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work on Gomory cut

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Signed-off-by: Lev <levnach@hotmail.com>
This commit is contained in:
Lev 2018-09-18 13:34:05 -07:00
parent 5bbe0508e4
commit ca3ce964ce
6 changed files with 160 additions and 47 deletions
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2
src/smt/smt_arith_value.h
View file

@ -17,7 +17,7 @@ Author:
Revision History:
--*/
#pragma once;
#pragma once
#include "ast/arith_decl_plugin.h"
#include "smt/smt_context.h"

23
src/util/lp/column_namer.h
View file

@ -33,29 +33,6 @@ public:
print_linear_combination_of_column_indices(coeff, out);
}
template <typename T>
void print_linear_combination_of_column_indices_only(const vector<std::pair<T, unsigned>> & coeffs, std::ostream & out) const {
bool first = true;
for (const auto & it : coeffs) {
auto val = it.first;
if (first) {
first = false;
} else {
if (numeric_traits<T>::is_pos(val)) {
out << " + ";
} else {
out << " - ";
val = -val;
}
}
if (val == -numeric_traits<T>::one())
out << " - ";
else if (val != numeric_traits<T>::one())
out << T_to_string(val);
out << "v" << it.second;
}
}
template <typename T>

141
src/util/lp/gomory.cpp
View file

@ -23,6 +23,16 @@
namespace lp {
class gomory::imp {
inline static bool is_rational(const impq & n) { return is_zero(n.y); }
inline static mpq fractional_part(const impq & n) {
lp_assert(is_rational(n));
return n.x - floor(n.x);
}
inline static mpq fractional_part(const mpq & n) {
return n - floor(n);
}
lar_term & m_t; // the term to return in the cut
mpq & m_k; // the right side of the cut
explanation& m_ex; // the conflict explanation
@ -43,32 +53,31 @@ class gomory::imp {
void int_case_in_gomory_cut(const mpq & a, unsigned j,
mpq & lcm_den, const mpq& f0, const mpq& one_minus_f0) {
lp_assert(is_int(j) && !a.is_int());
mpq fj = int_solver::fractional_part(a);
lp_assert(fj.is_pos());
mpq fj = fractional_part(a);
TRACE("gomory_cut_detail",
tout << a << " j=" << j << " k = " << m_k;
tout << ", fj: " << fj << ", ";
tout << "f0: " << f0 << ", ";
tout << "1 - f0: " << 1 - f0 << ", ";
tout << "a - fj = " << a - fj << ", ";
tout << (at_lower(j)?"at_lower":"at_upper")<< std::endl;
);
lp_assert(fj.is_pos() && (a - fj).is_int());
mpq new_a;
mpq one_minus_fj = 1 - fj;
if (at_lower(j)) {
new_a = fj < one_minus_f0? fj / one_minus_f0 : one_minus_fj / f0;
new_a = fj < one_minus_f0? fj / one_minus_f0 : (- one_minus_fj / f0);
m_k.addmul(new_a, lower_bound(j).x);
m_ex.push_justification(column_lower_bound_constraint(j), new_a);
}
else {
lp_assert(at_upper(j));
// the upper terms are inverted: therefore we have the minus
new_a = - (fj < f0? fj / f0 : one_minus_fj / one_minus_f0);
new_a = - (fj < f0? fj / f0 : (- one_minus_fj / one_minus_f0));
m_k.addmul(new_a, upper_bound(j).x);
m_ex.push_justification(column_upper_bound_constraint(j), new_a);
}
TRACE("gomory_cut_detail", tout << "new_a: " << new_a << " k: " << m_k << "\n";);
m_t.add_monomial(new_a, j);
lcm_den = lcm(lcm_den, denominator(new_a));
TRACE("gomory_cut_detail", tout << "new_a = " << new_a << ", k = " << m_k << ", lcm_den = " << lcm_den << "\n";);
}
void real_case_in_gomory_cut(const mpq & a, unsigned x_j, const mpq& f0, const mpq& one_minus_f0) {
@ -150,10 +159,117 @@ class gomory::imp {
TRACE("gomory_cut_detail", tout << "k = " << m_k << std::endl;);
lp_assert(m_k.is_int());
}
std::string var_name(unsigned j) const {
return std::string("x") + std::to_string(j);
}
void dump_coeff_val(std::ostream & out, const mpq & a) const {
if (a.is_int()) {
if ( a >= zero_of_type<mpq>())
out << a;
else {
out << "( - " << - a << ") ";
}
} else {
if ( a >= zero_of_type<mpq>())
out << "(div " << numerator(a) << " " << denominator(a) << ")";
else {
out << "(- ( div " << numerator(-a) << " " << denominator(-a) << "))";
}
}
}
template <typename T>
void dump_coeff(std::ostream & out, const T& c) const {
out << "( * ";
dump_coeff_val(out, c.coeff());
out << " " << var_name(c.var()) << ")";
}
void dump_row_coefficients(std::ostream & out) const {
for (const auto& p : m_row) {
dump_coeff(out, p);
}
}
void dump_the_row(std::ostream& out) const {
out << "; the row\n";
out << "(assert ( = ( + ";
dump_row_coefficients(out);
out << ") 0))\n";
}
void dump_declarations(std::ostream& out) const {
// for a column j the var name is vj
for (const auto & p : m_row) {
out << "(declare-fun " << var_name(p.var()) << " () "
<< (is_int(p.var())? "Int" : "Real") << ")\n";
}
}
void dump_lower_bound_expl(std::ostream & out, unsigned j) const {
out << "(assert ( >= " << var_name(j) << " " << lower_bound(j).x << "))\n";
}
void dump_upper_bound_expl(std::ostream & out, unsigned j) const {
out << "(assert ( <= " << var_name(j) << " " << upper_bound(j).x << "))\n";
}
void dump_explanations(std::ostream& out) const {
for (const auto & p : m_row) {
unsigned j = p.var();
if (j == m_inf_col) {
continue;
}
if (column_is_fixed(j)) {
dump_lower_bound_expl(out, j);
dump_upper_bound_expl(out, j);
continue;
}
if (at_lower(j)) {
dump_lower_bound_expl(out, j);
} else {
dump_upper_bound_expl(out, j);
}
}
}
void dump_terms_coefficients(std::ostream & out) const {
for (const auto& p : m_t) {
dump_coeff(out, p);
}
}
void dump_term_sum(std::ostream & out) const {
out << "( + ";
dump_terms_coefficients(out);
out << ")";
}
void dump_term_le_k(std::ostream & out) const {
out << "( <= ";
dump_term_sum(out);
out << m_k << ")";
}
void dump_the_cut_assert(std::ostream & out) const {
out <<"(assert (not ";
dump_term_le_k(out);
out << "))\n";
}
void dump_cut_and_constraints_as_smt_lemma(std::ostream& out) const {
dump_declarations(out);
dump_the_row(out);
dump_explanations(out);
dump_the_cut_assert(out);
out << "(check-sat)\n";
}
public:
lia_move create_cut() {
TRACE("gomory_cut",
tout << "applying cut at:\n"; m_int_solver.m_lar_solver->print_row(m_row, tout); tout << std::endl;
tout << "applying cut at:\n"; print_linear_combination_of_column_indices_only(m_row, tout); tout << std::endl;
for (auto & p : m_row) {
m_int_solver.m_lar_solver->m_mpq_lar_core_solver.m_r_solver.print_column_info(p.var(), tout);
}
@ -164,7 +280,11 @@ public:
m_k = 1;
mpq lcm_den(1);
bool some_int_columns = false;
mpq f0 = int_solver::fractional_part(get_value(m_inf_col));
mpq f0 = fractional_part(get_value(m_inf_col));
TRACE("gomory_cut_detail", tout << "f0: " << f0 << ", ";
tout << "1 - f0: " << 1 - f0 << ", get_value(m_inf_col).x - f0 = " << get_value(m_inf_col).x - f0;);
lp_assert(f0.is_pos() && (get_value(m_inf_col).x - f0).is_int());
mpq one_min_f0 = 1 - f0;
for (const auto & p : m_row) {
unsigned j = p.var();
@ -194,7 +314,8 @@ public:
adjust_term_and_k_for_some_ints_case_gomory(lcm_den);
lp_assert(m_int_solver.current_solution_is_inf_on_cut());
m_int_solver.m_lar_solver->subs_term_columns(m_t, m_k);
TRACE("gomory_cut", tout<<"gomory cut:"; m_int_solver.m_lar_solver->print_term(m_t, tout); tout << " <= " << m_k << std::endl;);
TRACE("gomory_cut", tout<<"gomory cut:"; print_linear_combination_of_column_indices_only(m_t, tout); tout << " <= " << m_k << std::endl;);
TRACE("gomory_cut_detail", dump_cut_and_constraints_as_smt_lemma(tout););
return lia_move::cut;
}
imp(lar_term & t, mpq & k, explanation& ex, unsigned basic_inf_int_j, const row_strip<mpq>& row, const int_solver& int_slv ) :

8
src/util/lp/int_solver.h
View file

@ -113,17 +113,9 @@ private:
bool has_low(unsigned j) const;
bool has_upper(unsigned j) const;
unsigned row_of_basic_column(unsigned j) const;
inline static bool is_rational(const impq & n) {
return is_zero(n.y);
}
public:
void display_column(std::ostream & out, unsigned j) const;
inline static
mpq fractional_part(const impq & n) {
lp_assert(is_rational(n));
return n.x - floor(n.x);
}
constraint_index column_upper_bound_constraint(unsigned j) const;
constraint_index column_lower_bound_constraint(unsigned j) const;
bool current_solution_is_inf_on_cut() const;

2
src/util/lp/lar_solver.cpp
View file

@ -1273,7 +1273,7 @@ std::ostream& lar_solver::print_term_as_indices(lar_term const& term, std::ostre
if (!numeric_traits<mpq>::is_zero(term.m_v)) {
out << term.m_v << " + ";
}
print_linear_combination_of_column_indices_only(term.coeffs_as_vector(), out);
print_linear_combination_of_column_indices_only(term, out);
return out;
}

31
src/util/lp/lp_utils.h
View file

@ -50,11 +50,34 @@ bool contains(const std::unordered_map<A, B> & map, const A& key) {
namespace lp {
inline void throw_exception(std::string && str) {
throw default_exception(std::move(str));
template <typename T>
void print_linear_combination_of_column_indices_only(const T & coeffs, std::ostream & out) {
bool first = true;
for (const auto & it : coeffs) {
auto val = it.coeff();
if (first) {
first = false;
} else {
if (val.is_pos()) {
out << " + ";
} else {
out << " - ";
val = -val;
}
}
if (val == 1)
out << " ";
else
out << T_to_string(val);
out << "x" << it.var();
}
typedef z3_exception exception;
}
inline void throw_exception(std::string && str) {
throw default_exception(std::move(str));
}
typedef z3_exception exception;
#define lp_assert(_x_) { SASSERT(_x_); }
inline void lp_unreachable() { lp_assert(false); }