package operations_research.glop
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parameters.proto:28next id = 73
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optional GlopParameters.ScalingAlgorithm scaling_method = 57
optional GlopParameters.PricingRule feasibility_rule = 1
PricingRule to use during the feasibility phase.
optional GlopParameters.PricingRule optimization_rule = 2
PricingRule to use during the optimization phase.
optional double refactorization_threshold = 6
We estimate the factorization accuracy of B during each pivot by using the fact that we can compute the pivot coefficient in two ways: - From direction[leaving_row]. - From update_row[entering_column]. If the two values have a relative difference above this threshold, we trigger a refactorization.
optional double recompute_reduced_costs_threshold = 8
We estimate the accuracy of the iteratively computed reduced costs. If it falls below this threshold, we reinitialize them from scratch. Note that such an operation is pretty fast, so we can use a low threshold. It is important to have a good accuracy here (better than the dual_feasibility_tolerance below) to be sure of the sign of such a cost.
optional double recompute_edges_norm_threshold = 9
Note that the threshold is a relative error on the actual norm (not the squared one) and that edge norms are always greater than 1. Recomputing norms is a really expensive operation and a large threshold is ok since this doesn't impact directly the solution but just the entering variable choice.
optional double primal_feasibility_tolerance = 10
This tolerance indicates by how much we allow the variable values to go out of bounds and still consider the current solution primal-feasible. We also use the same tolerance for the error A.x - b. Note that the two errors are closely related if A is scaled in such a way that the greatest coefficient magnitude on each column is 1.0. This is also simply called feasibility tolerance in other solvers.
optional double dual_feasibility_tolerance = 11
Variables whose reduced costs have an absolute value smaller than this tolerance are not considered as entering candidates. That is they do not take part in deciding whether a solution is dual-feasible or not. Note that this value can temporarily increase during the execution of the algorithm if the estimated precision of the reduced costs is higher than this tolerance. Note also that we scale the costs (in the presolve step) so that the cost magnitude range contains one. This is also known as the optimality tolerance in other solvers.
optional double ratio_test_zero_threshold = 12
During the primal simplex (resp. dual simplex), the coefficients of the direction (resp. update row) with a magnitude lower than this threshold are not considered during the ratio test. This tolerance is related to the precision at which a Solve() involving the basis matrix can be performed. TODO(user): Automatically increase it when we detect that the precision of the Solve() is worse than this.
optional double harris_tolerance_ratio = 13
This impacts the ratio test and indicates by how much we allow a basic variable value that we move to go out of bounds. The value should be in [0.0, 1.0) and should be interpreted as a ratio of the primal_feasibility_tolerance. Setting this to 0.0 basically disables the Harris ratio test while setting this too close to 1.0 will make it difficult to keep the variable values inside their bounds modulo the primal_feasibility_tolerance. Note that the same comment applies to the dual simplex ratio test. There, we allow the reduced costs to be of an infeasible sign by as much as this ratio times the dual_feasibility_tolerance.
optional double small_pivot_threshold = 14
When we choose the leaving variable, we want to avoid small pivot because they are the less precise and may cause numerical instabilities. For a pivot under this threshold times the infinity norm of the direction, we try various countermeasures in order to avoid using it.
optional double minimum_acceptable_pivot = 15
We never follow a basis change with a pivot under this threshold.
optional double drop_tolerance = 52
In order to increase the sparsity of the manipulated vectors, floating point values with a magnitude smaller than this parameter are set to zero (only in some places). This parameter should be positive or zero.
optional bool use_scaling = 16
Whether or not we scale the matrix A so that the maximum coefficient on each line and each column is 1.0.
optional GlopParameters.CostScalingAlgorithm cost_scaling = 60
optional GlopParameters.InitialBasisHeuristic initial_basis = 17
What heuristic is used to try to replace the fixed slack columns in the initial basis of the primal simplex.
optional bool use_transposed_matrix = 18
Whether or not we keep a transposed version of the matrix A to speed-up the pricing at the cost of extra memory and the initial tranposition computation.
optional int32 basis_refactorization_period = 19
Number of iterations between two basis refactorizations. Note that various conditions in the algorithm may trigger a refactorization before this period is reached. Set this to 0 if you want to refactorize at each step.
optional bool dynamically_adjust_refactorization_period = 63
If this is true, then basis_refactorization_period becomes a lower bound on the number of iterations between two refactorization (provided there is no numerical accuracy issues). Depending on the estimated time to refactorize vs the extra time spend in each solves because of the LU update, we try to balance the two times.
optional GlopParameters.SolverBehavior solve_dual_problem = 20
Whether or not we solve the dual of the given problem. With a value of auto, the algorithm decide which approach is probably the fastest depending on the problem dimensions (see dualizer_threshold).
optional double dualizer_threshold = 21
When solve_dual_problem is LET_SOLVER_DECIDE, take the dual if the number of constraints of the problem is more than this threshold times the number of variables.
optional double solution_feasibility_tolerance = 22
When the problem status is OPTIMAL, we check the optimality using this relative tolerance and change the status to IMPRECISE if an issue is detected. The tolerance is "relative" in the sense that our thresholds are: - tolerance * max(1.0, abs(bound)) for crossing a given bound. - tolerance * max(1.0, abs(cost)) for an infeasible reduced cost. - tolerance for an infeasible dual value.
optional bool provide_strong_optimal_guarantee = 24
If true, then when the solver returns a solution with an OPTIMAL status, we can guarantee that: - The primal variable are in their bounds. - The dual variable are in their bounds. - If we modify each component of the right-hand side a bit and each component of the objective function a bit, then the pair (primal values, dual values) is an EXACT optimal solution of the perturbed problem. - The modifications above are smaller than the associated tolerances as defined in the comment for solution_feasibility_tolerance (*). (*): This is the only place where the guarantee is not tight since we compute the upper bounds with scalar product of the primal/dual solution and the initial problem coefficients with only double precision. Note that whether or not this option is true, we still check the primal/dual infeasibility and objective gap. However if it is false, we don't move the primal/dual values within their bounds and leave them untouched.
optional bool change_status_to_imprecise = 58
If true, the internal API will change the return status to imprecise if the solution does not respect the internal tolerances.
optional double max_number_of_reoptimizations = 56
When the solution of phase II is imprecise, we re-run the phase II with the opposite algorithm from that imprecise solution (i.e., if primal or dual simplex was used, we use dual or primal simplex, respectively). We repeat such re-optimization until the solution is precise, or we hit this limit.
optional double lu_factorization_pivot_threshold = 25
Threshold for LU-factorization: for stability reasons, the magnitude of the chosen pivot at a given step is guaranteed to be greater than this threshold times the maximum magnitude of all the possible pivot choices in the same column. The value must be in [0,1].
optional double max_time_in_seconds = 26
Maximum time allowed in seconds to solve a problem.
optional double max_deterministic_time = 45
Maximum deterministic time allowed to solve a problem. The deterministic time is more or less correlated to the running time, and its unit should be around the second (at least on a Xeon(R) CPU E5-1650 v2 @ 3.50GHz). TODO(user): Improve the correlation.
optional int64 max_number_of_iterations = 27
Maximum number of simplex iterations to solve a problem. A value of -1 means no limit.
optional int32 markowitz_zlatev_parameter = 29
How many columns do we look at in the Markowitz pivoting rule to find a good pivot. See markowitz.h.
optional double markowitz_singularity_threshold = 30
If a pivot magnitude is smaller than this during the Markowitz LU factorization, then the matrix is assumed to be singular. Note that this is an absolute threshold and is not relative to the other possible pivots on the same column (see lu_factorization_pivot_threshold).
optional bool use_dual_simplex = 31
Whether or not we use the dual simplex algorithm instead of the primal.
optional bool allow_simplex_algorithm_change = 32
During incremental solve, let the solver decide if it use the primal or dual simplex algorithm depending on the current solution and on the new problem. Note that even if this is true, the value of use_dual_simplex still indicates the default algorithm that the solver will use.
optional int32 devex_weights_reset_period = 33
Devex weights will be reset to 1.0 after that number of updates.
optional bool use_preprocessing = 34
Whether or not we use advanced preprocessing techniques.
optional bool use_middle_product_form_update = 35
Whether or not to use the middle product form update rather than the standard eta LU update. The middle form product update should be a lot more efficient (close to the Forrest-Tomlin update, a bit slower but easier to implement). See for more details: Qi Huangfu, J. A. Julian Hall, "Novel update techniques for the revised simplex method", 28 january 2013, Technical Report ERGO-13-0001 http://www.maths.ed.ac.uk/hall/HuHa12/ERGO-13-001.pdf
optional bool initialize_devex_with_column_norms = 36
Whether we initialize devex weights to 1.0 or to the norms of the matrix columns.
optional bool exploit_singleton_column_in_initial_basis = 37
Whether or not we exploit the singleton columns already present in the problem when we create the initial basis.
optional double dual_small_pivot_threshold = 38
Like small_pivot_threshold but for the dual simplex. This is needed because the dual algorithm does not interpret this value in the same way. TODO(user): Clean this up and use the same small pivot detection.
optional double preprocessor_zero_tolerance = 39
A floating point tolerance used by the preprocessors. This is used for things like detecting if two columns/rows are proportional or if an interval is empty. Note that the preprocessors also use solution_feasibility_tolerance() to detect if a problem is infeasible.
optional double objective_lower_limit = 40
The solver will stop as soon as it has proven that the objective is smaller than objective_lower_limit or greater than objective_upper_limit. Depending on the simplex algorithm (primal or dual) and the optimization direction, note that only one bound will be used at the time. Important: The solver does not add any tolerances to these values, and as soon as the objective (as computed by the solver, so with some imprecision) crosses one of these bounds (strictly), the search will stop. It is up to the client to add any tolerance if needed.
optional double objective_upper_limit = 41
optional double degenerate_ministep_factor = 42
During a degenerate iteration, the more conservative approach is to do a step of length zero (while shifting the bound of the leaving variable). That is, the variable values are unchanged for the primal simplex or the reduced cost are unchanged for the dual simplex. However, instead of doing a step of length zero, it seems to be better on degenerate problems to do a small positive step. This is what is recommended in the EXPAND procedure described in: P. E. Gill, W. Murray, M. A. Saunders, and M. H. Wright. "A practical anti- cycling procedure for linearly constrained optimization". Mathematical Programming, 45:437\u2013474, 1989. Here, during a degenerate iteration we do a small positive step of this factor times the primal (resp. dual) tolerance. In the primal simplex, this may effectively push variable values (very slightly) further out of their bounds (resp. reduced costs for the dual simplex). Setting this to zero reverts to the more conservative approach of a zero step during degenerate iterations.
optional int32 random_seed = 43
At the beginning of each solve, the random number generator used in some part of the solver is reinitialized to this seed. If you change the random seed, the solver may make different choices during the solving process. Note that this may lead to a different solution, for example a different optimal basis. For some problems, the running time may vary a lot depending on small change in the solving algorithm. Running the solver with different seeds enables to have more robust benchmarks when evaluating new features. Also note that the solver is fully deterministic: two runs of the same binary, on the same machine, on the exact same data and with the same parameters will go through the exact same iterations. If they hit a time limit, they might of course yield different results because one will have advanced farther than the other.
optional bool use_absl_random = 72
Whether to use absl::BitGen instead of MTRandom.
optional int32 num_omp_threads = 44
Number of threads in the OMP parallel sections. If left to 1, the code will not create any OMP threads and will remain single-threaded.
optional bool perturb_costs_in_dual_simplex = 53
When this is true, then the costs are randomly perturbed before the dual simplex is even started. This has been shown to improve the dual simplex performance. For a good reference, see Huangfu Q (2013) "High performance simplex solver", Ph.D, dissertation, University of Edinburgh.
optional bool use_dedicated_dual_feasibility_algorithm = 62
We have two possible dual phase I algorithms. Both work on an LP that minimize the sum of dual infeasiblities. One use dedicated code (when this param is true), the other one use exactly the same code as the dual phase II but on an auxiliary problem where the variable bounds of the original problem are changed. TODO(user): For now we have both, but ideally the non-dedicated version will win since it is a lot less code to maintain.
optional double relative_cost_perturbation = 54
The magnitude of the cost perturbation is given by RandomIn(1.0, 2.0) * ( relative_cost_perturbation * cost + relative_max_cost_perturbation * max_cost);
optional double relative_max_cost_perturbation = 55
optional double initial_condition_number_threshold = 59
If our upper bound on the condition number of the initial basis (from our heurisitic or a warm start) is above this threshold, we revert to an all slack basis.
optional bool log_search_progress = 61
If true, logs the progress of a solve to LOG(INFO). Note that the same messages can also be turned on by displaying logs at level 1 for the relevant files.
optional bool log_to_stdout = 66
If true, logs will be displayed to stdout instead of using Google log info.
optional double crossover_bound_snapping_distance = 64
If the starting basis contains FREE variable with bounds, we will move any such variable to their closer bounds if the distance is smaller than this parameter. The starting statuses can contains FREE variables with bounds, if a user set it like this externally. Also, any variable with an initial BASIC status that was not kept in the initial basis is marked as FREE before this step is applied. Note that by default a FREE variable is assumed to be zero unless a starting value was specified via SetStartingVariableValuesForNextSolve(). Note that, at the end of the solve, some of these FREE variable with bounds and an interior point value might still be left in the final solution. Enable push_to_vertex to clean these up.
optional bool push_to_vertex = 65
If the optimization phases finishes with super-basic variables (i.e., variables that either 1) have bounds but are FREE in the basis, or 2) have no bounds and are FREE in the basis at a nonzero value), then run a "push" phase to push these variables to bounds, obtaining a vertex solution. Note this situation can happen only if a starting value was specified via SetStartingVariableValuesForNextSolve().
optional bool use_implied_free_preprocessor = 67
If presolve runs, include the pass that detects implied free variables.
optional double max_valid_magnitude = 70
Any finite values in the input LP must be below this threshold, otherwise the model will be reported invalid. This is needed to avoid floating point overflow when evaluating bounds * coeff for instance. In practice, users shouldn't use super large values in an LP. With the default threshold, even evaluating large constraint with variables at their bound shouldn't cause any overflow.
optional double drop_magnitude = 71
Value in the input LP lower than this will be ignored. This is similar to drop_tolerance but more aggressive as this is used before scaling. This is mainly here to avoid underflow and have simpler invariant in the code, like a * b == 0 iff a or b is zero and things like this.
optional bool dual_price_prioritize_norm = 69
On some problem like stp3d or pds-100 this makes a huge difference in speed and number of iterations of the dual simplex.
This is only used if use_scaling is true. After the scaling is done, we also scale the objective by a constant factor. This is important because scaling the cost has a direct influence on the meaning of the dual_feasibility_tolerance. Because we usually use a fixed tolerance, the objective must be well scaled to make sense.
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NO_COST_SCALING = 0
Leave the cost as is.
CONTAIN_ONE_COST_SCALING = 1
This is the most defensive option. It makes sure that [min_cost_magnitude, max_cost_magnitude] contains 1.0, and if not, it makes the closest magnitude bound equal to one.
MEAN_COST_SCALING = 2
Make the mean of the non-zero costs equals to one.
MEDIAN_COST_SCALING = 3
Make the median of the non-zero costs equals to one.
Heuristics to use in the primal simplex to remove fixed slack variables from the initial basis.
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NONE = 0
Leave the fixed slack variables in the basis.
BIXBY = 1
Use the heuristic described in: Robert E. Bixby, "Implementing the Simplex Method: The Initial Basis" ORSA Jounal on Computing, Vol. 4, No. 3, Summer 1992. http://joc.journal.informs.org/content/4/3/267.abstract It requires use_scaling to be true, otherwise it behaves like NONE.
TRIANGULAR = 2
Replace the fixed columns while keeping the initial basis triangular. The heuristic to select which column to use first is similar to the one used for BIXBY. This algorithm is similar to the "advanced initial basis" GLPK uses by default. Both algorithm produce a triangular initial basis, however the heuristics used are not exactly the same.
MAROS = 3
Use a version of Maros's triangular feasibility crash https://books.google.fr/books?isbn=1461502578 Chapter 9.8.2.1
General strategy used during pricing.
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DANTZIG = 0
Strategy using only the reduced cost of a variable. Note that compared to a textbook rule, we normalize the reduced cost of a variable using the norm of the associated column. This improves quite a bit the rule at almost no extra complexity. See the first paper from Ping-Qi Pan cited in primal_edge_norms.h.
STEEPEST_EDGE = 1
Normalize the reduced costs by the norm of the edges. Since computing norms at each step is too expensive, reduced costs and norms are updated iteratively from one iteration to the next.
DEVEX = 2
Normalize the reduced costs by an approximation of the norm of the edges. This should offer a good tradeoff between steepest edge and speed.
Supported algorithms for scaling: EQUILIBRATION - progressive scaling by row and column norms until the marginal difference passes below a threshold. LINEAR_PROGRAM - EXPERIMENTAL: finding optimal scale factors using a linear program in the log scale.
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DEFAULT = 0
EQUILIBRATION = 1
LINEAR_PROGRAM = 2
Like a Boolean with an extra value to let the algorithm decide what is the best choice.
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ALWAYS_DO = 0
NEVER_DO = 1
LET_SOLVER_DECIDE = 2