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class implements an abstract base class for a subproblem of the enumeration, i.e., a node of the \ tree.
#include <sub.h>
Inheritance diagram for ABA_SUB::
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Unprocessed, Active, Dormant, Processed,
Fathomed }
The optimization of the subproblem can be in one of the following phases:.
The constructor for the root node of the enumeration tree.
The constructor for non-root nodes of the enumeration tree.
Sets the dual bound of the subproblem, and if the subproblem is the root node of the enumeration tree and the new value is better than its dual bound, also the global dual bound is updated. It is an error if the dual bound gets worse.
This version of the function uBound() sets thef local upper bound of a variable.
With function removeVars() variables can be removed from the set of active variables.
If all variables are Binary or Integer and all objective function coefficients are integral, then all objective function values of feasible solutions are integral. The function objAllInteger() tests this condition for the current set of active variables.
Adds constraints to the buffer of the removed constraints, which will be removed at the beginning of the next iteration of the cutting plane algorithm.
The following version of the function removeCon() adds a single constraint to the set of constraints which are removed from the active set at the beginning of the next iteration.
Can be used to determine the maximal number of the constraints which still can be added to the constraint buffer.
Can be used to determine the maximal number of the variables which still can be added to the variable buffer.
Adds a branching constraint to the constraint buffer such that it is automatically added at the beginning of the cutting plane algorithm.
Does nothing but can be used as an entrance point for problem specific activations by a reimplementation in derived classes.
Can be used as entrance point for problem specific deactivations after the subproblem optimization.
Generates branching rules for two new subproblems by selecting a branching variable with the function selectBranchingVariable().
Selects depending on the branching variable strategy given by the parameter { BranchingStrategy} in the file { .abacus} candidates that for branching variables.
Evaluates branching samples (we denote a branching sample the set of rules defining all sons of a subproblem in the enumeration tree). For each sample the ranks are determined with the function rankBranchingSample(). The ranks of the various samples are compared with the function compareBranchingSample().
Computes for each branching rule of a branching sample a rank with the function rankBranchingRule().
Computes the rank of a branching rule by modifying the linear programming relaxation of the subproblem according to the branching rule and solving it. This modifiction is undone after the solution of the linear program.
Selects a single branching variable of type branchVarType, with fractional part close to 0.5 and high absolute objective function coefficient.
This version of the function closeHalfExpensive() selects several candidates for branching variables of type branchVarType.
Searches a branching variable of type branchVarType, with fraction as close to 0.5 as possible.
Searches searches several possible branching variable of type branchVarType, with fraction as close to 0.5 as possible.
The default implementation of the virtual initMakeFeas() does nothing.
The default implementation of makeFeasible() does nothing.
The default implementation of setByLogImp() does nothing.
The pure virtual function feasible() checks for the feasibility of a solution of the LP-relaxation.
Can be used to check if the solution of the LP-relaxation is primally feasible if for feasibility an integral value for all binary and integer variables is sufficient.
Is a virtual function which controls, if during the cutting plane phase a (primal) separation step or a pricing step (dual separation) should be performed.
Can be used as an entry point for application specific elimination of constraints by redefinig it in derived classes.
Retrieves the dynamic constraints with slack exceeding the value given by the parameter { ConElimEps}.
Provides an entry point for application specific variable elimination that can be implemented by redefining this function in a derived class.
Can be redefined in derived classes in order to implement primal heuristics for finding feasible solutions.
Returns a pointer to an object of a problem specific subproblem derived from the class ABA_SUB, which is generated from the current subproblem by the branching rule rule.
Reallocates memory that at most newSize variables can be handled in the subproblem.
Reallocates memory that at most newSize constraints can be handled in the subproblem.
Should collect the numbers of the variables to be fixed in variable and the respective statuses in status.
Tries to fix and set variables both by logical implications and reduced cost criteria.
Tries to set variables by reduced cost criteria and logical implications like fixing(), but instead of global conditions only locally valid conditions have to be satisfied.
Is called if the global lower bound of a \ node is still strictly less than the local upper bound, but either no violated cutting planes or variables are found, or we abort the cutting phase for some other strategic reason (e.g., observation of a tailing off effect, or branch pausing).
Fathoms the node, and if certain conditions are satisfied, also its ancestor.
Iteratively solves the LP-relaxation, generates constraints and/or variables.
Can be used to specify a problem specific fathoming criterium that is checked before the separation or pricing.
A pointer to an array storing the status of fixing and setting of the active variables. Although fixed and set variables are already kept at their value by the adaption of the lower and upper bounds, we store this information, since, e.g., a fixed or set variable should not be removed, but a variable with an upper bound equal to the lower bound can be removed.
A pointer to an array storing the status of each active variable in the linear program.
A pointer to an array storing the statuses of the slack variables of the last solved linear program.
If true, then the branching rule of the subproblem and of all ancestor on the path to the root node are branching on a binary variable.
The buffer of the variables which are removed at the beginning of the next iteration.
The buffer of the constraints which are removed at the beginning of the next iteration.
A row of the basis inverse associated with the infeasible variable infeasVar_ or slack variable infeasCon_.
Returns 1, if a contradiction has been found, 0 otherwise.
Returns the value which the upper and lower bounds of a variable should take after it is fixed or set.
Allocates and initializes memory of the subproblem at the beginning of the optimization.
Deallocates the memory which is not required after the optimization of the subproblem.
Tries to add variables to restore infeasibilities detected at initialization time.
Is called if the LP is infeasible and adds inactive variables, which can make the LP feasible again, to the set of active variables.
Tries to set variables according to logical implications of already set and fixed variables.
Adds the variables stored in the pool slots of newVars to the set of active variables, but not to the linear program.
Adds the variables stored in the pool slots of newVars to the linear program. localStatus can specify a local status of fixing and setting.
Selects the master_->maxConAdd() best constraints from the buffered constraints and stores them in newCons.
If this member is true then the space reserve of the following three members varReserve_, conReserve_, and nnzReserve_ is relative to the initial numbers of constraints, variables, and nonzeros, respectively. Otherwise, the values are casted to integers and regarded as absolute values.
The number of subproblem optimizations the subproblem has already the status Dormant.
The variable is true if the function activate() has been called from the function _activate(). This memorization is required such that a deactivate() is only called when activate() has been called.
If this flag is set to true then the next LP-solution is ignored in the tailing-off control. The default value of the variable is false. It can be set to true by the function ignoreInTailingOff().
The method that was used to solve the last LP.
Indicates whether to force the use of an exact solver to prepare branching etc.
class implements an abstract base class for a subproblem of the enumeration, i.e., a node of the \ tree.
Definition at line 75 of file sub.h.
A subproblem can have different statuses:
Definition at line 98 of file sub.h.
The optimization of the subproblem can be in one of the following phases:.
Definition at line 111 of file sub.h.
The constructor for the root node of the enumeration tree.
The constructor for non-root nodes of the enumeration tree.
The destructor only deletes the sons of the node.
The deletion of allocated memory is already performed when the node is fathomed. We recursively call the destructors of all subproblems contained in the enumeration tree below this subproblem itself.
If a subproblem has no sons and its status is either Unprocessed or Dormant, then it is still contained in the set of open subproblems, where it is removed from.
Whether using the exact solver is forced.
Definition at line 2207 of file sub.h.
The level of the subproblem in the \ tree.
Definition at line 2212 of file sub.h.
The identity number of the subproblem.
Definition at line 2217 of file sub.h.
The status of the subproblem optimization.
Definition at line 2244 of file sub.h.
The number of active variables.
Definition at line 2259 of file sub.h.
The maximum number of variables which can be handled without reallocation.
Definition at line 2269 of file sub.h.
The number of active constraints.
Definition at line 2264 of file sub.h.
The maximum number of constraints which can be handled without reallocation.
Definition at line 2274 of file sub.h.
A lower bound on the optimal solution of the subproblem.
An upper bound on the optimal solution of the subproblem.
A bound which is better than the optimal solution of the subproblem in respect to the sense of the optimization, i.e., an upper for a maximization problem or a lower bound for a minimization problem, respectively.
Definition at line 2229 of file sub.h.
Sets the dual bound of the subproblem, and if the subproblem is the root node of the enumeration tree and the new value is better than its dual bound, also the global dual bound is updated. It is an error if the dual bound gets worse.
In normal applications it is not required to call this function explicitly. This is already done by \ during the subproblem optimization.
A pointer to the father of the subproblem in the \ tree.
Definition at line 2234 of file sub.h.
A pointer to the linear program of the subproblem.
Definition at line 2239 of file sub.h.
Sets the maximal number of iterations in the cutting plane phase.
Setting this value to 1 implies that no cuts are generated in the optimization process of the subproblem.
A pointer to the currently active constraints.
Definition at line 2249 of file sub.h.
A pointer to the currently active variables.
Definition at line 2254 of file sub.h.
A pointer to the i-th active constraint.
A pointer to the status of the slack variable i in the last solved linear program.
Definition at line 2202 of file sub.h.
A pointer to the i-th active variable.
Can be used to access the lower of an active variable of the subproblem.
This is the lower bound of the variable within the current subproblem which can differ from its global lower bound.
The lower bound of the i-th variable.
Definition at line 2168 of file sub.h.
Sets the local lower bound of a variable.
It does not change the global lower bound of the variable. The bound of a fixed or set variable should not be changed.
Definition at line 2173 of file sub.h.
Can be used to access the upper of an active variable of the subproblem.
This is the upper bound of the variable within the current subproblem which can differ from its global upper bound.
The upper bound of the i-th variable.
Definition at line 2180 of file sub.h.
This version of the function uBound() sets thef local upper bound of a variable.
This does not change the global lower bound of the variable. The bound of a fixed or set variable should not be changed.
Definition at line 2185 of file sub.h.
In a \ algorithm we also would have to refer to the global variable status. While this subproblem is processed another subproblem could change the global status.
A pointer to the status of fixing/setting of the i-th variable.
This is the local status of fixing/setting that might differ from the global status of fixing/setting of the variable (variable(i)->fsVarStat()).
Definition at line 2192 of file sub.h.
A pointer to the status of the variable i in the last solvedlinear program.
Definition at line 2197 of file sub.h.
The value of the i-th variable in the last solved linear program.
Definition at line 2108 of file sub.h.
The value of the i-th dual variable in the last solved linear program.
Definition at line 2113 of file sub.h.
true If this subproblem is an ancestor of the subproblem sub. We define that a subproblem is its own ancestor,
false otherwise.
Definition at line 2118 of file sub.h.
With function removeVars() variables can be removed from the set of active variables.
The variables are not removed when this function is called, but are buffered and removed at the beginning of the next iteration.
Can be used to remove a single variable from the set of active variables.
Like in the function removeVars() the variable is buffered and removed at the beginning of the next iteration.
Definition at line 2123 of file sub.h.
The additional space for nonzero elements of the constraint matrix when it is passed to the LP-solver.
Definition at line 2128 of file sub.h.
true If the reserve space for variables, constraints, and nonzeros is given in percent of the original space, and false if its given as absolute value,
false otherwise.
Definition at line 2133 of file sub.h.
A pointer to the branching rule of the subproblem.
Definition at line 2138 of file sub.h.
If all variables are Binary or Integer and all objective function coefficients are integral, then all objective function values of feasible solutions are integral. The function objAllInteger() tests this condition for the current set of active variables.
The result of this function can only be used to set the global parameter if actVar contains all variables of the problem formulation.
true If this condition is satisfied by the currently active variable set,
false otherwise.
Adds constraints to the buffer of the removed constraints, which will be removed at the beginning of the next iteration of the cutting plane algorithm.
The following version of the function removeCon() adds a single constraint to the set of constraints which are removed from the active set at the beginning of the next iteration.
Can be used to determine the maximal number of the constraints which still can be added to the constraint buffer.
A separation algorithm should stop as soon as the number of generated constraints reaches this number because further work is useless.
The number of constraints which still can be inserted into the constraint buffer.
Definition at line 2148 of file sub.h.
Can be used to determine the maximal number of the variables which still can be added to the variable buffer.
A pricing algorithm should stop as soon as the number of generated variables reaches this number because further work is useless.
The number of variables which still can be inserted into the variable buffer.
Definition at line 2153 of file sub.h.
The number of subproblem optimization the subproblem is already dormant.
Definition at line 2158 of file sub.h.
Can be used to control better the tailing-off effect.
If this function is called, the next LP-solution is ignored in the tailing-off control. Calling ignoreInTailingOff() can e.g. be considered in the following situation: If only constraints that are required for the integer programming formulation of the optimization problem are added then the next LP-value could be ignored in the tailing-off control. Only “real” cutting planes should be considered in the tailing-off control (this is only an example strategy that might not be practical in many situations, but sometimes turned out to be efficient).
Adds a branching constraint to the constraint buffer such that it is automatically added at the beginning of the cutting plane algorithm.
It should be used in definitions of the pure virtual function BRANCHRULE::extract().
0 If the constraint could be added,
1 otherwise.
Definition at line 2143 of file sub.h.
Tries to add new constraints to the constraint buffer and a pool.
The memory management of added constraints is passed to \ by calling this function.
The number of added constraints.
Adds constraints to the active constraints and the linear program.
The number of added constraints.
Tries to add new variables to the variable buffer and a pool.
The memory management of added variables is passed to \ by calling this function.
The number of added variables.
Adds both the variables in newVars to the set of active variables and to the linear program of the subproblem.
If the new number of variables exceeds the maximal number of variables an automatic reallocation is performed.
The number of added variables. We require this feature in derived classes if variables of newVars can be discarded if they are already active.
Tries to generate inactive variables from a pool.
The number of generated variables.
Tries to generate inactive constraints from a pool.
The number of generated constraints.
Does nothing but can be used as an entrance point for problem specific activations by a reimplementation in derived classes.
Can be used as entrance point for problem specific deactivations after the subproblem optimization.
The default version of this function does nothing. This function is only called if the function activate() for the subproblem has been executed. This function is called from _deactivate().
Tries to find rules for splitting the current subproblem in further subproblems.
Per default we generate rules for branching on variables (branchingOnVariable()). But by redefining this function in a derived class any other branching strategy can be implemented.
0 If branching rules could be found,
1 otherwise.
Generates branching rules for two new subproblems by selecting a branching variable with the function selectBranchingVariable().
If a new branching variable selection strategy should be used the function selectBranchingVariable() should be redefined.
0 If branching rules could be found,
1 otherwise}
Chooses a branching variable.
The function selectBranchingVariableCandidates() is asked to generate depending in the parameter { NBranchingVariableCandidates} of the file { .abacus} candidates for branching variables. If only one candidate is generate, this one becomes the branching variable. Otherwise, the pairs of branching rules are generated for all candidates and the “best” branching variables is determined with the function selectBestBranchingSample().
0 If a branching variable is found,
1 otherwise.
Selects depending on the branching variable strategy given by the parameter { BranchingStrategy} in the file { .abacus} candidates that for branching variables.
Currently two branching variable selection strategies are implemented. The first one (CloseHalf ) first searches the binary variables with fractional part closest to 0.5. If there is no fractional binary variable it repeats this process with the integer variables.
The second strategy (CloseHalfExpensive) first tries to find binary variables with fraction close to 0.5 and high absolute objective function coefficient. If this fails, it tries to find an integer variable with fractional part close to 0.5 and high absolute objective function coefficient.
If neither a binary nor an integer variable with fractional value is found then for both strategies we try to find non-fixed and non-set binary variables. If this fails we repeat this process with the integer variables.
Other branching variable selection strategies can be implemented by redefining this virtual function in a derived class.
0 If a candidate is found,
1 otherwise.
Evaluates branching samples (we denote a branching sample the set of rules defining all sons of a subproblem in the enumeration tree). For each sample the ranks are determined with the function rankBranchingSample(). The ranks of the various samples are compared with the function compareBranchingSample().
The number of the best branching sample, or -1 in case of an internal error.
Computes for each branching rule of a branching sample a rank with the function rankBranchingRule().
Computes the rank of a branching rule.
This default implementation computes the rank with the function lpRankBranchingRule(). By redefining this virtual function the rank for a branching rule can be computed differently.
The rank of the branching rule.
Computes the rank of a branching rule by modifying the linear programming relaxation of the subproblem according to the branching rule and solving it. This modifiction is undone after the solution of the linear program.
It is useless, but no error, to call this function for branching rules for which the virtual dummy functions extract(ABA_LPSUB*) and unExtract(ABA_LPSUB*) of the base class ABA_BRANCHRULE are not redefined.
The value of he linear programming relaxation of the subproblem modified by the branching rule.
Compares the ranks of two branching samples.
For maximimization problem that rank is better for which the maximal rank of a rule is minimal, while for minimization problem the rank is better for which the minimal rank of a rule is maximal. If this value equals for both ranks we continue with the secand greatest value, etc.
1 If rank1 is better.
0 If both ranks are equal.
-1 If rank2 is better.
Selects a single branching variable of type branchVarType, with fractional part close to 0.5 and high absolute objective function coefficient.
This is the default strategy from the TSP project JRT94}.
0 If a branching variable is found,
1 otherwise.
This version of the function closeHalfExpensive() selects several candidates for branching variables of type branchVarType.
Thos variables with fractional part close to 0.5 and high absolute objective function coefficient are selected..
0 If at least one branching variable is found,
1 otherwise.
Searches a branching variable of type branchVarType, with fraction as close to 0.5 as possible.
0 If a branching variable is found,
1 otherwise.
Searches searches several possible branching variable of type branchVarType, with fraction as close to 0.5 as possible.
0 If at least one branching variable is found,
1 otherwise.
Selects the first variables that are neither fixed nor set.
0 If at least one variable neither fixed nor set is found,
1 otherwise.
Selects the first variable that is neither fixed nor set.
0 If a variable neither fixed nor set is found,
1 otherwise.
The default implementation of the virtual initMakeFeas() does nothing.
A reimplementation of this function should generate inactive variables until at least one variable v which satisfies the function ABA_INFEASCON::goodVar(v) for each infeasible constraint is found.
0 If the feasibility might have been restored,
1 otherwise.
The default implementation of makeFeasible() does nothing.
If there is an infeasible structural variable then it is stored in infeasVar_, otherwise infeasVar_ is -1. If there is an infeasible slack variable, it is stored in infeasCon_, otherwise it is -1. At most one of the two members infeasVar_ and infeasCon_ can be nonnegative. A reimplementation in a derived class should generate variables to restore feasibility or confirm that the subproblem is infeasible.
The strategy for the generation of inactive variables is completely problem and user specific. For testing if a variable might restore again the feasibility the functions ABA_VARIABLE::useful() and ABA_SUB::goodCol() might be helpful.
0 If feasibility can be restored,
1 otherwise.
true If the column col might restore feasibiblity if the variable with value x turns out to be infeasible,
false otherwise.
The default implementation of setByLogImp() does nothing.
In derived classes this function can be reimplemented.
The pure virtual function feasible() checks for the feasibility of a solution of the LP-relaxation.
If the function returns true and the value of the primal bound is worse than the value of this feasible solution, the value of the primal bound is updated automatically.
true If the LP-solution is feasible,
false otherwise.
Can be used to check if the solution of the LP-relaxation is primally feasible if for feasibility an integral value for all binary and integer variables is sufficient.
This function can be called from the function feasible() in derived classes.
true If the LP-value of all binary and integer variables is integral,
false otherwise.
Is a virtual function which controls, if during the cutting plane phase a (primal) separation step or a pricing step (dual separation) should be performed.
Per default a pure cutting plane algorithm performs always a primal separation step, a pure column generation algorithm never performs a primal separation, and a hybrid algorithm generates usually cutting planes but from time to time also inactive variables are priced out depending on the pricingFrequency().
true Then cutting planes are generated in this iteration.
false Then columns are generated in this iteration.
Must be redefined in derived classes for the generation of cutting planes.
The default implementation does nothing.
The number of generated cutting planes.
Can be used as an entry point for application specific elimination of constraints by redefinig it in derived classes.
The default implementation of this function calls either the function nonBindingConEliminate() or the function basicConEliminate() depending on the constraint elimination mode of the master that is initialized via the parameter file.
Retrieves the dynamic constraints with slack exceeding the value given by the parameter { ConElimEps}.
Retrieves all dynamic constraints having basic slack variable.
Provides an entry point for application specific variable elimination that can be implemented by redefining this function in a derived class.
The default implementation selects the variables with the function redCostVarEliminate().
Retrieves all variables with “wrong” reduced costs.
Should generate inactive variables which do not price out correctly.
The default implementation does nothing and returns 0.
The number of new variables.
Can be redefined in derived classes in order to implement primal heuristics for finding feasible solutions.
The default implementation does nothing.
0 If no better solution could be found,
1 otherwise.
Returns a pointer to an object of a problem specific subproblem derived from the class ABA_SUB, which is generated from the current subproblem by the branching rule rule.
true If the dual bound is worse than the best known primal bound,
false otherwise.
Sometimes it is appropriate to put a subproblem back into the list of open subproblems. This is called pausing. In the default implementation the virtual function pausing() always returns false.
It could be useful to enforce pausing a node if a tailing off effect is observed during its first optimization.
true The function pausing() should return true if this condition is satisfied,
false otherwise.
true If the subproblem does not contain a feasible solution,
false otherwise.
Reallocates memory that at most newSize variables can be handled in the subproblem.
Reallocates memory that at most newSize constraints can be handled in the subproblem.
Controls the method used to solve a linear programming relaxation.
The default implementation chooses the barrier method for the first linear program of the root node and for all other linear programs it tries to choose a method such that phase 1 of the simplex method is not required.
The method the next linear programming relaxation is solved with.
Is called when a tailing off effect according to the parameters { TailOffPercent} and { TailOffNLps} of the parameter file is observed.
This function can be redefined in derived classes in order to perform actions to resolve the tailing off (e.g., switching on an enhanced separation strategy).
true If a branching step should be enforced. But before branching a pricing operation is perfored. The branching step is only performed if no variables are added. Otherwise, the cutting plane algorithm is continued.
false If the cutting plane algorithm should be continued.
true If x is better than the best known dual bound of the subproblem,
false otherwise.
Is called before variables are selected from the variable buffer.
It can be redefined in a derived class e.g., to remove multiply inserted variables from the buffer.
Is called before constraint are selected from the constraint buffer.
It can be redefined in a derived class e.g., to remove multiply inserted constraints from the buffer.
Tries to fix variables according to the reduced cost criterion.
1 If a contradiction is found,
0 otherwise.
Should collect the numbers of the variables to be fixed in variable and the respective statuses in status.
The default implementation of fixByLogImp() does nothing. This function has to be redefined if variables should be fixed by logical implications in derived classes.
Tries to fix and set variables both by logical implications and reduced cost criteria.
Actually, variables fixed or set to 0 could be eliminated. However, this could lead to a loss of important structural information for fixing and setting further variables later, for the computation of feasible solutions, for the separation and for detecting contradictions. Therefore, we do not eliminate these variables per default.
1 If a contradiction is found,
0 otherwise.
Tries to fix variables by reduced cost criteria and logical implications.
1 If a contradiction is found,
0 otherwise.
Tries to set variables by reduced cost criteria and logical implications like fixing(), but instead of global conditions only locally valid conditions have to be satisfied.
1 If a contradiction has been found,
0 otherwise.
Tries to set variables according to the reduced cost criterion.
1 If a contradiction is found,
0 otherwise.
Fathoms a node and recursively tries to fathom its father.
If the root of the remaining \ tree is fathomed we are done since the optimization problem has been solved.
Otherwise, we count the number of unfathomed sons of the father of the subproblem being fathomed. If all sons of the father are fathomed it is recursively fathomed, too. If the father is the root of the remaining \ tree and only one of its sons is unfathomed, then this unfathomed son becomes the new root of the remaining \ tree.
We could stop the recursive fathoming already at the root of the remaining \ tree. But, we proceed until the root of the complete tree was visited to be really correct.
Use the function ExceptionFathom() for specifying problem specific fathoming criteria.
Controls if variables should be fixed or set when all variables price out corretly.
The default implementation always returns true.
true If variables should be fixed and set,
false otherwise.
Fixes a variable.
If the variable which is currently fixed is already set then we must not change its bounds in the LP since it might be eliminated.
1 If a contradiction is found,
0 otherwise.
Sets a variable.
1 If a contradiction is found,
0 otherwise.
Sets a variable.
1 If a contradiction is found,
0 otherwise.
Sets a variable.
1 If a contradiction is found,
0 otherwise.
If all objective function values of feasible solutions are integer the function dualRound() returns x rounded up to the next integer if this is a minimization problem, or x rounded down to the next integer if this is a maximization problem, respectively. Otherwise, the return value is x.
May not be called if the lower bound is 0 and upper bound not equal to 0.
The guarantee that can be given for the subproblem.
true If the lower and the upper bound of the subproblem satisfies the guarantee requirements,
false otherwise.
true If all active constraints can be lifted.
false otherwise. In this case the non-liftable constraints are removed and genNonLiftCons_ is set to false to avoid the generation of non-liftable constraints in the next cutting plane iterations.
Is called before a branching step to remove constraints.
1 If constraints have been removed,
0 otherwise.
Fathoms all nodes in the subtree rooted at this subproblem.
Dormant and Unprocessed nodes are also removed from the set of open subproblems.
If the subproblem is already Fathomed we do not have to proceed in this branch. Otherwise, we fathom the node and continue with all its sons. The actual fathoming starts at the unfathomed leaves of the subtree and recursively goes up through the tree.
Performs the optimization of the subproblem.
After activating the subproblem, i.e., allocating and initializing memory, and initializing the LP, the optimization process constitutes of the three phases Cutting, Branching, and Fathoming, which are alternately processed. The function fathoming() always returns Done. However, we think that the code is better readable instead of taking it out of the while loop. The optimization stops if the PHASE Done is reached. Note, Done does not necessarily mean that the subproblem is solved to optimality!
After the node is processed we deallocate memory, which is not required for further computations or of which the corresponding data can be easily reconstructed. This is performed in _deactivate().
0 If the optimization has been performed without error,
1 otherwise.
Repeats the optimization of an already optimized subproblem.
This function is used to determine the reduced costs for fixing variables of a new root of the remaining \ tree.
As the subproblem has been processed already earlier it is sufficient to perform the cutting plane algorithm. If the subproblem is fathomed the complete subtree rooted at this subproblem can be fathomed, too. Since this function is usually only called for the root of the remaining \ tree, we are done in this case.
It is not guaranteed that all constraints and variables of this subproblem can be regenerated in _activate(). Therefore, the result of a call to reoptimize() can differ from the result obtained by the cutting plane algorithm in optimize().
Initializes the active variable set.
Initializes the active constraint set.
Is called if the global lower bound of a \ node is still strictly less than the local upper bound, but either no violated cutting planes or variables are found, or we abort the cutting phase for some other strategic reason (e.g., observation of a tailing off effect, or branch pausing).
Usually, two new subproblems are generated. However, our implementation of branching() is more sophisticated that allows different branching. Moreover, we also check if this node is only paused. If this is the case the node is put back into the list of open \ nodes without generating sons of this node.
Finally if none of the previous conditions is satisfied we generate new subproblems.
Done If sons of the subproblem could be generated,
Fathoming otherwise.
Fathoms the node, and if certain conditions are satisfied, also its ancestor.
The third central phase of the optimization of a subproblem is the Fathoming of a subproblem. A subproblem is fathomed if it can be guaranteed that this subproblem cannot contain a better solution than the best known one. This is the case if the global upper bound does not exceed the local lower bound (maximization problem assumed) or the subproblem cannot contain a feasible solution either if there is a fixing/setting contradiction or the LP-relaxation turns out to be infeasible.
Use the function ExceptionFathom() for specifying problem specific fathoming criteria.
The called function fathom() fathoms the subproblem itself and recursively also tries to fathom its father in the enumeration tree. The argument of fathom() is true as a possibly detected new root should be reoptimized in order to receive better criteria for fixing variables by reduced costs.
In the parallel version, only the subproblem itself is fathomed. No processed unfathomed nodes are kept in memory (father_=0).
The function always returns Done.
Iteratively solves the LP-relaxation, generates constraints and/or variables.
Also generating variables can be regarded as “cutting”, namely as generating cuts for the dual problem. A reader even studying these lines has been very brave! Therefore, the first reader of these lines is invited to a beer from the author.
Fathoming If one of the conditions for fathoming the subproblem is satisfied.
Branching If the subproblem should be splitted in further subproblems.
Instantiates an LP for the solution of the LP-relaxation in this subproblem.
This function is redefined in a derived class for a specific LP-solver interface
This function is defined in the file lpif.cc.
A pointer to an object of type ABA_LPSUB.
Initializes the linear program.
Since not all variables might be active we first have to try making the LP feasible again by the addition of variables. If this fails, i.e., _initMakeFeas() has a nonzero return value, we return 1 in order to indicate that the corresponding subproblem can be fathomed. Otherwise, we continue with the initialization of the LP.
0 If the linear program could be initialized successfully.
1 If the linear program turns out to be infeasible.
Solves the LP-relaxation of the subproblem.
As soon as the LP-relaxation becomes infeasible in a static branch and cut algorithm the respective subproblem can be fathomed. Otherwise, we memorize the value of the LP-solution to control the tailing off effect.
{ We assume that the LP is never primal unbounded.
0 The linear program has an optimimal solution.
1 If the linear program is infeasible.
2 If the linear program is infeasible for the current variable set, but non-liftable constraints have to be removed before a pricing step can be performed.
Can be used to specify a problem specific fathoming criterium that is checked before the separation or pricing.
The default implementation always returns false.
true If the subproblem should be fathomed,
false otherwise.
Can be used to specify a problem specific criteria for enforcing a branching step.
This criterium is checked before the separation or pricing. The default implementation always returns false.
true If the subproblem should be fathomed,
false otherwise.
True, if the approximative solver should be used to solve the next linear program, false otherwise.
The default implementation always returns false.
Returns the number of generated cutting planes.
Returns the number of eliminated constraints.
Only dynamic constraints are eliminated from the LP.
It might be worth to implement problem specific versions of this function.
Returns the number of eliminated variables.
Only dynamic variables can be eliminated.
If doFixSet is true, then we try to fix and set variables, if all inactive variables price out correctly. In this case newValues becomes true of a variable is set or fixed to a value different from its value in the last linear program.
In a pricing step the reduced costs of inactive variables are computed and variables with positive (negative) reduced costs in a maximization (minimization) problem are activated.
The function _pricing() returns the 1 if no global optimality can be guaranteed, since variables have negative reduced costs, it returns 2 if before a pricing step can be performed, non-liftable constraints have to be removed, and 0 if the LP-solution is global dual feasible.
Also if there are no inactive variables, this function is called since it will also try to fix and set variables.
true is the default value of doFixSet. No variables should be fixed or set if _pricing() is called from _makeFeasible().
Tries to find a better feasible solution.
If a better solution is found its value is stored in primalValue and we return 1, otherwise we return 0.
If the upper bound has been initialized with the optimum solution or with the optimum solution plus/minus one these primal heuristics are skipped.
The primal bound, if improved, is either updated in the function cutting(), from which _improved() is called, are can be updated in the function improve() of an application in a derived class.
Returns 1, if a contradiction has been found, 0 otherwise.
The parameter newValues is set to true if a variable is fixed to value different from its value in the last solved linear program.
Adapts the bound of a fixed or set variable i also in the linear program.
This can be only done if a linear program is available and the variable is not eliminated.
Returns the value which the upper and lower bounds of a variable should take after it is fixed or set.
Increments the counter for the number of rounds the subproblem is dormant.
This function is called, when the set of open subproblems is scanned for the selection of the next subproblem.
Definition at line 2163 of file sub.h.
Allocates and initializes memory of the subproblem at the beginning of the optimization.
The function returns the next phase of the optimization. This is either Cutting or Fathoming if the subproblem immediately turns out to be infeasible.
Since many objects of the class ABA_SUB can exist at the same time, yet in a sequential algorithm only one problem is active, a lot of memory can be saved if some memory is dynamically allocated when the subproblem becomes active and other information is stored in a compressed format for dormant problems.
These allocations and decompressions are performed by the function _activate(), the respective deallocations and compression of data is executed by the function _deactivate().
Currently for all subproblems which have not been processed already (except for the root) we initialize the active constraints and variables with the respective data from the father node adapted by the branching information since so we can make sure that all fixed and set variables are active. A more flexible strategy might be desirable but also dangerous.
The virtual function activate() can perform problem specific activations. It is called before variables are fixed by logical implications, because, e.g., for problems on graphs, the graph associated with the subproblem might have to be activated.
Moreover, the function _activate() is redundant in the sense that it is called only once and could be substituted by a function. However, having a future generalization to non \ in mind, we keep this function.
Deallocates the memory which is not required after the optimization of the subproblem.
The virtual dummy function deactivate() can perform problem specific deactivations.
As the function _activate(), the function _deactivate() is redundant in the sense that it is called only once and could be substituted by a function. However, having a future generalization to non \ in mind, we keep this function.
Tries to add variables to restore infeasibilities detected at initialization time.
It returns 0 if variables could be activated which might restore feasibility, otherwise it returns 1.
The function should analyse the constraints stored in ABA_LPSUB::infeasCons_ and try to add inactive variables which could restore the infeasibility.
The new variables are only added to the set of active variables but not to the linear program since no linear program exists when this function is called.
Is called if the LP is infeasible and adds inactive variables, which can make the LP feasible again, to the set of active variables.
The function returns 0 if feasibility might have been restored and 1 if it is guaranteed that the linear program is infeasible on the complete variable set.
Tries to set variables according to logical implications of already set and fixed variables.
Since logical implications are problem specific the virtual function setByLogImp() is called to find variables which can be set. If a variable is set to a new value, i.e., a value different from the one in the last solved LP, newValues is set to true. If such a setting implies a contradiction, _setByLogImp() returns 1, otherwise it returns 0.
Should be called if a subproblem turns out to be infeasible.
It sets the dual bound of the subproblem correctly.
Updates the status of the variables and the slack variables.
Adds the variables stored in the pool slots of newVars to the set of active variables, but not to the linear program.
If the new number of variables exceeds the maximal number of variables an automatic reallocation is performed.
Adds the variables stored in the pool slots of newVars to the linear program. localStatus can specify a local status of fixing and setting.
If the local ABA_FSVARSTAT of the added variables differs from their global status, then this local status can be stated in localStatus. Per default the value of localStatus is 0.
Selects the master_->maxVarAdd() best variables from the buffered variables.
Selects the master_->maxConAdd() best constraints from the buffered constraints and stores them in newCons.
Removes the constraints with numbers remove from the set of active constraints.
Definition at line 76 of file sub.h.
Definition at line 77 of file sub.h.
Definition at line 78 of file sub.h.
Definition at line 79 of file sub.h.
Definition at line 80 of file sub.h.
A pointer to the corresponding master of the optimization.
Definition at line 1656 of file sub.h.
The active constraints of the subproblem.
Definition at line 1660 of file sub.h.
The active variables of the subproblem.
Definition at line 1664 of file sub.h.
A pointer to the father in the \ tree.
Definition at line 1668 of file sub.h.
A pointer to the corresponding linear program.
Definition at line 1672 of file sub.h.
A pointer to an array storing the status of fixing and setting of the active variables. Although fixed and set variables are already kept at their value by the adaption of the lower and upper bounds, we store this information, since, e.g., a fixed or set variable should not be removed, but a variable with an upper bound equal to the lower bound can be removed.
Definition at line 1681 of file sub.h.
A pointer to an array storing the status of each active variable in the linear program.
Definition at line 1686 of file sub.h.
A pointer to an array with the local lower bound of the active variables.
Definition at line 1690 of file sub.h.
A pointer to an array with the local upper bounds of the active variables.
Definition at line 1694 of file sub.h.
A pointer to an array storing the statuses of the slack variables of the last solved linear program.
Definition at line 1699 of file sub.h.
A pointer to the tailing off manager.
Definition at line 1703 of file sub.h.
The dual bound of the subproblem.
Definition at line 1707 of file sub.h.
The number of iterations in the cutting plane phase.
Definition at line 1711 of file sub.h.
The last iteration in which constraints have been added.
Definition at line 1715 of file sub.h.
The last iteration in which variables have been added.
Definition at line 1719 of file sub.h.
The branching rule for the subproblem.
Definition at line 1723 of file sub.h.
If true, then the branching rule of the subproblem and of all ancestor on the path to the root node are branching on a binary variable.
Definition at line 1729 of file sub.h.
The solution method for the next linear program.
Definition at line 1733 of file sub.h.
The buffer of the newly generated variables.
Definition at line 1737 of file sub.h.
The buffer of the newly generated constraints.
Definition at line 1741 of file sub.h.
The buffer of the variables which are removed at the beginning of the next iteration.
Definition at line 1746 of file sub.h.
The buffer of the constraints which are removed at the beginning of the next iteration.
Definition at line 1751 of file sub.h.
The last LP-solution.
Definition at line 1755 of file sub.h.
The dual variables of the last linear program.
Definition at line 1759 of file sub.h.
A row of the basis inverse associated with the infeasible variable infeasVar_ or slack variable infeasCon_.
Definition at line 1764 of file sub.h.
The number of an infeasible constraint.
Definition at line 1768 of file sub.h.
The number of an infeasible variable.
Definition at line 1772 of file sub.h.
If true, then the management of non-liftable constraints is performed.
Definition at line 1776 of file sub.h.
The level of the subproblem in the enumeration tree.
Definition at line 2024 of file sub.h.
The number of the subproblem.
Definition at line 2028 of file sub.h.
The status of the subproblem.
Definition at line 2035 of file sub.h.
The sons of the node in the \ tree.
Definition at line 2039 of file sub.h.
The maximum number of iterations in the cutting plane phase.
Definition at line 2043 of file sub.h.
The number of optimizations of the subproblem.
Definition at line 2047 of file sub.h.
If this member is true then the space reserve of the following three members varReserve_, conReserve_, and nnzReserve_ is relative to the initial numbers of constraints, variables, and nonzeros, respectively. Otherwise, the values are casted to integers and regarded as absolute values.
Definition at line 2056 of file sub.h.
The additional space for variables.
Definition at line 2060 of file sub.h.
The additional space for constraints.
Definition at line 2064 of file sub.h.
The additional space for nonzeros.
Definition at line 2068 of file sub.h.
The number of subproblem optimizations the subproblem has already the status Dormant.
Definition at line 2073 of file sub.h.
The variable is true if the function activate() has been called from the function _activate(). This memorization is required such that a deactivate() is only called when activate() has been called.
Definition at line 2080 of file sub.h.
If this flag is set to true then the next LP-solution is ignored in the tailing-off control. The default value of the variable is false. It can be set to true by the function ignoreInTailingOff().
Definition at line 2086 of file sub.h.
The method that was used to solve the last LP.
Definition at line 2089 of file sub.h.
Definition at line 2091 of file sub.h.
Indicates whether to force the use of an exact solver to prepare branching etc.
Definition at line 2096 of file sub.h.
The documentation for this class was generated from the following file:
