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separate the gomory cut functionality in a separate file

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Signed-off-by: Lev <levnach@hotmail.com>
This commit is contained in:
Lev 2018-09-14 17:12:49 -07:00
parent 26764b076f
commit 324396e403
7 changed files with 284 additions and 232 deletions
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1
src/util/lp/CMakeLists.txt
View file

@ -6,6 +6,7 @@ z3_add_component(lp
core_solver_pretty_printer.cpp
dense_matrix.cpp
eta_matrix.cpp
gomory.cpp
indexed_vector.cpp
int_solver.cpp
lar_solver.cpp

227
src/util/lp/gomory.cpp Normal file
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@ -0,0 +1,227 @@
/*++
Copyright (c) 2017 Microsoft Corporation
Module Name:
<name>
Abstract:
<abstract>
Author:
Nikolaj Bjorner (nbjorner)
Lev Nachmanson (levnach)
Revision History:
--*/
#include "util/lp/gomory.h"
#include "util/lp/int_solver.h"
#include "util/lp/lar_solver.h"
namespace lp {
class gomory::imp {
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
unsigned m_inf_col; // a basis column which has to be an integer but has a not integral value
const row_strip<mpq>& m_row;
const int_solver& m_int_solver;
const impq & get_value(unsigned j) const { return m_int_solver.get_value(j); }
bool is_real(unsigned j) const { return m_int_solver.is_real(j); }
bool at_lower(unsigned j) const { return m_int_solver.at_lower(j); }
bool at_upper(unsigned j) const { return m_int_solver.at_upper(j); }
const impq & lower_bound(unsigned j) const { return m_int_solver.lower_bound(j); }
const impq & upper_bound(unsigned j) const { return m_int_solver.upper_bound(j); }
constraint_index column_lower_bound_constraint(unsigned j) const { return m_int_solver.column_lower_bound_constraint(j); }
constraint_index column_upper_bound_constraint(unsigned j) const { return m_int_solver.column_upper_bound_constraint(j); }
void int_case_in_gomory_cut(const mpq & a, unsigned x_j,
mpq & lcm_den, const mpq& f_0, const mpq& one_minus_f_0) {
lp_assert(is_int(x_j));
lp_assert(!a.is_int());
mpq f_j = int_solver::fractional_part(a);
TRACE("gomory_cut_detail",
tout << a << " x_j" << x_j << " k = " << m_k << "\n";
tout << "f_j: " << f_j << "\n";
tout << "f_0: " << f_0 << "\n";
tout << "1 - f_0: " << 1 - f_0 << "\n";
tout << "at_lower(" << x_j << ") = " << at_lower(x_j) << std::endl;
);
lp_assert (!f_j.is_zero());
mpq new_a;
if (at_lower(x_j)) {
if (f_j <= one_minus_f_0) {
new_a = f_j / one_minus_f_0;
}
else {
new_a = (1 - f_j) / f_0;
}
m_k.addmul(new_a, lower_bound(x_j).x);
m_ex.push_justification(column_lower_bound_constraint(x_j), new_a);
}
else {
lp_assert(at_upper(x_j));
if (f_j <= f_0) {
new_a = f_j / f_0;
}
else {
new_a = (mpq(1) - f_j) / one_minus_f_0;
}
new_a.neg(); // the upper terms are inverted
m_k.addmul(new_a, upper_bound(x_j).x);
m_ex.push_justification(column_upper_bound_constraint(x_j), new_a);
}
TRACE("gomory_cut_detail", tout << "new_a: " << new_a << " k: " << m_k << "\n";);
m_t.add_monomial(new_a, x_j);
lcm_den = lcm(lcm_den, denominator(new_a));
}
void real_case_in_gomory_cut(const mpq & a, unsigned x_j, const mpq& f_0, const mpq& one_minus_f_0) {
TRACE("gomory_cut_detail_real", tout << "real\n";);
mpq new_a;
if (at_lower(x_j)) {
if (a.is_pos()) {
new_a = a / one_minus_f_0;
}
else {
new_a = a / f_0;
new_a.neg();
}
m_k.addmul(new_a, lower_bound(x_j).x); // is it a faster operation than
// k += lower_bound(x_j).x * new_a;
m_ex.push_justification(column_lower_bound_constraint(x_j), new_a);
}
else {
lp_assert(at_upper(x_j));
if (a.is_pos()) {
new_a = a / f_0;
new_a.neg(); // the upper terms are inverted.
}
else {
new_a = a / one_minus_f_0;
}
m_k.addmul(new_a, upper_bound(x_j).x); // k += upper_bound(x_j).x * new_a;
m_ex.push_justification(column_upper_bound_constraint(x_j), new_a);
}
TRACE("gomory_cut_detail_real", tout << a << "*v" << x_j << " k: " << m_k << "\n";);
m_t.add_monomial(new_a, x_j);
}
lia_move report_conflict_from_gomory_cut() {
lp_assert(m_k.is_pos());
// conflict 0 >= k where k is positive
m_k.neg(); // returning 0 <= -k
return lia_move::conflict;
}
void adjust_term_and_k_for_some_ints_case_gomory(mpq &lcm_den) {
lp_assert(!m_t.is_empty());
auto pol = m_t.coeffs_as_vector();
m_t.clear();
if (pol.size() == 1) {
TRACE("gomory_cut_detail", tout << "pol.size() is 1" << std::endl;);
unsigned v = pol[0].second;
lp_assert(is_int(v));
const mpq& a = pol[0].first;
m_k /= a;
if (a.is_pos()) { // we have av >= k
if (!m_k.is_int())
m_k = ceil(m_k);
// switch size
m_t.add_monomial(- mpq(1), v);
m_k.neg();
} else {
if (!m_k.is_int())
m_k = floor(m_k);
m_t.add_monomial(mpq(1), v);
}
} else {
TRACE("gomory_cut_detail", tout << "pol.size() > 1" << std::endl;);
lcm_den = lcm(lcm_den, denominator(m_k));
lp_assert(lcm_den.is_pos());
if (!lcm_den.is_one()) {
// normalize coefficients of integer parameters to be integers.
for (auto & pi: pol) {
pi.first *= lcm_den;
SASSERT(!is_int(pi.second) || pi.first.is_int());
}
m_k *= lcm_den;
}
// negate everything to return -pol <= -m_k
for (const auto & pi: pol)
m_t.add_monomial(-pi.first, pi.second);
m_k.neg();
}
TRACE("gomory_cut_detail", tout << "k = " << m_k << std::endl;);
lp_assert(m_k.is_int());
}
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;
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);
}
tout << "inf_col = " << m_inf_col << std::endl;
);
// gomory will be t <= k and the current solution has a property t > k
m_k = 1;
mpq lcm_den(1);
unsigned x_j;
mpq a;
bool some_int_columns = false;
mpq f_0 = int_solver::fractional_part(get_value(m_inf_col));
mpq one_min_f_0 = 1 - f_0;
for (const auto & p : m_row) {
x_j = p.var();
if (x_j == m_inf_col)
continue;
// make the format compatible with the format used in: Integrating Simplex with DPLL(T)
a = p.coeff();
a.neg();
if (is_real(x_j))
real_case_in_gomory_cut(a, x_j, f_0, one_min_f_0);
else if (!a.is_int()) { // f_j will be zero and no monomial will be added
some_int_columns = true;
int_case_in_gomory_cut(a, x_j, lcm_den, f_0, one_min_f_0);
}
}
if (m_t.is_empty())
return report_conflict_from_gomory_cut();
if (some_int_columns)
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;);
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 ) :
m_t(t),
m_k(k),
m_ex(ex),
m_inf_col(basic_inf_int_j),
m_row(row),
m_int_solver(int_slv)
{
}
};
lia_move gomory::create_cut() {
return m_imp->create_cut();
}
gomory::gomory(lar_term & t, mpq & k, explanation& ex, unsigned basic_inf_int_j, const row_strip<mpq>& row, const int_solver& s) {
m_imp = alloc(imp, t, k, ex, basic_inf_int_j, row, s);
}
gomory::~gomory() { dealloc(m_imp); }
}

36
src/util/lp/gomory.h Normal file
View file

@ -0,0 +1,36 @@
/*++
Copyright (c) 2017 Microsoft Corporation
Module Name:
<name>
Abstract:
<abstract>
Author:
Nikolaj Bjorner (nbjorner)
Lev Nachmanson (levnach)
Revision History:
--*/
#pragma once
#include "util/lp/lar_term.h"
#include "util/lp/lia_move.h"
#include "util/lp/explanation.h"
#include "util/lp/static_matrix.h"
namespace lp {
class int_solver;
class gomory {
class imp;
imp *m_imp;
public :
gomory(lar_term & t, mpq & k, explanation& ex, unsigned basic_inf_int_j, const row_strip<mpq>& row, const int_solver& s);
lia_move create_cut();
~gomory();
};
}

221
src/util/lp/int_solver.cpp
View file

@ -8,6 +8,7 @@
#include "util/lp/lp_utils.h"
#include <utility>
#include "util/lp/monomial.h"
#include "util/lp/gomory.h"
namespace lp {
@ -101,12 +102,7 @@ bool int_solver::is_gomory_cut_target(const row_strip<mpq>& row) {
unsigned j;
for (const auto & p : row) {
j = p.var();
if (is_base(j)) continue;
if (is_free(j))
return false;
if (!at_bound(j))
return false;
if (!is_zero(get_value(j).y)) {
if (!is_base(j) && (!at_bound(j) || !is_zero(get_value(j).y))) {
TRACE("gomory_cut", tout << "row is not gomory cut target:\n";
display_column(tout, j);
tout << "infinitesimal: " << !is_zero(get_value(j).y) << "\n";);
@ -117,36 +113,6 @@ bool int_solver::is_gomory_cut_target(const row_strip<mpq>& row) {
}
void int_solver::real_case_in_gomory_cut(const mpq & a, unsigned x_j, const mpq& f_0, const mpq& one_minus_f_0) {
TRACE("gomory_cut_detail_real", tout << "real\n";);
mpq new_a;
if (at_low(x_j)) {
if (a.is_pos()) {
new_a = a / one_minus_f_0;
}
else {
new_a = a / f_0;
new_a.neg();
}
m_k->addmul(new_a, lower_bound(x_j).x); // is it a faster operation than
// k += lower_bound(x_j).x * new_a;
m_ex->push_justification(column_lower_bound_constraint(x_j), new_a);
}
else {
lp_assert(at_upper(x_j));
if (a.is_pos()) {
new_a = a / f_0;
new_a.neg(); // the upper terms are inverted.
}
else {
new_a = a / one_minus_f_0;
}
m_k->addmul(new_a, upper_bound(x_j).x); // k += upper_bound(x_j).x * new_a;
m_ex->push_justification(column_upper_bound_constraint(x_j), new_a);
}
TRACE("gomory_cut_detail_real", tout << a << "*v" << x_j << " k: " << *m_k << "\n";);
m_t->add_monomial(new_a, x_j);
}
constraint_index int_solver::column_upper_bound_constraint(unsigned j) const {
return m_lar_solver->get_column_upper_bound_witness(j);
@ -157,99 +123,6 @@ constraint_index int_solver::column_lower_bound_constraint(unsigned j) const {
}
void int_solver::int_case_in_gomory_cut(const mpq & a, unsigned x_j,
mpq & lcm_den, const mpq& f_0, const mpq& one_minus_f_0) {
lp_assert(is_int(x_j));
lp_assert(!a.is_int());
mpq f_j = fractional_part(a);
TRACE("gomory_cut_detail",
tout << a << " x_j" << x_j << " k = " << *m_k << "\n";
tout << "f_j: " << f_j << "\n";
tout << "f_0: " << f_0 << "\n";
tout << "1 - f_0: " << 1 - f_0 << "\n";
tout << "at_low(" << x_j << ") = " << at_low(x_j) << std::endl;
);
lp_assert (!f_j.is_zero());
mpq new_a;
if (at_low(x_j)) {
if (f_j <= one_minus_f_0) {
new_a = f_j / one_minus_f_0;
}
else {
new_a = (1 - f_j) / f_0;
}
m_k->addmul(new_a, lower_bound(x_j).x);
m_ex->push_justification(column_lower_bound_constraint(x_j), new_a);
}
else {
lp_assert(at_upper(x_j));
if (f_j <= f_0) {
new_a = f_j / f_0;
}
else {
new_a = (mpq(1) - f_j) / one_minus_f_0;
}
new_a.neg(); // the upper terms are inverted
m_k->addmul(new_a, upper_bound(x_j).x);
m_ex->push_justification(column_upper_bound_constraint(x_j), new_a);
}
TRACE("gomory_cut_detail", tout << "new_a: " << new_a << " k: " << *m_k << "\n";);
m_t->add_monomial(new_a, x_j);
lcm_den = lcm(lcm_den, denominator(new_a));
}
lia_move int_solver::report_conflict_from_gomory_cut() {
TRACE("empty_pol",);
lp_assert(m_k->is_pos());
// conflict 0 >= k where k is positive
m_k->neg(); // returning 0 <= -k
return lia_move::conflict;
}
void int_solver::gomory_cut_adjust_t_and_k(vector<std::pair<mpq, unsigned>> & pol,
lar_term & t,
mpq &k,
bool some_ints,
mpq & lcm_den) {
if (!some_ints)
return;
t.clear();
if (pol.size() == 1) {
unsigned v = pol[0].second;
lp_assert(is_int(v));
bool k_is_int = k.is_int();
const mpq& a = pol[0].first;
k /= a;
if (a.is_pos()) { // we have av >= k
if (!k_is_int)
k = ceil(k);
// switch size
t.add_monomial(- mpq(1), v);
k.neg();
} else {
if (!k_is_int)
k = floor(k);
t.add_monomial(mpq(1), v);
}
} else if (some_ints) {
lcm_den = lcm(lcm_den, denominator(k));
lp_assert(lcm_den.is_pos());
if (!lcm_den.is_one()) {
// normalize coefficients of integer parameters to be integers.
for (auto & pi: pol) {
pi.first *= lcm_den;
SASSERT(!is_int(pi.second) || pi.first.is_int());
}
k *= lcm_den;
}
// negate everything to return -pol <= -k
for (const auto & pi: pol)
t.add_monomial(-pi.first, pi.second);
k.neg();
}
}
bool int_solver::current_solution_is_inf_on_cut() const {
const auto & x = m_lar_solver->m_mpq_lar_core_solver.m_r_x;
impq v = m_t->apply(x);
@ -261,95 +134,11 @@ bool int_solver::current_solution_is_inf_on_cut() const {
return v * sign > (*m_k) * sign;
}
void int_solver::adjust_term_and_k_for_some_ints_case_gomory(mpq &lcm_den) {
lp_assert(!m_t->is_empty());
auto pol = m_t->coeffs_as_vector();
m_t->clear();
if (pol.size() == 1) {
TRACE("gomory_cut_detail", tout << "pol.size() is 1" << std::endl;);
unsigned v = pol[0].second;
lp_assert(is_int(v));
const mpq& a = pol[0].first;
(*m_k) /= a;
if (a.is_pos()) { // we have av >= k
if (!(*m_k).is_int())
(*m_k) = ceil((*m_k));
// switch size
m_t->add_monomial(- mpq(1), v);
(*m_k).neg();
} else {
if (!(*m_k).is_int())
(*m_k) = floor((*m_k));
m_t->add_monomial(mpq(1), v);
}
} else {
TRACE("gomory_cut_detail", tout << "pol.size() > 1" << std::endl;);
lcm_den = lcm(lcm_den, denominator((*m_k)));
lp_assert(lcm_den.is_pos());
if (!lcm_den.is_one()) {
// normalize coefficients of integer parameters to be integers.
for (auto & pi: pol) {
pi.first *= lcm_den;
SASSERT(!is_int(pi.second) || pi.first.is_int());
}
(*m_k) *= lcm_den;
}
// negate everything to return -pol <= -(*m_k)
for (const auto & pi: pol)
m_t->add_monomial(-pi.first, pi.second);
(*m_k).neg();
}
TRACE("gomory_cut_detail", tout << "k = " << (*m_k) << std::endl;);
lp_assert((*m_k).is_int());
}
lia_move int_solver::mk_gomory_cut( unsigned inf_col, const row_strip<mpq> & row) {
lp_assert(column_is_int_inf(inf_col));
TRACE("gomory_cut",
tout << "applying cut at:\n"; m_lar_solver->print_row(row, tout); tout << std::endl;
for (auto & p : row) {
m_lar_solver->m_mpq_lar_core_solver.m_r_solver.print_column_info(p.var(), tout);
}
tout << "inf_col = " << inf_col << std::endl;
);
// gomory will be t <= k and the current solution has a property t > k
*m_k = 1;
mpq lcm_den(1);
unsigned x_j;
mpq a;
bool some_int_columns = false;
mpq f_0 = int_solver::fractional_part(get_value(inf_col));
mpq one_min_f_0 = 1 - f_0;
for (const auto & p : row) {
x_j = p.var();
if (x_j == inf_col)
continue;
// make the format compatible with the format used in: Integrating Simplex with DPLL(T)
a = p.coeff();
a.neg();
if (is_real(x_j))
real_case_in_gomory_cut(a, x_j, f_0, one_min_f_0);
else if (!a.is_int()) { // f_j will be zero and no monomial will be added
some_int_columns = true;
int_case_in_gomory_cut(a, x_j, lcm_den, f_0, one_min_f_0);
}
}
if (m_t->is_empty())
return report_conflict_from_gomory_cut();
if (some_int_columns)
adjust_term_and_k_for_some_ints_case_gomory(lcm_den);
lp_assert(current_solution_is_inf_on_cut());
m_lar_solver->subs_term_columns(*m_t);
TRACE("gomory_cut", tout<<"precut:"; m_lar_solver->print_term(*m_t, tout); tout << " <= " << *m_k << std::endl;);
return lia_move::cut;
gomory gc(*m_t, *m_k, *m_ex, inf_col, row, *this);
return gc.create_cut();
}
lia_move int_solver::proceed_with_gomory_cut(unsigned j) {
@ -1121,7 +910,7 @@ bool int_solver::at_bound(unsigned j) const {
}
}
bool int_solver::at_low(unsigned j) const {
bool int_solver::at_lower(unsigned j) const {
auto & mpq_solver = m_lar_solver->m_mpq_lar_core_solver.m_r_solver;
switch (mpq_solver.m_column_types[j] ) {
case column_type::fixed:

25
src/util/lp/int_solver.h
View file

@ -53,6 +53,13 @@ public:
bool move_non_basic_column_to_bounds(unsigned j);
lia_move check_wrapper(lar_term& t, mpq& k, explanation& ex);
bool is_base(unsigned j) const;
bool is_real(unsigned j) const;
const impq & lower_bound(unsigned j) const;
const impq & upper_bound(unsigned j) const;
bool is_int(unsigned j) const;
const impq & get_value(unsigned j) const;
bool at_lower(unsigned j) const;
bool at_upper(unsigned j) const;
private:
@ -79,10 +86,7 @@ private:
void add_to_explanation_from_fixed_or_boxed_column(unsigned j);
lia_move patch_nbasic_columns();
bool get_freedom_interval_for_column(unsigned j, bool & inf_l, impq & l, bool & inf_u, impq & u, mpq & m);
const impq & lower_bound(unsigned j) const;
const impq & upper_bound(unsigned j) const;
bool is_int(unsigned j) const;
bool is_real(unsigned j) const;
private:
bool is_boxed(unsigned j) const;
bool is_fixed(unsigned j) const;
bool is_free(unsigned j) const;
@ -91,7 +95,6 @@ private:
void set_value_for_nbasic_column_ignore_old_values(unsigned j, const impq & new_val);
bool non_basic_columns_are_at_bounds() const;
bool is_feasible() const;
const impq & get_value(unsigned j) const;
bool column_is_int_inf(unsigned j) const;
void trace_inf_rows() const;
lia_move branch_or_sat();
@ -104,13 +107,9 @@ private:
bool move_non_basic_columns_to_bounds();
void branch_infeasible_int_var(unsigned);
lia_move mk_gomory_cut(unsigned inf_col, const row_strip<mpq>& row);
lia_move report_conflict_from_gomory_cut();
void adjust_term_and_k_for_some_ints_case_gomory(mpq& lcm_den);
lia_move proceed_with_gomory_cut(unsigned j);
bool is_gomory_cut_target(const row_strip<mpq>&);
bool at_bound(unsigned j) const;
bool at_low(unsigned j) const;
bool at_upper(unsigned j) const;
bool has_low(unsigned j) const;
bool has_upper(unsigned j) const;
unsigned row_of_basic_column(unsigned j) const;
@ -125,17 +124,13 @@ public:
lp_assert(is_rational(n));
return n.x - floor(n.x);
}
private:
void real_case_in_gomory_cut(const mpq & a, unsigned x_j, const mpq& f_0, const mpq& one_minus_f_0);
void int_case_in_gomory_cut(const mpq & a, unsigned x_j, mpq & lcm_den, const mpq& f_0, const mpq& one_minus_f_0);
constraint_index column_upper_bound_constraint(unsigned j) const;
constraint_index column_lower_bound_constraint(unsigned j) const;
void display_row_info(std::ostream & out, unsigned row_index) const;
void gomory_cut_adjust_t_and_k(vector<std::pair<mpq, unsigned>> & pol, lar_term & t, mpq &k, bool num_ints, mpq &lcm_den);
bool current_solution_is_inf_on_cut() const;
public:
bool shift_var(unsigned j, unsigned range);
private:
void display_row_info(std::ostream & out, unsigned row_index) const;
unsigned random();
bool has_inf_int() const;
lia_move create_branch_on_column(int j);

1
src/util/lp/lar_solver.cpp
View file

@ -1645,6 +1645,7 @@ void lar_solver::push_and_register_term(lar_term* t) {
// terms
var_index lar_solver::add_term(const vector<std::pair<mpq, var_index>> & coeffs,
const mpq &m_v) {
TRACE("add_term_lar_solver", print_linear_combination_of_column_indices(coeffs, tout););
if (strategy_is_undecided())
return add_term_undecided(coeffs, m_v);

5
src/util/lp/lar_solver.h
View file

@ -535,7 +535,7 @@ public:
return m_columns_to_ul_pairs()[j].lower_bound_witness();
}
void subs_term_columns(lar_term& t) {
void subs_term_columns(lar_term& t, mpq & rs) {
vector<std::pair<unsigned,unsigned>> columns_to_subs;
for (const auto & m : t.m_coeffs) {
unsigned tj = adjust_column_index_to_term_index(m.first);
@ -545,9 +545,12 @@ public:
for (const auto & p : columns_to_subs) {
auto it = t.m_coeffs.find(p.first);
lp_assert(it != t.m_coeffs.end());
const lar_term& lt = get_term(p.second);
mpq v = it->second;
t.m_coeffs.erase(it);
t.m_coeffs[p.second] = v;
if (lt.m_v.is_zero()) continue;
rs -= v * lt.m_v;
}
}