	{0,…,∞}	0
Dual.Relaxation.IterationLimit The max number of relaxed LP problems to solve initially	{0,…,∞}	200
Dual.Relaxation.MaxLazyConstraints Max number of lazy constraints to add in relaxed solutions in single-tree strategy	{0,…,∞}	0
Dual.Relaxation.TerminationTolerance Stop solving relaxed problems when the maximum constraint deviation is at most this value	[0,∞]	0.5
Dual.Relaxation.TimeLimit Time limit (s) when solving LP problems initially	[0,∞]	30
Dual.Relaxation.Use Initially solve continuous dual relaxations Nonconvex default: false	true/false	true

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,…,∞}	5
Model.BoundTightening.FeasibilityBased.TimeLimit Time limit for bound tightening	[0,∞]	2
Model.BoundTightening.FeasibilityBased.Use Perform feasibility-based bound tightening	true/false	true
Model.BoundTightening.FeasibilityBased.UseAfterCallback Perform feasibility-based bound tightening again after a BoundTightening callback has tightened bounds	true/false	false
Model.BoundTightening.FeasibilityBased.UseNonlinear Perform feasibility-based bound tightening on nonlinear expressions	true/false	true
Model.BoundTightening.InitialPOA.ConstraintTolerance Constraint termination tolerance	[0,∞]	0.1
Model.BoundTightening.InitialPOA.CutStrategy Dual cut strategy 0: ESH 1: ECP	{0,1}	1
Model.BoundTightening.InitialPOA.DirectionalSolves Maximum number of additional solves minimizing or maximizing a variable in a convex constraint without cuts	{0,…,∞}	10
Model.BoundTightening.InitialPOA.IterationLimit Iteration limit for POA	{1,…,∞}	50
Model.BoundTightening.InitialPOA.ObjectiveConstraintTolerance Objective constraint termination tolerance	[0,∞]	0.001
Model.BoundTightening.InitialPOA.ObjectiveGapAbsolute Absolute objective gap termination level	[0,∞]	0.1
Model.BoundTightening.InitialPOA.ObjectiveGapRelative Relative objective gap termination level	[0,∞]	0.1
Model.BoundTightening.InitialPOA.StagnationConstraintTolerance Tolerance factor for when no progress is made	[0,∞]	0.01
Model.BoundTightening.InitialPOA.StagnationIterationLimit Limit for iterations without significant progress	{0,…,∞}	5
Model.BoundTightening.InitialPOA.TimeLimit Time limit for all the problems solved for the initial POA	[0,∞]	5
Model.BoundTightening.InitialPOA.Use Create an initial polyhedral outer approximation	true/false	false

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,∞]	1e-05

Automatic reformulations

These settings control the automatic reformulations performed in SHOT.

Name and description	Valid values	Default value
Model.Reformulation.AbsoluteValue.MaximumBigM The largest big-M used to bound an absolute value from above with a binary variable; above it, the absolute value is only bounded from below	[0,∞]	100000000
Model.Reformulation.Bilinear.AddConvexEnvelope Add convex envelopes (subject to original bounds) to bilinear terms	true/false	false
Model.Reformulation.Bilinear.IntegerFormulation Reformulate integer bilinear terms 0: No 1: No if nonconvex quadratic terms allowed by MIP solver 2: Yes	{0,…,2}	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,…,∞}	250
Model.Reformulation.Bilinear.InverseFormulation Reformulate constraints ax1x2 >= c with positive variables as c/(ax1) - x2 <= 0 (and c/(ax2) - x1 <= 0) 0: None 1: One constraint 2: Both constraints	{0,…,2}	2
Model.Reformulation.Constraint.PartitionNonlinearTerms When to partition nonlinear sums in constraints 0: Always 1: If result is convex 2: Never	{0,…,2}	1
Model.Reformulation.Constraint.PartitionQuadraticTerms When to partition quadratic sums in constraints, also in nonlinear constraints 0: Always 1: If result is convex 2: Never	{0,…,2}	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,…,2}	1
Model.Reformulation.ObjectiveFunction.EpigraphStrategy How to choose between objective-function and epigraph-constraint form for the objective. ‘Unchanged’ performs no epigraph or anti-epigraph reformulation, keeping the objective function exactly as given; ‘Objective function’ always keeps (or folds back to) a direct objective function; ‘Epigraph constraint’ always introduces an epigraph auxiliary-variable constraint for nonlinear or quadratic objectives 0: Unchanged 1: Objective function 2: Epigraph constraint	{0,…,2}	0
Model.Reformulation.ObjectiveFunction.PartitionNonlinearTerms When to partition nonlinear sums in objective function 0: Always 1: If result is convex 2: Never	{0,…,2}	1
Model.Reformulation.ObjectiveFunction.PartitionQuadraticTerms When to partition quadratic sums in the objective function, also in a nonlinear objective function 0: Always 1: If result is convex 2: Never	{0,…,2}	1
Model.Reformulation.Quadratics.Decomposition.Formulation Placement of the original term coefficient when decomposing a quadratic term 0: Coefficient is included in reformulation 1: Coefficient remains	{0,1}	0
Model.Reformulation.Quadratics.Decomposition.LDLMaximumFill Skip the LDL decomposition if L would have more than this times the nonzeros of the quadratic matrix, and over a million (0 = no limit)	[0,∞]	100
Model.Reformulation.Quadratics.Decomposition.Method How to decompose convex quadratic functions 0: No decomposition 1: Eigenvalue decomposition 2: LDL decomposition	{0,…,2}	2
Model.Reformulation.Quadratics.Decomposition.Tolerance Terms with corresponding eigenvalues or diagonal elements in D-matrix smaller than this value will be ignored	[0,∞]	1e-07
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,…,3}	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 Nonconvex default with Gurobi: 3 (Use nonconvex quadratic objective and constraints)	{0,…,3}	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	[0,∞]	1e+50
Model.Variables.Continuous.MinimumLowerBound Minimum lower bound for continuous variables	[-∞,0]	-1e+50
Model.Variables.Integer.MaximumUpperBound Maximum upper bound for integer variables	[0,∞]	2000000000
Model.Variables.Integer.MinimumLowerBound Minimum lower bound for integer variables	[-∞,0]	-2000000000
Model.Variables.NonlinearObjectiveVariable.Bound Absolute bound for the auxiliary nonlinear objective variable, used when the bounds of the objective function cannot be calculated with interval arithmetic	[0,∞]	1000000000000

Modeling system

These settings control functionality used in the interfaces to different modeling environments.

GAMS interface

These settings control functionality used in the GAMS interface. Requires SHOT compiled with GAMS (API 21 or newer).

Name and description	Valid values	Default value
ModelingSystem.GAMS.QExtractAlg Extraction algorithm for quadratic equations in GAMS interface 0: automatic 1: threepass 2: doubleforward 3: concurrent (GAMS API 25 or newer)	{0,…,3}	0
ModelingSystem.GAMS.QExtractDenseSwitchFactor Sparse/dense factor for quadratic extraction algorithm in GAMS interface (GAMS API 28 or newer).	[0,∞]	0.008
ModelingSystem.GAMS.QExtractDenseSwitchLog Whether to print additional information about sparse/dense factor choice in quadratic extraction algorithm in GAMS interface (GAMS API 28 or newer).	true/false	false

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.OutputDirectory Where to save the output files 0: Problem directory 1: Program directory	{0,1}	1
Output.SaveNumberOfSolutions Max number of primal solutions to keep and to save to OSrL or GDX files	{1,…,∞}	1
Output.Console.DualSolver.Show Show output from dual solver on console	true/false	false
Output.Console.Iteration.Detail Which iterations are shown on the console: all, or only those that update the objective gap (and those with a primal NLP call). Some iterations are shown regardless after 100 hidden ones or 2 s 0: Full 1: On objective gap update 2: On objective gap update and all primal NLP calls	{0,…,2}	1
Output.Console.LogLevel Log level for console output 0: Trace 1: Debug 2: Info 3: Warning 4: Error 5: Critical 6: Off	{0,…,6}	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,…,6}	2
Output.GAMS.AlternateSolutionsFile Name of GAMS GDX file to write alternative solutions to	string

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 whenever a MIP solution fulfils the nonlinear constraints Nonconvex default: 0 (Use each iteration)	{0,…,2}	2
Primal.FixedInteger.CreateInfeasibilityCut Create cutting planes in the solution point of the fixed-integer NLP problem for the nonlinear constraints it violates	true/false	false
Primal.FixedInteger.CreateSupportingHyperplanes Create supporting hyperplanes in a feasible solution of the fixed-integer NLP problem for the convex nonlinear objective function and the nonlinear constraints active in it.	true/false	true
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,∞]	0.001
Primal.FixedInteger.Enumeration.MaxCombinations Max number of combinations of the discrete variables for the exhaustive search to be performed	{1,…,∞}	50
Primal.FixedInteger.Enumeration.TimeLimit Time limit (s) for all NLP problems in the exhaustive search	[0,∞]	20
Primal.FixedInteger.Enumeration.UseAsFallback Solve NLP problems for all combinations of the discrete variables if the objective gap could not be closed	true/false	true
Primal.FixedInteger.Enumeration.UseInitially Solve NLP problems for all combinations of the discrete variables before the dual strategy Nonconvex default: true	true/false	false
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,…,∞}	10
Primal.FixedInteger.Frequency.Time Max duration (s) between calls	[0,∞]	5
Primal.FixedInteger.IterationLimit Max number of iterations per call of the NLP solver: 0: The default of the NLP solver	{0,…,∞}	0
Primal.FixedInteger.NumberOfThreads Number of threads for each NLP problem, in the NLP solver and its BLAS and OpenMP libraries: 0: Automatic	{0,…,∞}	1
Primal.FixedInteger.OnlyUniqueIntegerCombinations Solve the NLP problem only once for each combination of the discrete variables. If false, it is solved again from different continuous values, e.g. for nonconvex problems Nonconvex default: false	true/false	true
Primal.FixedInteger.Solver NLP solver to use. Default: Ipopt. If it is not available, the first available of CONOPT, the GAMS NLP solvers (only for GAMS models), Uno and SHOT is used 0: Ipopt 1: GAMS 2: SHOT 3: Uno 4: Conopt	{0,…,4}	0
Primal.FixedInteger.Source Which solutions of the dual problem the fixed-integer NLP problem is solved from. In single-tree, the callbacks use each new incumbent, and this applies to the solution pool after the search 0: All 1: First 2: All feasible 3: First and the one with the smallest constraint deviation 4: With smallest constraint deviation Nonconvex default: 0 (All)	{0,…,4}	3
Primal.FixedInteger.SourceProblem Which problem formulation to use for NLP problem 0: Original problem 1: Reformulated problem 2: Both Nonconvex default: 2 (Both)	{0,…,2}	1
Primal.FixedInteger.SupportingHyperplanes.ActiveTolerance A constraint with a value within this tolerance of its bound is active in the fixed-integer NLP solution	[0,∞]	1e-05
Primal.FixedInteger.SupportingHyperplanes.MaxPerSolution Max number of supporting hyperplanes in each fixed-integer NLP solution	{0,…,∞}	50
Primal.FixedInteger.SupportingHyperplanes.Nonconvex Also create the supporting hyperplanes for nonconvex constraints and objective functions. As the hyperplanes of the dual strategy for these, they are not global and can be relaxed if they cut away a primal solution	true/false	false
Primal.FixedInteger.SupportingHyperplanes.OnlyViolated Only create the supporting hyperplanes that cut away the dual solution the integer assignment comes from	true/false	false
Primal.FixedInteger.TimeLimit Time limit (s) per NLP problem	[0,∞]	10
Primal.FixedInteger.Use Use the fixed integer primal strategy	true/false	true
Primal.FixedInteger.UseStartingPoint Solve an NLP problem from a given starting point that is not feasible, e.g. the levels of the variables in GAMS or the initial values in AMPL, before the first dual problem, and from such points given by the PrimalCandidateSearch callback at the next NLP call	true/false	true
Primal.FixedInteger.Warmstart Warm start the NLP solver	true/false	true
Primal.PolishSolution.NumberOfPoints After the search, polish the solution with NLP problems started from the best primal solution and from the dual solutions of this many last iterations, not for LP, MILP or convex continuous problems: 0: Off	{0,…,∞}	1

Primal root search

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 solution tolerances

These settings sets various tolerances for accepting primal solutions.

Name and description	Valid values	Default value
Primal.Tolerance.Integer Integer tolerance for accepting primal solutions	[0,0.5]	1e-05
Primal.Tolerance.LinearConstraint Linear constraint tolerance for accepting primal solutions	[0,∞]	1e-06
Primal.Tolerance.NonlinearConstraint Nonlinear constraint tolerance for accepting primal solutions	[0,∞]	1e-05
Primal.Tolerance.TrustLinearConstraintValues Trust that fixed-integer NLP and LP solvers respect linear constraints; MIP candidates are always checked	true/false	true

Strategy

Overall strategy parameters used in SHOT.

Name and description	Valid values	Default value
Strategy.UseRecommendedSettings Use the recommended defaults for nonconvex problems and MIP solvers, shown in the setting descriptions, and the solver-specific adjustments	true/false	true

Subsolver functionality

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

Cbc

Requires SHOT compiled with 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.Cuts Use the cut generators of Cbc, which can give a wrong optimal value for a MILP problem	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,…,6}	4
Subsolver.Cbc.Scaling Whether to scale problem 0: automatic 1: dynamic 2: equilibrium 3: geometric 4: off 5: rowsonly	{0,…,5}	0
Subsolver.Cbc.Strategy This turns on newer features 0: easy problems 1: default 2: aggressive	{0,…,2}	1

CONOPT settings

Options for the CONOPT NLP solver. Requires SHOT compiled with CONOPT.

Name and description	Valid values	Default value
Subsolver.Conopt.DerivativeCheck CONOPT compares the first and second derivatives with numerical ones (Lkdebg, Lkdeb2): 0 = never, -1 = at the initial point, n = every n-th iteration	{-1,…,∞}	0
Subsolver.Conopt.FeasibilityTolerance CONOPT feasibility tolerance (Rtnwma)	[1e-12,0.01]	1e-09
Subsolver.Conopt.OptimalityTolerance CONOPT reduced-gradient tolerance (Rtredg)	[1e-12,0.01]	1e-09

Cplex

Requires SHOT compiled with 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 number of constraints and bounds requiring relaxation in first phase and execute second phase to find optimum among minimal relaxations 4: Minimize the sum of squares of required relaxations in first phase only 5: Minimize the sum of squares of required relaxations in first phase and execute second phase to find optimum among minimal relaxations	{0,…,5}	0
Subsolver.Cplex.MIPEmphasis Sets the MIP emphasis 0: Balanced 1: Feasibility 2: Optimality 3: Best bound 4: Hidden feasible	{0,…,4}	0
Subsolver.Cplex.MemoryEmphasis Try to conserve memory when possible	{0,1}	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,…,3}	1
Subsolver.Cplex.NumericalEmphasis Emphasis on numerical stability	{0,1}	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,…,3}	0
Subsolver.Cplex.ParallelMode Parallel mode in CPLEX, i.e., whether it runs deterministically when using several threads -1: Opportunistic 0: Automatic 1: Deterministic	{-1,…,1}	0
Subsolver.Cplex.Probe Sets the MIP probing level -1: No probing 0: Automatic 1: Moderate 2: Aggressive 3: Very aggressive	{-1,…,3}	0
Subsolver.Cplex.SolutionPoolGap Sets the relative gap filter on objective values in the solution pool	[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,…,4}	0
Subsolver.Cplex.SolutionPoolReplace How to replace solutions in the solution pool when full 0: Replace oldest 1: Replace worst 2: Find diverse	{0,…,2}	0
Subsolver.Cplex.WorkDirectory Directory for swap file	string
Subsolver.Cplex.WorkMemory Memory limit for when to start swapping to disk	[0,∞]	0

GAMS

Settings for the GAMS NLP solvers. Requires SHOT compiled with GAMS.

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

Requires SHOT compiled with Gurobi.

Name and description	Valid values	Default value
Subsolver.Gurobi.Heuristics The relative amount of time spent in MIP heuristics.	[0,1]	0.05
Subsolver.Gurobi.MIPFocus MIP focus 0: Automatic 1: Feasibility 2: Optimality 3: Best bound	{0,…,3}	0
Subsolver.Gurobi.NumericFocus How much effort Gurobi spends on detecting and managing numerical issues 0: Automatic 1: Mild 2: Moderate 3: Aggressive	{0,…,3}	0
Subsolver.Gurobi.PoolSearchMode Finds extra solutions 0: No extra effort 1: Try to find solutions 2: Find n best solutions	{0,…,2}	0
Subsolver.Gurobi.ScaleFlag Controls model scaling -1: Automatic 0: Off 1: Mild 2: Moderate 3: Aggressive	{-1,…,3}	-1

Highs

Requires SHOT compiled with HiGHS.

Name and description	Valid values	Default value
Subsolver.Highs.DebugLevel Debug level for HiGHS internal assertions 0: off 1: low 2: medium 3: high	{0,…,3}	0
Subsolver.Highs.MIPAllowRestart Whether MIP restart is permitted	true/false	true
Subsolver.Highs.MIPDetectSymmetry Whether MIP symmetry should be detected	true/false	true
Subsolver.Highs.MIPHeuristicEffort Effort spent for MIP heuristics	[0,1]	0.05
Subsolver.Highs.MIPHeuristicRunShifting Run Shifting heuristic	true/false	false
Subsolver.Highs.MIPHeuristicRunZiRound Run Zi Round heuristic	true/false	false
Subsolver.Highs.MIPIPMSolver Interior point solver that HiGHS uses in the MIP solver, e.g., for the analytic center 0: choose 1: ipx 2: hipo (only if HiGHS has been built with HiPO)	{0,…,2}	0
Subsolver.Highs.Parallel Use parallelization 0: off 1: choose 2: on	{0,…,2}	1
Subsolver.Highs.Presolve Use presolve 0: off 1: choose 2: on	{0,…,2}	1
Subsolver.Highs.RunCrossover Run crossover 0: off 1: choose 2: on	{0,…,2}	0

Ipopt

Requires SHOT compiled with Ipopt.

Name and description	Valid values	Default value
Subsolver.Ipopt.ConstraintViolationTolerance Constraint violation tolerance in Ipopt	[0,∞]	1e-08
Subsolver.Ipopt.HessianApproximation The Hessian of the Lagrangian used by Ipopt. Automatic uses a limited-memory approximation if the exact Hessian of a nonlinear expression with at least 64 variables is nearly dense, since it is then expensive 0: Exact 1: Limited memory 2: Automatic	{0,…,2}	2
Subsolver.Ipopt.LinearSolver Ipopt linear subsolver 0: Default 1: MA27 2: MA57 3: MA86 4: MA97 5: MUMPS	{0,…,5}	0
Subsolver.Ipopt.OptionsFile An Ipopt options file with any Ipopt options, read instead of ipopt.opt in the working directory. Its options override those set by SHOT, e.g. the linear solver, except the time limit (max_wall_time) of each solve	string
Subsolver.Ipopt.RelativeConvergenceTolerance Relative convergence tolerance in Ipopt (tol)	[0,∞]	1e-08

Root search solver

Settings for the Boost rootsearch functionality.

Name and description	Valid values	Default value
Subsolver.Rootsearch.MaxIterations Maximal root search iterations	{0,…,∞}	100
Subsolver.Rootsearch.Method Root search method to use 0: TOMS748 1: Bisection	{0,1}	0
Subsolver.Rootsearch.TerminationTolerance Termination tolerance for the length of the root search interval for lambda in [0, 1], which also stops when the interval cannot be divided further	[0,∞]	1e-16

SHOT primal NLP solver

Name and description	Valid values	Default value
Subsolver.SHOT.ReuseHyperplanes.Fraction The fraction of generated hyperplanes to reuse.	[0,1]	0.1
Subsolver.SHOT.ReuseHyperplanes.Use Reuse valid generated hyperplanes in main dual model.	true/false	true
Subsolver.SHOT.UseFBBT Do FBBT on NLP problem.	true/false	true

Uno

Requires SHOT compiled with Uno.

Name and description	Valid values	Default value
Subsolver.Uno.ConstraintViolationTolerance Constraint violation tolerance in Uno	[0,∞]	1e-06
Subsolver.Uno.HessianModel How Uno models the Hessian 0: Exact 1: L-BFGS 2: L-SR1	{0,…,2}	0
Subsolver.Uno.OptionsFile Uno option file to read additional options from	string
Subsolver.Uno.Preset The Uno algorithm to use 0: Automatic 1: Ipopt 2: filterSQP	{0,…,2}	0
Subsolver.Uno.RelativeConvergenceTolerance Dual (stationarity) tolerance in Uno (dual_tolerance)	[0,∞]	1e-06

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 (not used for termination in the multi-tree strategy)	[0,∞]	1e-08
Termination.IterationLimit Iteration limit for main strategy	{1,…,∞}	200000
Termination.ObjectiveConstraintTolerance Termination tolerance for the nonlinear objective constraint	[0,∞]	1e-08
Termination.TimeLimit Time limit (s) for solver	[0,∞]	1.7976931348623157e+308
Termination.DualStagnation.ConstraintTolerance Min absolute difference between max nonlinear constraint errors in subsequent iterations for termination	[0,∞]	1e-06
Termination.DualStagnation.IterationLimit Max number of iterations without significant dual objective value improvement	{0,…,∞}	1000
Termination.ObjectiveGap.Absolute Absolute gap termination tolerance for objective function	[0,∞]	0.001
Termination.ObjectiveGap.Relative Relative gap termination tolerance for objective function	[0,∞]	0.001
Termination.PrimalStagnation.IterationLimit Number of iterations without significant primal improvement after which an objective cut is added (nonconvex problems with reduction cuts only)	{0,…,∞}	50