LP and MILP Settings

This page describes the parameter settings available for cuOpt’s LP and MILP solvers. These parameters are set as string constants in case of C API and in case of Server Thin client as raw strings. Please refer to examples in C and Server Thin client for more details.

Note

When setting parameters in thin client solver settings, remove CUOPT_ from the parameter name and convert to lowercase. For example, CUOPT_TIME_LIMIT would be set as time_limit.

Parameters common to LP/MILP

We begin by describing parameters common to both the MILP and LP solvers

Time Limit

CUOPT_TIME_LIMIT controls the time limit in seconds after which the solver will stop and return the current solution. For performance reasons, cuOpt does not constantly checks for time limit. Thus, the solver may run slightly over the limit. If set along with the iteration limit, cuOpt will stop when the first limit (iteration or time) is hit.

Note: by default there is no time limit. So cuOpt will run until it finds an optimal solution, or proves the problem is infeasible or unbounded.

Log to Console

CUOPT_LOG_TO_CONSOLE controls whether cuOpt should log information to the console during a solve. If true, a logging info is written to the console, if false no logging info is written to the console (logs may still be written to a file.)

Note: the default value is true.

Log File

CUOPT_LOG_FILE controls the name of a log file where cuOpt should write information about the solve.

Note: the default value is "" and no log file is written.

Num CPU Threads

CUOPT_NUM_CPU_THREADS controls the number of CPU threads used in the LP and MIP solvers. Set this to a small value to limit the amount of CPU resources cuOpt uses. Set this to a large value to improve solve times for CPU parallel parts of the solvers.

Note: by default the number of CPU threads is automatically determined based on the number of CPU cores.

Linear Programming

We now describe the parameter settings used to control cuOpt’s Linear Programming solvers

Method

CUOPT_METHOD controls the method to solve the linear programming problem. Three methods are available:

• Concurrent: Use both PDLP and dual simplex in parallel.

• PDLP: Use the PDLP method.

• Dual Simplex: Use the dual simplex method.

Note: The default method is Concurrent.

C API users should use the constants defined in C API Section for Methods for this parameter.

Server Thin client users should use the Method enum for this parameter.

PDLP Solver Mode

CUOPT_PDLP_MODE controls the mode under which PDLP should operate. The mode will change the way the PDLP internally optimizes the problem. The mode choice can drastically impact how fast a specific problem will be solved. Users are encouraged to test different modes to see which one fits the best their problem. By default, the solver uses Stable2, the best overall mode from our experiments. For now, only three modes are available: Stable2, Methodical1, and Fast1.

For now, we do not offer a mechanism to know upfront which solver mode will be the best for a specific problem.

C API users should use the constants defined in C API Section for PDLP Solver Modes for this parameter.

Server Thin client users should use the PDLPSolverMode enum for this parameter.

Iteration Limit

CUOPT_ITERATION_LIMIT controls the iteration limit after which the solver will stop and return the current solution. For performance reasons, cuOpt’s does not constantly checks for iteration limit, thus, the solver might run a few extra iterations over the limit. If set along with the time limit, cuOpt will stop at the first limit (iteration or time) reached.

Note: by default there is no iteration limit. So, cuOpt will run until it finds an optimal solution, or proves the problem is infeasible or unbounded.

Infeasiblity Detection

CUOPT_INFEASIBILITY_DETECTION controls whether PDLP should detect infeasibility. Note that infeasibility detection in PDLP is not always accurate. Some problems detected as infeasible may converge under a different tolerance factor. Detecting infeasibility consumes both more runtime and memory. The added runtime is between 3% and 7%, the added memory consumpution is between 10% and 20%.

Note: by default PDLP will not detect infeasibility. Dual simplex will always detect infeasibility regardless of this setting.

Strict Infeasibility

CUOPT_STRICT_INFEASIBILITY controls the strict infeasibility mode in PDLP. When true if either the current or the average solution is detected as infeasible, PDLP will stop. When false both the current and average solution need to be detected as infeasible for PDLP to stop.

Note: the default value is false.

Crossover

CUOPT_CROSSOVER controls whether PDLP should crossover to a basic solution after a optimal solution is found. Changing this value has a significant impact on accuracy and runtime. By default the solutions provided by PDLP are low accuracy and may have many variables that lie between their bounds. Enabling crossover allows the user to obtain a high-quality basic solution that lies at a vertex of the feasible region. If n is the number of variables, and m is the number of constraints, n - m variables will be on their bounds in a basic solution.

Note: the default value is false.

Save Best Primal So Far

CUOPT_SAVE_BEST_PRIMAL_SOLUTION controls whether PDLP should save the best primal solution so far With this parameter set to true, PDLP * Will always prioritize a primal feasible to a non primal feasible * If a new primal feasible is found, the one with the best primal objective will be kept * If no primal feasible was found, the one with the lowest primal residual will be kept * If two have the same primal residual, the one with the best objective will be kept

Note: the default value is false.

First Primal Feasible

CUOPT_FIRST_PRIMAL_FEASIBLE controls whether PDLP should stop when the first primal feasible solution is found.

Note: the default value is false.

Per Constraint Residual

CUOPT_PER_CONSTRAINT_RESIDUAL controls whether PDLP should compute the primal & dual residual per constraint instead of globally.

Note: the default value is false.

Absolute Primal Tolerance

CUOPT_ABSOLUTE_PRIMAL_TOLERANCE controls the absolute primal tolerance used in the primal feasibility check. Changing this value might have a significant impact on accuracy and runtime if the relative part (the right-hand side vector b L2 norm) is close to, or equal to, 0.

The primal feasibility condition is computed as follows:

primal_feasiblity < absolute_primal_tolerance + relative_primal_tolerance * l2_norm(b)

Default value is 1e-4.

Relative Primal Tolerance

CUOPT_RELATIVE_PRIMAL_TOLERANCE controls the relative primal tolerance used in PDLP’s primal feasibility check. Changing this value has a significant impact on accuracy and runtime. The primal feasibility condition is computed as follows:

primal_feasiblity < absolute_primal_tolerance + relative_primal_tolerance * l2_norm(b)

Note: the default value is 1e-4.

Absolute Dual Tolerance

CUOPT_ABSOLUTE_DUAL_TOLERANCE controls the absolute dual tolerance used in PDLP’s dual feasibility check. Changing this value might have a significant impact on accuracy and runtime if the relative part (the objective vector L2 norm) is close to, or equal to, 0.

The dual feasibility condition is computed as follows:

dual_feasiblity < absolute_dual_tolerance + relative_dual_tolerance * l2_norm(c)

Note: the default value is 1e-4.

Relative Dual Tolerance

CUOPT_RELATIVE_DUAL_TOLERANCE controls the relative dual tolerance used in PDLP’s dual feasibility check. Changing this value has a significant impact on accuracy and runtime. The dual feasibility condition is computed as follows:

dual_feasiblity < absolute_dual_tolerance + relative_dual_tolerance * l2_norm(c)

Note: the default value is 1e-4.

Absolute Gap Tolerance

CUOPT_ABSOLUTE_GAP_TOLERANCE controls the absolute gap tolerance used in PDLP’s duality gap check. Changing this value might have a significant impact on accuracy and runtime if the relative part (|primal_objective| + |dual_objective|) is close to, or equal to, 0.

The duality gap is computed as follows:

duality_gap < absolute_gap_tolerance + relative_gap_tolerance * (|primal_objective| + |dual_objective|)

Note: the default value is 1e-4.

Relative Gap Tolerance

CUOPT_RELATIVE_GAP_TOLERANCE controls the relative gap tolerance used in PDLP’s duality gap check. Changing this value has a significant impact on accuracy and runtime. The duality gap is computed as follows:

duality_gap < absolute_gap_tolerance + relative_gap_tolerance * (|primal_objective| + |dual_objective|)

Note: the default value is 1e-4.

Mixed Integer Linear Programming

We now describe parameter settings for the MILP solvers

Heuristics only

CUOPT_HEURISTICS_ONLY controls if only the GPU heuristics should be run. When set to true, only the primal bound is improved via the GPU. When set to false, both the GPU and CPU are used and the dual bound is improved on the CPU.

Note: the default value is false.

Scaling

CUOPT_MIP_SCALING controls if scaling should be applied to the MIP problem. When true scaling is applied, when false, no scaling is applied.

Note: the defaulte value is true.

Absolute Tolerance

CUOPT_ABSOLUTE_TOLERANCE controls the MIP absolute tolerance.

Note: the default value is 1e-4.

Relative Tolerance

CUOPT_RELATIVE_TOLERANCE controls the MIP relative tolerance.

Note: the default value is 1e-6.

Integrality Tolerance

CUOPT_INTEGRALITY_TOLERANCE controls the MIP integrality tolerance. A variable is considered to be integral, if it is within the integrality tolerance of an integer.

Note: the default value is 1e-5.

Absolute MIP Gap

CUOPT_MIP_ABSOLUTE_GAP controls the absolute tolerance used to terminate the MIP solve. The solve terminates when:

Best Objective - Dual Bound  <= absolute tolerance

when minimizing or

Dual Bound - Best Objective <= absolute tolerance

when maximizing.

Note: the default value is 1e-10.

Relative MIP Gap

CUOPT_MIP_RELATIVE_GAP controls the relative tolerance used to terminate the MIP solve. The solve terminates when:

abs(Best Objective - Dual Bound) / abs(Best Objective) <= relative tolerance

If the Best Objective and the Dual Bound are both zero the gap is zero. If the best objective value is zero, the gap is infinity.

Note: the default value is 1e-4.