3 * This file is a part of LEMON, a generic C++ optimization library
5 * Copyright (C) 2003-2007
6 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
7 * (Egervary Research Group on Combinatorial Optimization, EGRES).
9 * Permission to use, modify and distribute this software is granted
10 * provided that this copyright notice appears in all copies. For
11 * precise terms see the accompanying LICENSE file.
13 * This software is provided "AS IS" with no warranty of any kind,
14 * express or implied, and with no claim as to its suitability for any
19 #ifndef LEMON_LP_BASE_H
20 #define LEMON_LP_BASE_H
29 #include<lemon/error.h>
30 #include<lemon/bits/invalid.h>
31 #include<lemon/bits/utility.h>
32 #include<lemon/bits/lp_id.h>
35 ///\brief The interface of the LP solver interface.
39 ///Common base class for LP solvers
41 ///\todo Much more docs
52 ///Possible outcomes of an LP solving procedure
53 enum SolveExitStatus {
54 ///This means that the problem has been successfully solved: either
55 ///an optimal solution has been found or infeasibility/unboundedness
58 ///Any other case (including the case when some user specified
59 ///limit has been exceeded)
65 ///Feasible solution hasn't been found (but may exist).
67 ///\todo NOTFOUND might be a better name.
70 ///The problem has no feasible solution
72 ///Feasible solution found
74 ///Optimal solution exists and found
76 ///The cost function is unbounded
78 ///\todo Give a feasible solution and an infinite ray (and the
79 ///corresponding bases)
83 ///\e The type of the investigated LP problem
85 ///Primal-dual feasible
86 PRIMAL_DUAL_FEASIBLE = 0,
87 ///Primal feasible dual infeasible
88 PRIMAL_FEASIBLE_DUAL_INFEASIBLE = 1,
89 ///Primal infeasible dual feasible
90 PRIMAL_INFEASIBLE_DUAL_FEASIBLE = 2,
91 ///Primal-dual infeasible
92 PRIMAL_DUAL_INFEASIBLE = 3,
93 ///Could not determine so far
97 ///The floating point type used by the solver
99 ///The infinity constant
100 static const Value INF;
101 ///The not a number constant
102 static const Value NaN;
104 static inline bool isNaN(const Value& v) { return v!=v; }
110 ///Refer to a column of the LP.
112 ///This type is used to refer to a column of the LP.
114 ///Its value remains valid and correct even after the addition or erase of
117 ///\todo Document what can one do with a Col (INVALID, comparing,
118 ///it is similar to Node/Edge)
122 friend class LpSolverBase;
123 friend class MipSolverBase;
124 explicit Col(int _id) : id(_id) {}
126 typedef Value ExprValue;
127 typedef True LpSolverCol;
129 Col(const Invalid&) : id(-1) {}
130 bool operator< (Col c) const {return id< c.id;}
131 bool operator> (Col c) const {return id> c.id;}
132 bool operator==(Col c) const {return id==c.id;}
133 bool operator!=(Col c) const {return id!=c.id;}
136 class ColIt : public Col {
137 const LpSolverBase *_lp;
140 ColIt(const LpSolverBase &lp) : _lp(&lp)
142 _lp->cols.firstFix(id);
144 ColIt(const Invalid&) : Col(INVALID) {}
147 _lp->cols.nextFix(id);
152 static int id(const Col& col) { return col.id; }
155 ///Refer to a row of the LP.
157 ///This type is used to refer to a row of the LP.
159 ///Its value remains valid and correct even after the addition or erase of
162 ///\todo Document what can one do with a Row (INVALID, comparing,
163 ///it is similar to Node/Edge)
167 friend class LpSolverBase;
168 explicit Row(int _id) : id(_id) {}
170 typedef Value ExprValue;
171 typedef True LpSolverRow;
173 Row(const Invalid&) : id(-1) {}
175 bool operator< (Row c) const {return id< c.id;}
176 bool operator> (Row c) const {return id> c.id;}
177 bool operator==(Row c) const {return id==c.id;}
178 bool operator!=(Row c) const {return id!=c.id;}
181 class RowIt : public Row {
182 const LpSolverBase *_lp;
185 RowIt(const LpSolverBase &lp) : _lp(&lp)
187 _lp->rows.firstFix(id);
189 RowIt(const Invalid&) : Row(INVALID) {}
192 _lp->rows.nextFix(id);
197 static int id(const Row& row) { return row.id; }
201 int _lpId(const Col& c) const {
202 return cols.floatingId(id(c));
205 int _lpId(const Row& r) const {
206 return rows.floatingId(id(r));
209 Col _item(int i, Col) const {
210 return Col(cols.fixId(i));
213 Row _item(int i, Row) const {
214 return Row(rows.fixId(i));
220 ///Linear expression of variables and a constant component
222 ///This data structure stores a linear expression of the variables
223 ///(\ref Col "Col"s) and also has a constant component.
225 ///There are several ways to access and modify the contents of this
227 ///- Its it fully compatible with \c std::map<Col,double>, so for expamle
228 ///if \c e is an Expr and \c v and \c w are of type \ref Col, then you can
229 ///read and modify the coefficients like
236 ///or you can also iterate through its elements.
239 ///for(LpSolverBase::Expr::iterator i=e.begin();i!=e.end();++i)
242 ///(This code computes the sum of all coefficients).
243 ///- Numbers (<tt>double</tt>'s)
244 ///and variables (\ref Col "Col"s) directly convert to an
245 ///\ref Expr and the usual linear operations are defined, so
248 ///2*v-3.12*(v-w/2)+2
249 ///v*2.1+(3*v+(v*12+w+6)*3)/2
251 ///are valid \ref Expr "Expr"essions.
252 ///The usual assignment operations are also defined.
255 ///e+=2*v-3.12*(v-w/2)+2;
259 ///- The constant member can be set and read by \ref constComp()
262 ///double c=e.constComp();
265 ///\note \ref clear() not only sets all coefficients to 0 but also
266 ///clears the constant components.
270 class Expr : public std::map<Col,Value>
273 typedef LpSolverBase::Col Key;
274 typedef LpSolverBase::Value Value;
277 typedef std::map<Col,Value> Base;
281 typedef True IsLinExpression;
283 Expr() : Base(), const_comp(0) { }
285 Expr(const Key &v) : const_comp(0) {
286 Base::insert(std::make_pair(v, 1));
289 Expr(const Value &v) : const_comp(v) {}
291 void set(const Key &v,const Value &c) {
292 Base::insert(std::make_pair(v, c));
295 Value &constComp() { return const_comp; }
297 const Value &constComp() const { return const_comp; }
299 ///Removes the components with zero coefficient.
301 for (Base::iterator i=Base::begin(); i!=Base::end();) {
304 if ((*i).second==0) Base::erase(i);
309 void simplify() const {
310 const_cast<Expr*>(this)->simplify();
313 ///Removes the coefficients closer to zero than \c tolerance.
314 void simplify(double &tolerance) {
315 for (Base::iterator i=Base::begin(); i!=Base::end();) {
318 if (std::fabs((*i).second)<tolerance) Base::erase(i);
323 ///Sets all coefficients and the constant component to 0.
330 Expr &operator+=(const Expr &e) {
331 for (Base::const_iterator j=e.begin(); j!=e.end(); ++j)
332 (*this)[j->first]+=j->second;
333 const_comp+=e.const_comp;
337 Expr &operator-=(const Expr &e) {
338 for (Base::const_iterator j=e.begin(); j!=e.end(); ++j)
339 (*this)[j->first]-=j->second;
340 const_comp-=e.const_comp;
344 Expr &operator*=(const Value &c) {
345 for (Base::iterator j=Base::begin(); j!=Base::end(); ++j)
351 Expr &operator/=(const Value &c) {
352 for (Base::iterator j=Base::begin(); j!=Base::end(); ++j)
359 void prettyPrint(std::ostream &os) {
360 //std::fmtflags os.flags();
361 //os.setf(std::ios::showpos);
362 Base::iterator j=Base::begin();
364 os<<j->second<<"*x["<<id(j->first)<<"]";
366 for (; j!=Base::end(); ++j){
369 os<<j->second<<"*x["<<id(j->first)<<"]";
371 //Nem valami korrekt, de nem talaltam meg, hogy kell
372 //os.unsetf(std::ios::showpos);
381 ///This data stucture represents a linear constraint in the LP.
382 ///Basically it is a linear expression with a lower or an upper bound
383 ///(or both). These parts of the constraint can be obtained by the member
384 ///functions \ref expr(), \ref lowerBound() and \ref upperBound(),
386 ///There are two ways to construct a constraint.
387 ///- You can set the linear expression and the bounds directly
388 /// by the functions above.
389 ///- The operators <tt>\<=</tt>, <tt>==</tt> and <tt>\>=</tt>
390 /// are defined between expressions, or even between constraints whenever
391 /// it makes sense. Therefore if \c e and \c f are linear expressions and
392 /// \c s and \c t are numbers, then the followings are valid expressions
393 /// and thus they can be used directly e.g. in \ref addRow() whenever
402 ///\warning The validity of a constraint is checked only at run time, so
403 ///e.g. \ref addRow(<tt>x[1]\<=x[2]<=5</tt>) will compile, but will throw a
404 ///\ref LogicError exception.
408 typedef LpSolverBase::Expr Expr;
409 typedef Expr::Key Key;
410 typedef Expr::Value Value;
417 Constr() : _expr(), _lb(NaN), _ub(NaN) {}
419 Constr(Value lb,const Expr &e,Value ub) :
420 _expr(e), _lb(lb), _ub(ub) {}
422 Constr(const Expr &e,Value ub) :
423 _expr(e), _lb(NaN), _ub(ub) {}
425 Constr(Value lb,const Expr &e) :
426 _expr(e), _lb(lb), _ub(NaN) {}
428 Constr(const Expr &e) :
429 _expr(e), _lb(NaN), _ub(NaN) {}
437 ///Reference to the linear expression
438 Expr &expr() { return _expr; }
439 ///Cont reference to the linear expression
440 const Expr &expr() const { return _expr; }
441 ///Reference to the lower bound.
444 ///- \ref INF "INF": the constraint is lower unbounded.
445 ///- \ref NaN "NaN": lower bound has not been set.
446 ///- finite number: the lower bound
447 Value &lowerBound() { return _lb; }
448 ///The const version of \ref lowerBound()
449 const Value &lowerBound() const { return _lb; }
450 ///Reference to the upper bound.
453 ///- \ref INF "INF": the constraint is upper unbounded.
454 ///- \ref NaN "NaN": upper bound has not been set.
455 ///- finite number: the upper bound
456 Value &upperBound() { return _ub; }
457 ///The const version of \ref upperBound()
458 const Value &upperBound() const { return _ub; }
459 ///Is the constraint lower bounded?
460 bool lowerBounded() const {
464 ///Is the constraint upper bounded?
465 bool upperBounded() const {
470 void prettyPrint(std::ostream &os) {
471 if (_lb==-LpSolverBase::INF||isNaN(_lb))
475 _expr.prettyPrint(os);
476 if (_ub==LpSolverBase::INF)
485 ///Linear expression of rows
487 ///This data structure represents a column of the matrix,
488 ///thas is it strores a linear expression of the dual variables
489 ///(\ref Row "Row"s).
491 ///There are several ways to access and modify the contents of this
493 ///- Its it fully compatible with \c std::map<Row,double>, so for expamle
494 ///if \c e is an DualExpr and \c v
495 ///and \c w are of type \ref Row, then you can
496 ///read and modify the coefficients like
503 ///or you can also iterate through its elements.
506 ///for(LpSolverBase::DualExpr::iterator i=e.begin();i!=e.end();++i)
509 ///(This code computes the sum of all coefficients).
510 ///- Numbers (<tt>double</tt>'s)
511 ///and variables (\ref Row "Row"s) directly convert to an
512 ///\ref DualExpr and the usual linear operations are defined, so
516 ///v*2.1+(3*v+(v*12+w)*3)/2
518 ///are valid \ref DualExpr "DualExpr"essions.
519 ///The usual assignment operations are also defined.
522 ///e+=2*v-3.12*(v-w/2);
529 class DualExpr : public std::map<Row,Value>
532 typedef LpSolverBase::Row Key;
533 typedef LpSolverBase::Value Value;
536 typedef std::map<Row,Value> Base;
539 typedef True IsLinExpression;
541 DualExpr() : Base() { }
543 DualExpr(const Key &v) {
544 Base::insert(std::make_pair(v, 1));
547 void set(const Key &v,const Value &c) {
548 Base::insert(std::make_pair(v, c));
551 ///Removes the components with zero coefficient.
553 for (Base::iterator i=Base::begin(); i!=Base::end();) {
556 if ((*i).second==0) Base::erase(i);
561 void simplify() const {
562 const_cast<DualExpr*>(this)->simplify();
565 ///Removes the coefficients closer to zero than \c tolerance.
566 void simplify(double &tolerance) {
567 for (Base::iterator i=Base::begin(); i!=Base::end();) {
570 if (std::fabs((*i).second)<tolerance) Base::erase(i);
575 ///Sets all coefficients to 0.
581 DualExpr &operator+=(const DualExpr &e) {
582 for (Base::const_iterator j=e.begin(); j!=e.end(); ++j)
583 (*this)[j->first]+=j->second;
587 DualExpr &operator-=(const DualExpr &e) {
588 for (Base::const_iterator j=e.begin(); j!=e.end(); ++j)
589 (*this)[j->first]-=j->second;
593 DualExpr &operator*=(const Value &c) {
594 for (Base::iterator j=Base::begin(); j!=Base::end(); ++j)
599 DualExpr &operator/=(const Value &c) {
600 for (Base::iterator j=Base::begin(); j!=Base::end(); ++j)
609 template <typename _Expr>
610 class MappedOutputIterator {
613 typedef std::insert_iterator<_Expr> Base;
615 typedef std::output_iterator_tag iterator_category;
616 typedef void difference_type;
617 typedef void value_type;
618 typedef void reference;
619 typedef void pointer;
621 MappedOutputIterator(const Base& _base, const LpSolverBase& _lp)
622 : base(_base), lp(_lp) {}
624 MappedOutputIterator& operator*() {
628 MappedOutputIterator& operator=(const std::pair<int, Value>& value) {
629 *base = std::make_pair(lp._item(value.first, typename _Expr::Key()),
634 MappedOutputIterator& operator++() {
639 MappedOutputIterator operator++(int) {
640 MappedOutputIterator tmp(*this);
645 bool operator==(const MappedOutputIterator& it) const {
646 return base == it.base;
649 bool operator!=(const MappedOutputIterator& it) const {
650 return base != it.base;
655 const LpSolverBase& lp;
658 template <typename Expr>
659 class MappedInputIterator {
662 typedef typename Expr::const_iterator Base;
664 typedef typename Base::iterator_category iterator_category;
665 typedef typename Base::difference_type difference_type;
666 typedef const std::pair<int, Value> value_type;
667 typedef value_type reference;
670 pointer(value_type& _value) : value(_value) {}
671 value_type* operator->() { return &value; }
676 MappedInputIterator(const Base& _base, const LpSolverBase& _lp)
677 : base(_base), lp(_lp) {}
679 reference operator*() {
680 return std::make_pair(lp._lpId(base->first), base->second);
683 pointer operator->() {
684 return pointer(operator*());
687 MappedInputIterator& operator++() {
692 MappedInputIterator operator++(int) {
693 MappedInputIterator tmp(*this);
698 bool operator==(const MappedInputIterator& it) const {
699 return base == it.base;
702 bool operator!=(const MappedInputIterator& it) const {
703 return base != it.base;
708 const LpSolverBase& lp;
713 /// STL compatible iterator for lp col
714 typedef MappedInputIterator<Expr> ConstRowIterator;
715 /// STL compatible iterator for lp row
716 typedef MappedInputIterator<DualExpr> ConstColIterator;
718 /// STL compatible iterator for lp col
719 typedef MappedOutputIterator<Expr> RowIterator;
720 /// STL compatible iterator for lp row
721 typedef MappedOutputIterator<DualExpr> ColIterator;
723 //Abstract virtual functions
724 virtual LpSolverBase &_newLp() = 0;
725 virtual LpSolverBase &_copyLp(){
726 ///\todo This should be implemented here, too, when we have
727 ///problem retrieving routines. It can be overriden.
730 LpSolverBase & newlp(_newLp());
732 //return *(LpSolverBase*)0;
735 virtual int _addCol() = 0;
736 virtual int _addRow() = 0;
738 virtual void _eraseCol(int col) = 0;
739 virtual void _eraseRow(int row) = 0;
741 virtual void _getColName(int col, std::string & name) const = 0;
742 virtual void _setColName(int col, const std::string & name) = 0;
743 virtual int _colByName(const std::string& name) const = 0;
745 virtual void _setRowCoeffs(int i, ConstRowIterator b,
746 ConstRowIterator e) = 0;
747 virtual void _getRowCoeffs(int i, RowIterator b) const = 0;
748 virtual void _setColCoeffs(int i, ConstColIterator b,
749 ConstColIterator e) = 0;
750 virtual void _getColCoeffs(int i, ColIterator b) const = 0;
751 virtual void _setCoeff(int row, int col, Value value) = 0;
752 virtual Value _getCoeff(int row, int col) const = 0;
753 virtual void _setColLowerBound(int i, Value value) = 0;
754 virtual Value _getColLowerBound(int i) const = 0;
755 virtual void _setColUpperBound(int i, Value value) = 0;
756 virtual Value _getColUpperBound(int i) const = 0;
757 virtual void _setRowBounds(int i, Value lower, Value upper) = 0;
758 virtual void _getRowBounds(int i, Value &lower, Value &upper) const = 0;
760 virtual void _setObjCoeff(int i, Value obj_coef) = 0;
761 virtual Value _getObjCoeff(int i) const = 0;
762 virtual void _clearObj()=0;
764 virtual SolveExitStatus _solve() = 0;
765 virtual Value _getPrimal(int i) const = 0;
766 virtual Value _getDual(int i) const = 0;
767 virtual Value _getPrimalValue() const = 0;
768 virtual bool _isBasicCol(int i) const = 0;
769 virtual SolutionStatus _getPrimalStatus() const = 0;
770 virtual SolutionStatus _getDualStatus() const = 0;
771 virtual ProblemTypes _getProblemType() const = 0;
773 virtual void _setMax() = 0;
774 virtual void _setMin() = 0;
777 virtual bool _isMax() const = 0;
779 //Own protected stuff
781 //Constant component of the objective function
782 Value obj_const_comp;
787 LpSolverBase() : obj_const_comp(0) {}
790 virtual ~LpSolverBase() {}
792 ///Creates a new LP problem
793 LpSolverBase &newLp() {return _newLp();}
794 ///Makes a copy of the LP problem
795 LpSolverBase ©Lp() {return _copyLp();}
797 ///\name Build up and modify the LP
801 ///Add a new empty column (i.e a new variable) to the LP
802 Col addCol() { Col c; _addCol(); c.id = cols.addId(); return c;}
804 ///\brief Adds several new columns
805 ///(i.e a variables) at once
807 ///This magic function takes a container as its argument
808 ///and fills its elements
809 ///with new columns (i.e. variables)
811 ///- a standard STL compatible iterable container with
812 ///\ref Col as its \c values_type
815 ///std::vector<LpSolverBase::Col>
816 ///std::list<LpSolverBase::Col>
818 ///- a standard STL compatible iterable container with
819 ///\ref Col as its \c mapped_type
822 ///std::map<AnyType,LpSolverBase::Col>
824 ///- an iterable lemon \ref concepts::WriteMap "write map" like
826 ///ListGraph::NodeMap<LpSolverBase::Col>
827 ///ListGraph::EdgeMap<LpSolverBase::Col>
829 ///\return The number of the created column.
832 int addColSet(T &t) { return 0;}
835 typename enable_if<typename T::value_type::LpSolverCol,int>::type
836 addColSet(T &t,dummy<0> = 0) {
838 for(typename T::iterator i=t.begin();i!=t.end();++i) {*i=addCol();s++;}
842 typename enable_if<typename T::value_type::second_type::LpSolverCol,
844 addColSet(T &t,dummy<1> = 1) {
846 for(typename T::iterator i=t.begin();i!=t.end();++i) {
853 typename enable_if<typename T::MapIt::Value::LpSolverCol,
855 addColSet(T &t,dummy<2> = 2) {
857 for(typename T::MapIt i(t); i!=INVALID; ++i)
866 ///Set a column (i.e a dual constraint) of the LP
868 ///\param c is the column to be modified
869 ///\param e is a dual linear expression (see \ref DualExpr)
871 void col(Col c,const DualExpr &e) {
873 _setColCoeffs(_lpId(c), ConstColIterator(e.begin(), *this),
874 ConstColIterator(e.end(), *this));
877 ///Get a column (i.e a dual constraint) of the LP
879 ///\param r is the column to get
880 ///\return the dual expression associated to the column
881 DualExpr col(Col c) const {
883 _getColCoeffs(_lpId(c), ColIterator(std::inserter(e, e.end()), *this));
887 ///Add a new column to the LP
889 ///\param e is a dual linear expression (see \ref DualExpr)
890 ///\param obj is the corresponding component of the objective
891 ///function. It is 0 by default.
892 ///\return The created column.
893 Col addCol(const DualExpr &e, Value o = 0) {
900 ///Add a new empty row (i.e a new constraint) to the LP
902 ///This function adds a new empty row (i.e a new constraint) to the LP.
903 ///\return The created row
904 Row addRow() { Row r; _addRow(); r.id = rows.addId(); return r;}
906 ///\brief Add several new rows
907 ///(i.e a constraints) at once
909 ///This magic function takes a container as its argument
910 ///and fills its elements
911 ///with new row (i.e. variables)
913 ///- a standard STL compatible iterable container with
914 ///\ref Row as its \c values_type
917 ///std::vector<LpSolverBase::Row>
918 ///std::list<LpSolverBase::Row>
920 ///- a standard STL compatible iterable container with
921 ///\ref Row as its \c mapped_type
924 ///std::map<AnyType,LpSolverBase::Row>
926 ///- an iterable lemon \ref concepts::WriteMap "write map" like
928 ///ListGraph::NodeMap<LpSolverBase::Row>
929 ///ListGraph::EdgeMap<LpSolverBase::Row>
931 ///\return The number of rows created.
934 int addRowSet(T &t) { return 0;}
937 typename enable_if<typename T::value_type::LpSolverRow,int>::type
938 addRowSet(T &t,dummy<0> = 0) {
940 for(typename T::iterator i=t.begin();i!=t.end();++i) {*i=addRow();s++;}
944 typename enable_if<typename T::value_type::second_type::LpSolverRow,
946 addRowSet(T &t,dummy<1> = 1) {
948 for(typename T::iterator i=t.begin();i!=t.end();++i) {
955 typename enable_if<typename T::MapIt::Value::LpSolverRow,
957 addRowSet(T &t,dummy<2> = 2) {
959 for(typename T::MapIt i(t); i!=INVALID; ++i)
968 ///Set a row (i.e a constraint) of the LP
970 ///\param r is the row to be modified
971 ///\param l is lower bound (-\ref INF means no bound)
972 ///\param e is a linear expression (see \ref Expr)
973 ///\param u is the upper bound (\ref INF means no bound)
974 ///\bug This is a temporary function. The interface will change to
976 ///\todo Option to control whether a constraint with a single variable is
978 void row(Row r, Value l, const Expr &e, Value u) {
980 _setRowCoeffs(_lpId(r), ConstRowIterator(e.begin(), *this),
981 ConstRowIterator(e.end(), *this));
982 _setRowBounds(_lpId(r),l-e.constComp(),u-e.constComp());
985 ///Set a row (i.e a constraint) of the LP
987 ///\param r is the row to be modified
988 ///\param c is a linear expression (see \ref Constr)
989 void row(Row r, const Constr &c) {
990 row(r, c.lowerBounded()?c.lowerBound():-INF,
991 c.expr(), c.upperBounded()?c.upperBound():INF);
995 ///Get a row (i.e a constraint) of the LP
997 ///\param r is the row to get
998 ///\return the expression associated to the row
999 Expr row(Row r) const {
1001 _getRowCoeffs(_lpId(r), RowIterator(std::inserter(e, e.end()), *this));
1005 ///Add a new row (i.e a new constraint) to the LP
1007 ///\param l is the lower bound (-\ref INF means no bound)
1008 ///\param e is a linear expression (see \ref Expr)
1009 ///\param u is the upper bound (\ref INF means no bound)
1010 ///\return The created row.
1011 ///\bug This is a temporary function. The interface will change to
1013 Row addRow(Value l,const Expr &e, Value u) {
1019 ///Add a new row (i.e a new constraint) to the LP
1021 ///\param c is a linear expression (see \ref Constr)
1022 ///\return The created row.
1023 Row addRow(const Constr &c) {
1028 ///Erase a coloumn (i.e a variable) from the LP
1030 ///\param c is the coloumn to be deleted
1031 ///\todo Please check this
1032 void eraseCol(Col c) {
1033 _eraseCol(_lpId(c));
1036 ///Erase a row (i.e a constraint) from the LP
1038 ///\param r is the row to be deleted
1039 ///\todo Please check this
1040 void eraseRow(Row r) {
1041 _eraseRow(_lpId(r));
1045 /// Get the name of a column
1047 ///\param c is the coresponding coloumn
1048 ///\return The name of the colunm
1049 std::string colName(Col c) const {
1051 _getColName(_lpId(c), name);
1055 /// Set the name of a column
1057 ///\param c is the coresponding coloumn
1058 ///\param name The name to be given
1059 void colName(Col c, const std::string& name) {
1060 _setColName(_lpId(c), name);
1063 /// Get the column by its name
1065 ///\param name The name of the column
1066 ///\return the proper column or \c INVALID
1067 Col colByName(const std::string& name) const {
1068 int k = _colByName(name);
1069 return k != -1 ? Col(cols.fixId(k)) : Col(INVALID);
1072 /// Set an element of the coefficient matrix of the LP
1074 ///\param r is the row of the element to be modified
1075 ///\param c is the coloumn of the element to be modified
1076 ///\param val is the new value of the coefficient
1078 void coeff(Row r, Col c, Value val) {
1079 _setCoeff(_lpId(r),_lpId(c), val);
1082 /// Get an element of the coefficient matrix of the LP
1084 ///\param r is the row of the element in question
1085 ///\param c is the coloumn of the element in question
1086 ///\return the corresponding coefficient
1088 Value coeff(Row r, Col c) const {
1089 return _getCoeff(_lpId(r),_lpId(c));
1092 /// Set the lower bound of a column (i.e a variable)
1094 /// The lower bound of a variable (column) has to be given by an
1095 /// extended number of type Value, i.e. a finite number of type
1096 /// Value or -\ref INF.
1097 void colLowerBound(Col c, Value value) {
1098 _setColLowerBound(_lpId(c),value);
1101 /// Get the lower bound of a column (i.e a variable)
1103 /// This function returns the lower bound for column (variable) \t c
1104 /// (this might be -\ref INF as well).
1105 ///\return The lower bound for coloumn \t c
1106 Value colLowerBound(Col c) const {
1107 return _getColLowerBound(_lpId(c));
1110 ///\brief Set the lower bound of several columns
1111 ///(i.e a variables) at once
1113 ///This magic function takes a container as its argument
1114 ///and applies the function on all of its elements.
1115 /// The lower bound of a variable (column) has to be given by an
1116 /// extended number of type Value, i.e. a finite number of type
1117 /// Value or -\ref INF.
1120 void colLowerBound(T &t, Value value) { return 0;}
1123 typename enable_if<typename T::value_type::LpSolverCol,void>::type
1124 colLowerBound(T &t, Value value,dummy<0> = 0) {
1125 for(typename T::iterator i=t.begin();i!=t.end();++i) {
1126 colLowerBound(*i, value);
1130 typename enable_if<typename T::value_type::second_type::LpSolverCol,
1132 colLowerBound(T &t, Value value,dummy<1> = 1) {
1133 for(typename T::iterator i=t.begin();i!=t.end();++i) {
1134 colLowerBound(i->second, value);
1138 typename enable_if<typename T::MapIt::Value::LpSolverCol,
1140 colLowerBound(T &t, Value value,dummy<2> = 2) {
1141 for(typename T::MapIt i(t); i!=INVALID; ++i){
1142 colLowerBound(*i, value);
1147 /// Set the upper bound of a column (i.e a variable)
1149 /// The upper bound of a variable (column) has to be given by an
1150 /// extended number of type Value, i.e. a finite number of type
1151 /// Value or \ref INF.
1152 void colUpperBound(Col c, Value value) {
1153 _setColUpperBound(_lpId(c),value);
1156 /// Get the upper bound of a column (i.e a variable)
1158 /// This function returns the upper bound for column (variable) \t c
1159 /// (this might be \ref INF as well).
1160 ///\return The upper bound for coloumn \t c
1161 Value colUpperBound(Col c) const {
1162 return _getColUpperBound(_lpId(c));
1165 ///\brief Set the upper bound of several columns
1166 ///(i.e a variables) at once
1168 ///This magic function takes a container as its argument
1169 ///and applies the function on all of its elements.
1170 /// The upper bound of a variable (column) has to be given by an
1171 /// extended number of type Value, i.e. a finite number of type
1172 /// Value or \ref INF.
1175 void colUpperBound(T &t, Value value) { return 0;}
1178 typename enable_if<typename T::value_type::LpSolverCol,void>::type
1179 colUpperBound(T &t, Value value,dummy<0> = 0) {
1180 for(typename T::iterator i=t.begin();i!=t.end();++i) {
1181 colUpperBound(*i, value);
1185 typename enable_if<typename T::value_type::second_type::LpSolverCol,
1187 colUpperBound(T &t, Value value,dummy<1> = 1) {
1188 for(typename T::iterator i=t.begin();i!=t.end();++i) {
1189 colUpperBound(i->second, value);
1193 typename enable_if<typename T::MapIt::Value::LpSolverCol,
1195 colUpperBound(T &t, Value value,dummy<2> = 2) {
1196 for(typename T::MapIt i(t); i!=INVALID; ++i){
1197 colUpperBound(*i, value);
1202 /// Set the lower and the upper bounds of a column (i.e a variable)
1204 /// The lower and the upper bounds of
1205 /// a variable (column) have to be given by an
1206 /// extended number of type Value, i.e. a finite number of type
1207 /// Value, -\ref INF or \ref INF.
1208 void colBounds(Col c, Value lower, Value upper) {
1209 _setColLowerBound(_lpId(c),lower);
1210 _setColUpperBound(_lpId(c),upper);
1213 ///\brief Set the lower and the upper bound of several columns
1214 ///(i.e a variables) at once
1216 ///This magic function takes a container as its argument
1217 ///and applies the function on all of its elements.
1218 /// The lower and the upper bounds of
1219 /// a variable (column) have to be given by an
1220 /// extended number of type Value, i.e. a finite number of type
1221 /// Value, -\ref INF or \ref INF.
1224 void colBounds(T &t, Value lower, Value upper) { return 0;}
1227 typename enable_if<typename T::value_type::LpSolverCol,void>::type
1228 colBounds(T &t, Value lower, Value upper,dummy<0> = 0) {
1229 for(typename T::iterator i=t.begin();i!=t.end();++i) {
1230 colBounds(*i, lower, upper);
1234 typename enable_if<typename T::value_type::second_type::LpSolverCol,
1236 colBounds(T &t, Value lower, Value upper,dummy<1> = 1) {
1237 for(typename T::iterator i=t.begin();i!=t.end();++i) {
1238 colBounds(i->second, lower, upper);
1242 typename enable_if<typename T::MapIt::Value::LpSolverCol,
1244 colBounds(T &t, Value lower, Value upper,dummy<2> = 2) {
1245 for(typename T::MapIt i(t); i!=INVALID; ++i){
1246 colBounds(*i, lower, upper);
1252 /// Set the lower and the upper bounds of a row (i.e a constraint)
1254 /// The lower and the upper bound of a constraint (row) have to be
1255 /// given by an extended number of type Value, i.e. a finite
1256 /// number of type Value, -\ref INF or \ref INF. There is no
1257 /// separate function for the lower and the upper bound because
1258 /// that would have been hard to implement for CPLEX.
1259 void rowBounds(Row c, Value lower, Value upper) {
1260 _setRowBounds(_lpId(c),lower, upper);
1263 /// Get the lower and the upper bounds of a row (i.e a constraint)
1265 /// The lower and the upper bound of
1266 /// a constraint (row) are
1267 /// extended numbers of type Value, i.e. finite numbers of type
1268 /// Value, -\ref INF or \ref INF.
1269 /// \todo There is no separate function for the
1270 /// lower and the upper bound because we had problems with the
1271 /// implementation of the setting functions for CPLEX:
1272 /// check out whether this can be done for these functions.
1273 void getRowBounds(Row c, Value &lower, Value &upper) const {
1274 _getRowBounds(_lpId(c),lower, upper);
1277 ///Set an element of the objective function
1278 void objCoeff(Col c, Value v) {_setObjCoeff(_lpId(c),v); };
1280 ///Get an element of the objective function
1281 Value objCoeff(Col c) const { return _getObjCoeff(_lpId(c)); };
1283 ///Set the objective function
1285 ///\param e is a linear expression of type \ref Expr.
1288 for (Expr::iterator i=e.begin(); i!=e.end(); ++i)
1289 objCoeff((*i).first,(*i).second);
1290 obj_const_comp=e.constComp();
1293 ///Get the objective function
1295 ///\return the objective function as a linear expression of type \ref Expr.
1298 for (ColIt it(*this); it != INVALID; ++it) {
1299 double c = objCoeff(it);
1301 e.insert(std::make_pair(it, c));
1309 void max() { _setMax(); }
1311 void min() { _setMin(); }
1313 ///Query function: is this a maximization problem?
1314 bool isMax() const {return _isMax(); }
1316 ///Query function: is this a minimization problem?
1317 bool isMin() const {return !isMax(); }
1322 ///\name Solve the LP
1326 ///\e Solve the LP problem at hand
1328 ///\return The result of the optimization procedure. Possible
1329 ///values and their meanings can be found in the documentation of
1330 ///\ref SolveExitStatus.
1332 ///\todo Which method is used to solve the problem
1333 SolveExitStatus solve() { return _solve(); }
1337 ///\name Obtain the solution
1341 /// The status of the primal problem (the original LP problem)
1342 SolutionStatus primalStatus() const {
1343 return _getPrimalStatus();
1346 /// The status of the dual (of the original LP) problem
1347 SolutionStatus dualStatus() const {
1348 return _getDualStatus();
1351 ///The type of the original LP problem
1352 ProblemTypes problemType() const {
1353 return _getProblemType();
1357 Value primal(Col c) const { return _getPrimal(_lpId(c)); }
1360 Value dual(Row r) const { return _getDual(_lpId(r)); }
1363 bool isBasicCol(Col c) const { return _isBasicCol(_lpId(c)); }
1368 ///- \ref INF or -\ref INF means either infeasibility or unboundedness
1369 /// of the primal problem, depending on whether we minimize or maximize.
1370 ///- \ref NaN if no primal solution is found.
1371 ///- The (finite) objective value if an optimal solution is found.
1372 Value primalValue() const { return _getPrimalValue()+obj_const_comp;}
1378 /// \ingroup lp_group
1380 /// \brief Common base class for MIP solvers
1381 /// \todo Much more docs
1382 class MipSolverBase : virtual public LpSolverBase{
1385 ///Possible variable (coloumn) types (e.g. real, integer, binary etc.)
1387 ///Continuous variable
1391 ///Unfortunately, cplex 7.5 somewhere writes something like
1392 ///#define INTEGER 'I'
1394 ///\todo No support for other types yet.
1397 ///Sets the type of the given coloumn to the given type
1399 ///Sets the type of the given coloumn to the given type.
1400 void colType(Col c, ColTypes col_type) {
1401 _colType(_lpId(c),col_type);
1404 ///Gives back the type of the column.
1406 ///Gives back the type of the column.
1407 ColTypes colType(Col c) const {
1408 return _colType(_lpId(c));
1411 ///Sets the type of the given Col to integer or remove that property.
1413 ///Sets the type of the given Col to integer or remove that property.
1414 void integer(Col c, bool enable) {
1421 ///Gives back whether the type of the column is integer or not.
1423 ///Gives back the type of the column.
1424 ///\return true if the column has integer type and false if not.
1425 bool integer(Col c) const {
1426 return (colType(c)==INT);
1429 /// The status of the MIP problem
1430 SolutionStatus mipStatus() const {
1431 return _getMipStatus();
1436 virtual ColTypes _colType(int col) const = 0;
1437 virtual void _colType(int col, ColTypes col_type) = 0;
1438 virtual SolutionStatus _getMipStatus() const = 0;
1442 ///\relates LpSolverBase::Expr
1444 inline LpSolverBase::Expr operator+(const LpSolverBase::Expr &a,
1445 const LpSolverBase::Expr &b)
1447 LpSolverBase::Expr tmp(a);
1453 ///\relates LpSolverBase::Expr
1455 inline LpSolverBase::Expr operator-(const LpSolverBase::Expr &a,
1456 const LpSolverBase::Expr &b)
1458 LpSolverBase::Expr tmp(a);
1464 ///\relates LpSolverBase::Expr
1466 inline LpSolverBase::Expr operator*(const LpSolverBase::Expr &a,
1467 const LpSolverBase::Value &b)
1469 LpSolverBase::Expr tmp(a);
1476 ///\relates LpSolverBase::Expr
1478 inline LpSolverBase::Expr operator*(const LpSolverBase::Value &a,
1479 const LpSolverBase::Expr &b)
1481 LpSolverBase::Expr tmp(b);
1487 ///\relates LpSolverBase::Expr
1489 inline LpSolverBase::Expr operator/(const LpSolverBase::Expr &a,
1490 const LpSolverBase::Value &b)
1492 LpSolverBase::Expr tmp(a);
1499 ///\relates LpSolverBase::Constr
1501 inline LpSolverBase::Constr operator<=(const LpSolverBase::Expr &e,
1502 const LpSolverBase::Expr &f)
1504 return LpSolverBase::Constr(-LpSolverBase::INF,e-f,0);
1509 ///\relates LpSolverBase::Constr
1511 inline LpSolverBase::Constr operator<=(const LpSolverBase::Value &e,
1512 const LpSolverBase::Expr &f)
1514 return LpSolverBase::Constr(e,f);
1519 ///\relates LpSolverBase::Constr
1521 inline LpSolverBase::Constr operator<=(const LpSolverBase::Expr &e,
1522 const LpSolverBase::Value &f)
1524 return LpSolverBase::Constr(e,f);
1529 ///\relates LpSolverBase::Constr
1531 inline LpSolverBase::Constr operator>=(const LpSolverBase::Expr &e,
1532 const LpSolverBase::Expr &f)
1534 return LpSolverBase::Constr(-LpSolverBase::INF,f-e,0);
1540 ///\relates LpSolverBase::Constr
1542 inline LpSolverBase::Constr operator>=(const LpSolverBase::Value &e,
1543 const LpSolverBase::Expr &f)
1545 return LpSolverBase::Constr(f,e);
1551 ///\relates LpSolverBase::Constr
1553 inline LpSolverBase::Constr operator>=(const LpSolverBase::Expr &e,
1554 const LpSolverBase::Value &f)
1556 return LpSolverBase::Constr(f,e);
1561 ///\relates LpSolverBase::Constr
1563 inline LpSolverBase::Constr operator==(const LpSolverBase::Expr &e,
1564 const LpSolverBase::Value &f)
1566 return LpSolverBase::Constr(f,e,f);
1571 ///\relates LpSolverBase::Constr
1573 inline LpSolverBase::Constr operator==(const LpSolverBase::Expr &e,
1574 const LpSolverBase::Expr &f)
1576 return LpSolverBase::Constr(0,e-f,0);
1581 ///\relates LpSolverBase::Constr
1583 inline LpSolverBase::Constr operator<=(const LpSolverBase::Value &n,
1584 const LpSolverBase::Constr&c)
1586 LpSolverBase::Constr tmp(c);
1587 ///\todo Create an own exception type.
1588 if(!LpSolverBase::isNaN(tmp.lowerBound())) throw LogicError();
1589 else tmp.lowerBound()=n;
1594 ///\relates LpSolverBase::Constr
1596 inline LpSolverBase::Constr operator<=(const LpSolverBase::Constr& c,
1597 const LpSolverBase::Value &n)
1599 LpSolverBase::Constr tmp(c);
1600 ///\todo Create an own exception type.
1601 if(!LpSolverBase::isNaN(tmp.upperBound())) throw LogicError();
1602 else tmp.upperBound()=n;
1608 ///\relates LpSolverBase::Constr
1610 inline LpSolverBase::Constr operator>=(const LpSolverBase::Value &n,
1611 const LpSolverBase::Constr&c)
1613 LpSolverBase::Constr tmp(c);
1614 ///\todo Create an own exception type.
1615 if(!LpSolverBase::isNaN(tmp.upperBound())) throw LogicError();
1616 else tmp.upperBound()=n;
1621 ///\relates LpSolverBase::Constr
1623 inline LpSolverBase::Constr operator>=(const LpSolverBase::Constr& c,
1624 const LpSolverBase::Value &n)
1626 LpSolverBase::Constr tmp(c);
1627 ///\todo Create an own exception type.
1628 if(!LpSolverBase::isNaN(tmp.lowerBound())) throw LogicError();
1629 else tmp.lowerBound()=n;
1635 ///\relates LpSolverBase::DualExpr
1637 inline LpSolverBase::DualExpr operator+(const LpSolverBase::DualExpr &a,
1638 const LpSolverBase::DualExpr &b)
1640 LpSolverBase::DualExpr tmp(a);
1646 ///\relates LpSolverBase::DualExpr
1648 inline LpSolverBase::DualExpr operator-(const LpSolverBase::DualExpr &a,
1649 const LpSolverBase::DualExpr &b)
1651 LpSolverBase::DualExpr tmp(a);
1657 ///\relates LpSolverBase::DualExpr
1659 inline LpSolverBase::DualExpr operator*(const LpSolverBase::DualExpr &a,
1660 const LpSolverBase::Value &b)
1662 LpSolverBase::DualExpr tmp(a);
1669 ///\relates LpSolverBase::DualExpr
1671 inline LpSolverBase::DualExpr operator*(const LpSolverBase::Value &a,
1672 const LpSolverBase::DualExpr &b)
1674 LpSolverBase::DualExpr tmp(b);
1680 ///\relates LpSolverBase::DualExpr
1682 inline LpSolverBase::DualExpr operator/(const LpSolverBase::DualExpr &a,
1683 const LpSolverBase::Value &b)
1685 LpSolverBase::DualExpr tmp(a);
1693 #endif //LEMON_LP_BASE_H