# AbcSimplexDual Class Reference

This solves LPs using the dual simplex method. More...

`#include <AbcSimplexDual.hpp>`

Inheritance diagram for AbcSimplexDual:
[legend]
Collaboration diagram for AbcSimplexDual:
[legend]

List of all members.

## Public Member Functions
Description of algorithm
int | dual ()
| Dual algorithm.
int | strongBranching (int numberVariables, const int *variables, double *newLower, double *newUpper, double **outputSolution, int *outputStatus, int *outputIterations, bool stopOnFirstInfeasible=true, bool alwaysFinish=false, int startFinishOptions=0)
| For strong branching.
AbcSimplexFactorization * | setupForStrongBranching (char *arrays, int numberRows, int numberColumns, bool solveLp=false)
| This does first part of StrongBranching.
void | cleanupAfterStrongBranching (AbcSimplexFactorization *factorization)
| This cleans up after strong branching.
Functions used in dual
int | whileIteratingSerial ()
| This has the flow between re-factorizations Broken out for clarity and will be used by strong branching.
void | whileIterating2 ()
int | whileIteratingParallel (int numberIterations)
int | whileIterating3 ()
void | updatePrimalSolution ()
int | noPivotRow ()
int | noPivotColumn ()
void | dualPivotColumn ()
void | createDualPricingVectorSerial ()
| Create dual pricing vector.
int | getTableauColumnFlipAndStartReplaceSerial ()
void | getTableauColumnPart1Serial ()
void | getTableauColumnPart2 ()
int | checkReplace ()
void | replaceColumnPart3 ()
void | checkReplacePart1 ()
void | checkReplacePart1a ()
void | checkReplacePart1b ()
void | updateDualsInDual ()
| The duals are updated.
int | flipBounds ()
| The duals are updated by the given arrays.
void | flipBack (int number)
| Undo a flip.
void | dualColumn1 (bool doAll=false)
| Array has tableau row (row section) Puts candidates for rows in list Returns guess at upper theta (infinite if no pivot) and may set sequenceIn_ if free Can do all (if tableauRow created).
double | dualColumn1A ()
| Array has tableau row (row section) Just does slack part Returns guess at upper theta (infinite if no pivot) and may set sequenceIn_ if free.
double | dualColumn1B ()
| Do all given tableau row.
void | dualColumn2 ()
| Chooses incoming Puts flipped ones in list If necessary will modify costs.
void | dualColumn2Most (dualColumnResult &result)
void | dualColumn2First (dualColumnResult &result)
void | dualColumn2 (dualColumnResult &result)
| Chooses part of incoming Puts flipped ones in list If necessary will modify costs.
void | checkPossibleCleanup (CoinIndexedVector *array)
| This sees what is best thing to do in branch and bound cleanup If sequenceIn_ < 0 then can't do anything.
void | dualPivotRow ()
| Chooses dual pivot row Would be faster with separate region to scan and will have this (with square of infeasibility) when steepest For easy problems we can just choose one of the first rows we look at.
int | changeBounds (int initialize, double &changeCost)
| Checks if any fake bounds active - if so returns number and modifies updatedDualBound_ and everything.
bool | changeBound (int iSequence)
| As changeBounds but just changes new bounds for a single variable.
void | originalBound (int iSequence)
| Restores bound to original bound.
int | checkUnbounded (CoinIndexedVector &ray, double changeCost)
| Checks if tentative optimal actually means unbounded in dual Returns -3 if not, 2 if is unbounded.
void | statusOfProblemInDual (int type)
| Refactorizes if necessary Checks if finished.
int | whatNext ()
| Fast iterations.
bool | checkCutoff (bool computeObjective)
| see if cutoff reached
int | bounceTolerances (int type)
| Does something about fake tolerances.
void | perturb (double factor)
| Perturbs problem.
void | perturbB (double factor, int type)
| Perturbs problem B.
int | makeNonFreeVariablesDualFeasible (bool changeCosts=false)
| Make non free variables dual feasible by moving to a bound.
int | fastDual (bool alwaysFinish=false)
int | numberAtFakeBound ()
| Checks number of variables at fake bounds.
int | pivotResultPart1 ()
| Pivot in a variable and choose an outgoing one.
int | nextSuperBasic ()
| Get next free , -1 if none.
void | startupSolve ()
| Startup part of dual.
void | finishSolve ()
| Ending part of dual.
void | gutsOfDual ()
int | resetFakeBounds (int type)

## Detailed Description

This solves LPs using the dual simplex method.

It inherits from AbcSimplex. It has no data of its own and is never created - only cast from a AbcSimplex object at algorithm time.

Definition at line 49 of file AbcSimplexDual.hpp.

## Member Function Documentation

int AbcSimplexDual::dual | ( |  | ) |

Dual algorithm.

Method

It tries to be a single phase approach with a weight of 1.0 being given to getting optimal and a weight of updatedDualBound_ being given to getting dual feasible. In this version I have used the idea that this weight can be thought of as a fake bound. If the distance between the lower and upper bounds on a variable is less than the feasibility weight then we are always better off flipping to other bound to make dual feasible. If the distance is greater then we make up a fake bound updatedDualBound_ away from one bound. If we end up optimal or primal infeasible, we check to see if bounds okay. If so we have finished, if not we increase updatedDualBound_ and continue (after checking if unbounded). I am undecided about free variables - there is coding but I am not sure about it. At present I put them in basis anyway.

The code is designed to take advantage of sparsity so arrays are seldom zeroed out from scratch or gone over in their entirety. The only exception is a full scan to find outgoing variable for Dantzig row choice. For steepest edge we keep an updated list of infeasibilities (actually squares). On easy problems we don't need full scan - just pick first reasonable.

One problem is how to tackle degeneracy and accuracy. At present I am using the modification of costs which I put in OSL and some of what I think is the dual analog of Gill et al. I am still not sure of the exact details.

The flow of dual is three while loops as follows:

while (not finished) {

while (not clean solution) {

Factorize and/or clean up solution by flipping variables so dual feasible. If looks finished check fake dual bounds. Repeat until status is iterating (-1) or finished (0,1,2)

}

while (status==-1) {

Iterate until no pivot in or out or time to re-factorize.

Flow is:

choose pivot row (outgoing variable). if none then we are primal feasible so looks as if done but we need to break and check bounds etc.

Get pivot row in tableau

Choose incoming column. If we don't find one then we look primal infeasible so break and check bounds etc. (Also the pivot tolerance is larger after any iterations so that may be reason)

If we do find incoming column, we may have to adjust costs to keep going forwards (anti-degeneracy). Check pivot will be stable and if unstable throw away iteration and break to re-factorize. If minor error re-factorize after iteration.

Update everything (this may involve flipping variables to stay dual feasible.

}

}

TODO's (or maybe not)

At present we never check we are going forwards. I overdid that in OSL so will try and make a last resort.

Needs partial scan pivot out option.

May need other anti-degeneracy measures, especially if we try and use loose tolerances as a way to solve in fewer iterations.

I like idea of dynamic scaling. This gives opportunity to decouple different implications of scaling for accuracy, iteration count and feasibility tolerance.

for use of exotic parameter startFinishoptions see Abcsimplex.hpp

Reimplemented from AbcSimplex.

int AbcSimplexDual::strongBranching | ( | int | numberVariables,
|  | const int * | variables,
|  | double * | newLower,
|  | double * | newUpper,
|  | double ** | outputSolution,
|  | int * | outputStatus,
|  | int * | outputIterations,
|  | bool | stopOnFirstInfeasible = `true`,
|  | bool | alwaysFinish = `false`,
|  | int | startFinishOptions = `0` |
| ) |  |  |

For strong branching.

On input lower and upper are new bounds while on output they are change in objective function values (>1.0e50 infeasible). Return code is 0 if nothing interesting, -1 if infeasible both ways and +1 if infeasible one way (check values to see which one(s)) Solutions are filled in as well - even down, odd up - also status and number of iterations

Reimplemented from ClpSimplex.

AbcSimplexFactorization* AbcSimplexDual::setupForStrongBranching | ( | char * | arrays,
|  | int | numberRows,
|  | int | numberColumns,
|  | bool | solveLp = `false` |
| ) |  |  |

This does first part of StrongBranching.

void AbcSimplexDual::cleanupAfterStrongBranching | ( | AbcSimplexFactorization * | factorization | ) |

This cleans up after strong branching.

int AbcSimplexDual::whileIteratingSerial | ( |  | ) |

This has the flow between re-factorizations Broken out for clarity and will be used by strong branching.

Reasons to come out: -1 iterations etc -2 inaccuracy -3 slight inaccuracy (and done iterations) +0 looks optimal (might be unbounded - but we will investigate) +1 looks infeasible +3 max iterations

If givenPi not NULL then in values pass (copy from ClpSimplexDual)

void AbcSimplexDual::whileIterating2 | ( |  | ) |

int AbcSimplexDual::whileIteratingParallel | ( | int | numberIterations | ) |

int AbcSimplexDual::whileIterating3 | ( |  | ) |

void AbcSimplexDual::updatePrimalSolution | ( |  | ) |

int AbcSimplexDual::noPivotRow | ( |  | ) |

int AbcSimplexDual::noPivotColumn | ( |  | ) |

void AbcSimplexDual::dualPivotColumn | ( |  | ) |

void AbcSimplexDual::createDualPricingVectorSerial | ( |  | ) |

Create dual pricing vector.

int AbcSimplexDual::getTableauColumnFlipAndStartReplaceSerial | ( |  | ) |

void AbcSimplexDual::getTableauColumnPart1Serial | ( |  | ) |

void AbcSimplexDual::getTableauColumnPart2 | ( |  | ) |

int AbcSimplexDual::checkReplace | ( |  | ) |

void AbcSimplexDual::replaceColumnPart3 | ( |  | ) |

void AbcSimplexDual::checkReplacePart1 | ( |  | ) |

void AbcSimplexDual::checkReplacePart1a | ( |  | ) |

void AbcSimplexDual::checkReplacePart1b | ( |  | ) |

void AbcSimplexDual::updateDualsInDual | ( |  | ) |

The duals are updated.

int AbcSimplexDual::flipBounds | ( |  | ) |

The duals are updated by the given arrays.

This is in values pass - so no changes to primal is made While dualColumn gets flips this does actual flipping. returns number flipped

void AbcSimplexDual::flipBack | ( | int | number | ) |

Undo a flip.

void AbcSimplexDual::dualColumn1 | ( | bool | doAll = `false` | ) |

Array has tableau row (row section) Puts candidates for rows in list Returns guess at upper theta (infinite if no pivot) and may set sequenceIn_ if free Can do all (if tableauRow created).

double AbcSimplexDual::dualColumn1A | ( |  | ) |

Array has tableau row (row section) Just does slack part Returns guess at upper theta (infinite if no pivot) and may set sequenceIn_ if free.

double AbcSimplexDual::dualColumn1B | ( |  | ) |

Do all given tableau row.

void AbcSimplexDual::dualColumn2 | ( |  | ) |

Chooses incoming Puts flipped ones in list If necessary will modify costs.

void AbcSimplexDual::dualColumn2Most | ( | dualColumnResult & | result | ) |

void AbcSimplexDual::dualColumn2First | ( | dualColumnResult & | result | ) |

void AbcSimplexDual::dualColumn2 | ( | dualColumnResult & | result | ) |

Chooses part of incoming Puts flipped ones in list If necessary will modify costs.

void AbcSimplexDual::checkPossibleCleanup | ( | CoinIndexedVector * | array | ) |

This sees what is best thing to do in branch and bound cleanup If sequenceIn_ < 0 then can't do anything.

void AbcSimplexDual::dualPivotRow | ( |  | ) |

Chooses dual pivot row Would be faster with separate region to scan and will have this (with square of infeasibility) when steepest For easy problems we can just choose one of the first rows we look at.

int AbcSimplexDual::changeBounds | ( | int | initialize,
|  | double & | changeCost |
| ) |  |  |

Checks if any fake bounds active - if so returns number and modifies updatedDualBound_ and everything.

Free variables will be left as free Returns number of bounds changed if >=0 Returns -1 if not initialize and no effect fills cost of change vector

bool AbcSimplexDual::changeBound | ( | int | iSequence | ) |

As changeBounds but just changes new bounds for a single variable.

Returns true if change

void AbcSimplexDual::originalBound | ( | int | iSequence | ) |

Restores bound to original bound.

int AbcSimplexDual::checkUnbounded | ( | CoinIndexedVector & | ray,
|  | double | changeCost |
| ) |  |  |

Checks if tentative optimal actually means unbounded in dual Returns -3 if not, 2 if is unbounded.

void AbcSimplexDual::statusOfProblemInDual | ( | int | type | ) |

Refactorizes if necessary Checks if finished.

Updates status. lastCleaned refers to iteration at which some objective/feasibility cleaning too place.

type - 0 initial so set up save arrays etc

- 1 normal -if good update save
- 2 restoring from saved

int AbcSimplexDual::whatNext | ( |  | ) |

Fast iterations.

Misses out a lot of initialization. Normally stops on maximum iterations, first re-factorization or tentative optimum. If looks interesting then continues as normal. Returns 0 if finished properly, 1 otherwise. Gets tableau column - does flips and checks what to do next Knows tableau column in 1, flips in 2 and gets an array for flips (as serial here)

bool AbcSimplexDual::checkCutoff | ( | bool | computeObjective | ) |

see if cutoff reached

int AbcSimplexDual::bounceTolerances | ( | int | type | ) |

Does something about fake tolerances.

void AbcSimplexDual::perturb | ( | double | factor | ) |

Perturbs problem.

void AbcSimplexDual::perturbB | ( | double | factor,
|  | int | type |
| ) |  |  |

Perturbs problem B.

int AbcSimplexDual::makeNonFreeVariablesDualFeasible | ( | bool | changeCosts = `false` | ) |

Make non free variables dual feasible by moving to a bound.

int AbcSimplexDual::fastDual | ( | bool | alwaysFinish = `false` | ) |

int AbcSimplexDual::numberAtFakeBound | ( |  | ) |

Checks number of variables at fake bounds.

This is used by fastDual so can exit gracefully before end

int AbcSimplexDual::pivotResultPart1 | ( |  | ) |

Pivot in a variable and choose an outgoing one.

Assumes dual feasible - will not go through a reduced cost. Returns step length in theta Return codes as before but -1 means no acceptable pivot

int AbcSimplexDual::nextSuperBasic | ( |  | ) |

Get next free , -1 if none.

void AbcSimplexDual::startupSolve | ( |  | ) |

Startup part of dual.

void AbcSimplexDual::finishSolve | ( |  | ) |

Ending part of dual.

void AbcSimplexDual::gutsOfDual | ( |  | ) |

int AbcSimplexDual::resetFakeBounds | ( | int | type | ) |

The documentation for this class was generated from the following file:

- /home/coin/svn-release/Clp-1.15.11/Clp/src/AbcSimplexDual.hpp

All Classes Namespaces Files Functions Variables Typedefs Enumerations Enumerator Friends Defines