mirror of
https://github.com/Z3Prover/z3
synced 2025-04-07 01:54:08 +00:00
3d99ed9dd4
Improve fairness of cut generation by switching to find_infeasible_int_var with cascading priorities, allow stronger cuts by inlining terms.
1036 lines
35 KiB
C++
1036 lines
35 KiB
C++
/*
|
|
Copyright (c) 2017 Microsoft Corporation
|
|
Author: Lev Nachmanson
|
|
*/
|
|
#include "math/lp/int_solver.h"
|
|
#include "math/lp/lar_solver.h"
|
|
#include "math/lp/lp_utils.h"
|
|
#include "math/lp/monic.h"
|
|
#include "math/lp/gomory.h"
|
|
#include "math/lp/int_branch.h"
|
|
#include "math/lp/int_cube.h"
|
|
|
|
namespace lp {
|
|
|
|
int_solver::patcher::patcher(int_solver& lia):
|
|
lia(lia),
|
|
lra(lia.lra),
|
|
lrac(lia.lrac)
|
|
{}
|
|
|
|
unsigned int_solver::patcher::count_non_int() {
|
|
unsigned non_int = 0;
|
|
for (auto j : lra.r_basis())
|
|
if (lra.column_is_int(j) && !lra.column_value_is_int(j))
|
|
++non_int;
|
|
return non_int;
|
|
}
|
|
|
|
lia_move int_solver::patcher::patch_basic_columns() {
|
|
lia.settings().stats().m_patches++;
|
|
lra.remove_fixed_vars_from_base();
|
|
lp_assert(lia.is_feasible());
|
|
for (unsigned j : lra.r_basis())
|
|
if (!lra.get_value(j).is_int() && lra.column_is_int(j) && !lia.is_fixed(j))
|
|
patch_basic_column(j);
|
|
if (!lia.has_inf_int()) {
|
|
lia.settings().stats().m_patches_success++;
|
|
return lia_move::sat;
|
|
}
|
|
return lia_move::undef;
|
|
}
|
|
|
|
// clang-format on
|
|
/**
|
|
* \brief find integral and minimal, in the absolute values, deltas such that x - alpha*delta is integral too.
|
|
*/
|
|
bool get_patching_deltas(const rational& x, const rational& alpha,
|
|
rational& delta_plus, rational& delta_minus) {
|
|
auto a1 = numerator(alpha);
|
|
auto a2 = denominator(alpha);
|
|
auto x1 = numerator(x);
|
|
auto x2 = denominator(x);
|
|
if (!divides(x2, a2))
|
|
return false;
|
|
|
|
// delta has to be integral.
|
|
// We need to find delta such that x1/x2 + (a1/a2)*delta is integral (we are going to flip the delta sign later).
|
|
// Then a2*x1/x2 + a1*delta is integral, but x2 and x1 are coprime:
|
|
// that means that t = a2/x2 is
|
|
// integral. We established that a2 = x2*t Then x1 + a1*delta*(x2/a2) = x1
|
|
// + a1*(delta/t) is integral. Taking into account that t and a1 are
|
|
// coprime we have delta = t*k, where k is an integer.
|
|
rational t = a2 / x2;
|
|
// Now we have x1/x2 + (a1/x2)*k is integral, or (x1 + a1*k)/x2 is integral.
|
|
// It is equivalent to x1 + a1*k = x2*m, where m is an integer
|
|
// We know that a2 and a1 are coprime, and x2 divides a2, so x2 and a1 are
|
|
// coprime. We can find u and v such that u*a1 + v*x2 = 1.
|
|
rational u, v;
|
|
gcd(a1, x2, u, v);
|
|
lp_assert(gcd(a1, x2, u, v).is_one());
|
|
lp_assert((x + (a1 / a2) * (-u * t) * x1).is_int());
|
|
// 1 = (u- l*x2 ) * a1 + (v + l*a1)*x2, for every integer l.
|
|
rational d = u * t * x1;
|
|
// We can prove that x+alpha*d is integral,
|
|
// and any other delta, satisfying x+alpha*delta, is equal to d modulo a2.
|
|
delta_plus = mod(d, a2);
|
|
lp_assert(delta_plus > 0);
|
|
delta_minus = delta_plus - a2;
|
|
lp_assert(delta_minus < 0);
|
|
|
|
return true;
|
|
}
|
|
/**
|
|
* \brief try to patch the basic column v
|
|
*/
|
|
bool int_solver::patcher::patch_basic_column_on_row_cell(unsigned v, row_cell<mpq> const& c) {
|
|
if (v == c.var())
|
|
return false;
|
|
if (!lra.column_is_int(c.var())) // could use real to patch integer
|
|
return false;
|
|
if (c.coeff().is_int())
|
|
return false;
|
|
mpq a = fractional_part(c.coeff());
|
|
mpq r = fractional_part(lra.get_value(v));
|
|
lp_assert(0 < r && r < 1);
|
|
lp_assert(0 < a && a < 1);
|
|
mpq delta_plus, delta_minus;
|
|
if (!get_patching_deltas(r, a, delta_plus, delta_minus))
|
|
return false;
|
|
|
|
if (lia.random() % 2)
|
|
return try_patch_column(v, c.var(), delta_plus) ||
|
|
try_patch_column(v, c.var(), delta_minus);
|
|
else
|
|
return try_patch_column(v, c.var(), delta_minus) ||
|
|
try_patch_column(v, c.var(), delta_plus);
|
|
}
|
|
|
|
bool int_solver::patcher::try_patch_column(unsigned v, unsigned j, mpq const& delta) {
|
|
const auto & A = lra.A_r();
|
|
if (delta < 0) {
|
|
if (lia.has_lower(j) && lia.get_value(j) + impq(delta) < lra.get_lower_bound(j))
|
|
return false;
|
|
}
|
|
else {
|
|
if (lia.has_upper(j) && lia.get_value(j) + impq(delta) > lra.get_upper_bound(j))
|
|
return false;
|
|
}
|
|
for (auto const& c : A.column(j)) {
|
|
unsigned row_index = c.var();
|
|
unsigned bj = lrac.m_r_basis[row_index];
|
|
auto old_val = lia.get_value(bj);
|
|
auto new_val = old_val - impq(c.coeff()*delta);
|
|
if (lia.has_lower(bj) && new_val < lra.get_lower_bound(bj))
|
|
return false;
|
|
if (lia.has_upper(bj) && new_val > lra.get_upper_bound(bj))
|
|
return false;
|
|
if (old_val.is_int() && !new_val.is_int()){
|
|
return false; // do not waste resources on this case
|
|
}
|
|
// if bj == v, then, because we are patching the lra.get_value(v),
|
|
// we just need to assert that the lra.get_value(v) would be integral.
|
|
lp_assert(bj != v || lra.from_model_in_impq_to_mpq(new_val).is_int());
|
|
}
|
|
|
|
lra.set_value_for_nbasic_column(j, lia.get_value(j) + impq(delta));
|
|
return true;
|
|
}
|
|
|
|
void int_solver::patcher::patch_basic_column(unsigned v) {
|
|
SASSERT(!lia.is_fixed(v));
|
|
for (auto const& c : lra.basic2row(v))
|
|
if (patch_basic_column_on_row_cell(v, c))
|
|
return;
|
|
}
|
|
|
|
|
|
int_solver::int_solver(lar_solver& lar_slv) :
|
|
lra(lar_slv),
|
|
lrac(lra.m_mpq_lar_core_solver),
|
|
m_gcd(*this),
|
|
m_patcher(*this),
|
|
m_number_of_calls(0),
|
|
m_hnf_cutter(*this),
|
|
m_hnf_cut_period(settings().hnf_cut_period()) {
|
|
lra.set_int_solver(this);
|
|
}
|
|
|
|
// this will allow to enable and disable tracking of the pivot rows
|
|
struct check_return_helper {
|
|
lar_solver& lra;
|
|
bool m_track_touched_rows;
|
|
check_return_helper(lar_solver& ls) :
|
|
lra(ls),
|
|
m_track_touched_rows(lra.touched_rows_are_tracked()) {
|
|
lra.track_touched_rows(false);
|
|
}
|
|
~check_return_helper() {
|
|
lra.track_touched_rows(m_track_touched_rows);
|
|
}
|
|
};
|
|
|
|
lia_move int_solver::check(lp::explanation * e) {
|
|
SASSERT(lra.ax_is_correct());
|
|
if (!has_inf_int())
|
|
return lia_move::sat;
|
|
|
|
m_t.clear();
|
|
m_k.reset();
|
|
m_ex = e;
|
|
m_ex->clear();
|
|
m_upper = false;
|
|
m_cut_vars.reset();
|
|
|
|
lia_move r = lia_move::undef;
|
|
|
|
if (m_gcd.should_apply())
|
|
r = m_gcd();
|
|
|
|
check_return_helper pc(lra);
|
|
|
|
if (settings().get_cancel_flag())
|
|
return lia_move::undef;
|
|
|
|
++m_number_of_calls;
|
|
if (r == lia_move::undef && m_patcher.should_apply()) r = m_patcher();
|
|
if (r == lia_move::undef && should_find_cube()) r = int_cube(*this)();
|
|
if (r == lia_move::undef) lra.move_non_basic_columns_to_bounds();
|
|
if (r == lia_move::undef && should_hnf_cut()) r = hnf_cut();
|
|
m_cut_vars.reset();
|
|
#if 0
|
|
if (r == lia_move::undef && should_gomory_cut()) r = gomory(*this)();
|
|
#else
|
|
if (r == lia_move::undef && should_gomory_cut()) r = local_gomory(2);
|
|
#endif
|
|
m_cut_vars.reset();
|
|
if (r == lia_move::undef) r = int_branch(*this)();
|
|
return r;
|
|
}
|
|
|
|
std::ostream& int_solver::display_inf_rows(std::ostream& out) const {
|
|
unsigned num = lra.A_r().column_count();
|
|
for (unsigned v = 0; v < num; v++) {
|
|
if (column_is_int(v) && !get_value(v).is_int()) {
|
|
display_column(out, v);
|
|
}
|
|
}
|
|
|
|
num = 0;
|
|
for (unsigned i = 0; i < lra.A_r().row_count(); i++) {
|
|
unsigned j = lrac.m_r_basis[i];
|
|
if (column_is_int_inf(j)) {
|
|
num++;
|
|
lra.print_row(lra.A_r().m_rows[i], out);
|
|
out << "\n";
|
|
}
|
|
}
|
|
out << "num of int infeasible: " << num << "\n";
|
|
return out;
|
|
}
|
|
|
|
bool int_solver::cut_indices_are_columns() const {
|
|
for (lar_term::ival p : m_t) {
|
|
if (p.column().index() >= lra.A_r().column_count())
|
|
return false;
|
|
}
|
|
return true;
|
|
}
|
|
|
|
bool int_solver::current_solution_is_inf_on_cut() const {
|
|
SASSERT(cut_indices_are_columns());
|
|
const auto & x = lrac.m_r_x;
|
|
impq v = m_t.apply(x);
|
|
mpq sign = m_upper ? one_of_type<mpq>() : -one_of_type<mpq>();
|
|
CTRACE("current_solution_is_inf_on_cut", v * sign <= impq(m_k) * sign,
|
|
tout << "m_upper = " << m_upper << std::endl;
|
|
tout << "v = " << v << ", k = " << m_k << std::endl;
|
|
);
|
|
return v * sign > impq(m_k) * sign;
|
|
}
|
|
|
|
bool int_solver::has_inf_int() const {
|
|
return lra.has_inf_int();
|
|
}
|
|
|
|
u_dependency* int_solver::column_upper_bound_constraint(unsigned j) const {
|
|
return lra.get_column_upper_bound_witness(j);
|
|
}
|
|
|
|
u_dependency* int_solver::column_lower_bound_constraint(unsigned j) const {
|
|
return lra.get_column_lower_bound_witness(j);
|
|
}
|
|
|
|
unsigned int_solver::row_of_basic_column(unsigned j) const {
|
|
return lra.row_of_basic_column(j);
|
|
}
|
|
|
|
lp_settings& int_solver::settings() {
|
|
return lra.settings();
|
|
}
|
|
|
|
const lp_settings& int_solver::settings() const {
|
|
return lra.settings();
|
|
}
|
|
|
|
bool int_solver::column_is_int(column_index const& j) const {
|
|
return lra.column_is_int(j);
|
|
}
|
|
|
|
bool int_solver::is_real(unsigned j) const {
|
|
return !column_is_int(j);
|
|
}
|
|
|
|
bool int_solver::value_is_int(unsigned j) const {
|
|
return lra.column_value_is_int(j);
|
|
}
|
|
|
|
unsigned int_solver::random() {
|
|
return settings().random_next();
|
|
}
|
|
|
|
const impq& int_solver::upper_bound(unsigned j) const {
|
|
return lra.column_upper_bound(j);
|
|
}
|
|
|
|
const impq& int_solver::lower_bound(unsigned j) const {
|
|
return lra.column_lower_bound(j);
|
|
}
|
|
|
|
bool int_solver::is_term(unsigned j) const {
|
|
return lra.column_corresponds_to_term(j);
|
|
}
|
|
|
|
unsigned int_solver::column_count() const {
|
|
return lra.column_count();
|
|
}
|
|
|
|
bool int_solver::should_find_cube() {
|
|
return m_number_of_calls % settings().m_int_find_cube_period == 0;
|
|
}
|
|
|
|
bool int_solver::should_gomory_cut() {
|
|
return m_number_of_calls % settings().m_int_gomory_cut_period == 0;
|
|
}
|
|
|
|
bool int_solver::should_hnf_cut() {
|
|
return settings().enable_hnf() && m_number_of_calls % m_hnf_cut_period == 0;
|
|
}
|
|
|
|
lia_move int_solver::hnf_cut() {
|
|
lia_move r = m_hnf_cutter.make_hnf_cut();
|
|
if (r == lia_move::undef)
|
|
m_hnf_cut_period *= 2;
|
|
else
|
|
m_hnf_cut_period = settings().hnf_cut_period();
|
|
return r;
|
|
}
|
|
|
|
bool int_solver::has_lower(unsigned j) const {
|
|
switch (lrac.m_column_types()[j]) {
|
|
case column_type::fixed:
|
|
case column_type::boxed:
|
|
case column_type::lower_bound:
|
|
return true;
|
|
default:
|
|
return false;
|
|
}
|
|
}
|
|
|
|
bool int_solver::has_upper(unsigned j) const {
|
|
switch (lrac.m_column_types()[j]) {
|
|
case column_type::fixed:
|
|
case column_type::boxed:
|
|
case column_type::upper_bound:
|
|
return true;
|
|
default:
|
|
return false;
|
|
}
|
|
}
|
|
|
|
static void set_lower(impq & l, bool & inf_l, impq const & v ) {
|
|
if (inf_l || v > l) {
|
|
l = v;
|
|
inf_l = false;
|
|
}
|
|
}
|
|
|
|
static void set_upper(impq & u, bool & inf_u, impq const & v) {
|
|
if (inf_u || v < u) {
|
|
u = v;
|
|
inf_u = false;
|
|
}
|
|
}
|
|
|
|
// this function assumes that all basic columns dependend on j are feasible
|
|
bool int_solver::get_freedom_interval_for_column(unsigned j, bool & inf_l, impq & l, bool & inf_u, impq & u, mpq & m) {
|
|
if (lrac.m_r_heading[j] >= 0 || is_fixed(j)) // basic or fixed var
|
|
return false;
|
|
|
|
TRACE("random_update", display_column(tout, j) << ", is_int = " << column_is_int(j) << "\n";);
|
|
impq const & xj = get_value(j);
|
|
|
|
inf_l = true;
|
|
inf_u = true;
|
|
l = u = zero_of_type<impq>();
|
|
m = mpq(1);
|
|
|
|
if (has_lower(j))
|
|
set_lower(l, inf_l, lower_bound(j) - xj);
|
|
|
|
if (has_upper(j))
|
|
set_upper(u, inf_u, upper_bound(j) - xj);
|
|
|
|
|
|
const auto & A = lra.A_r();
|
|
TRACE("random_update", tout << "m = " << m << "\n";);
|
|
|
|
auto delta = [](mpq const& x, impq const& y, impq const& z) {
|
|
if (x.is_one())
|
|
return y - z;
|
|
if (x.is_minus_one())
|
|
return z - y;
|
|
return (y - z) / x;
|
|
};
|
|
|
|
for (auto c : A.column(j)) {
|
|
unsigned row_index = c.var();
|
|
const mpq & a = c.coeff();
|
|
unsigned i = lrac.m_r_basis[row_index];
|
|
impq const & xi = get_value(i);
|
|
lp_assert(lrac.m_r_solver.column_is_feasible(i));
|
|
if (column_is_int(i) && !a.is_int() && xi.is_int())
|
|
m = lcm(m, denominator(a));
|
|
|
|
if (!inf_l && !inf_u && l == u)
|
|
continue;
|
|
|
|
if (a.is_neg()) {
|
|
if (has_lower(i))
|
|
set_lower(l, inf_l, delta(a, xi, lra.get_lower_bound(i)));
|
|
if (has_upper(i))
|
|
set_upper(u, inf_u, delta(a, xi, lra.get_upper_bound(i)));
|
|
}
|
|
else {
|
|
if (has_upper(i))
|
|
set_lower(l, inf_l, delta(a, xi, lra.get_upper_bound(i)));
|
|
if (has_lower(i))
|
|
set_upper(u, inf_u, delta(a, xi, lra.get_lower_bound(i)));
|
|
}
|
|
}
|
|
|
|
l += xj;
|
|
u += xj;
|
|
|
|
TRACE("freedom_interval",
|
|
tout << "freedom variable for:\n";
|
|
tout << lra.get_variable_name(j);
|
|
tout << "[";
|
|
if (inf_l) tout << "-oo"; else tout << l;
|
|
tout << "; ";
|
|
if (inf_u) tout << "oo"; else tout << u;
|
|
tout << "]\n";
|
|
tout << "val = " << get_value(j) << "\n";
|
|
tout << "return " << (inf_l || inf_u || l <= u);
|
|
);
|
|
return (inf_l || inf_u || l <= u);
|
|
}
|
|
|
|
|
|
bool int_solver::is_feasible() const {
|
|
lp_assert(
|
|
lrac.m_r_solver.calc_current_x_is_feasible_include_non_basis() ==
|
|
lrac.m_r_solver.current_x_is_feasible());
|
|
return lrac.m_r_solver.current_x_is_feasible();
|
|
}
|
|
|
|
const impq & int_solver::get_value(unsigned j) const {
|
|
return lrac.m_r_x[j];
|
|
}
|
|
|
|
std::ostream& int_solver::display_column(std::ostream & out, unsigned j) const {
|
|
return lrac.m_r_solver.print_column_info(j, out);
|
|
}
|
|
|
|
bool int_solver::column_is_int_inf(unsigned j) const {
|
|
return column_is_int(j) && (!value_is_int(j));
|
|
}
|
|
|
|
bool int_solver::is_base(unsigned j) const {
|
|
return lrac.m_r_heading[j] >= 0;
|
|
}
|
|
|
|
bool int_solver::is_boxed(unsigned j) const {
|
|
return lrac.m_column_types[j] == column_type::boxed;
|
|
}
|
|
|
|
bool int_solver::is_fixed(unsigned j) const {
|
|
return lrac.m_column_types[j] == column_type::fixed;
|
|
}
|
|
|
|
bool int_solver::is_free(unsigned j) const {
|
|
return lrac.m_column_types[j] == column_type::free_column;
|
|
}
|
|
|
|
bool int_solver::at_bound(unsigned j) const {
|
|
auto & mpq_solver = lrac.m_r_solver;
|
|
switch (mpq_solver.m_column_types[j] ) {
|
|
case column_type::fixed:
|
|
case column_type::boxed:
|
|
return
|
|
mpq_solver.m_lower_bounds[j] == get_value(j) ||
|
|
mpq_solver.m_upper_bounds[j] == get_value(j);
|
|
case column_type::lower_bound:
|
|
return mpq_solver.m_lower_bounds[j] == get_value(j);
|
|
case column_type::upper_bound:
|
|
return mpq_solver.m_upper_bounds[j] == get_value(j);
|
|
default:
|
|
return false;
|
|
}
|
|
}
|
|
|
|
bool int_solver::at_lower(unsigned j) const {
|
|
auto & mpq_solver = lrac.m_r_solver;
|
|
switch (mpq_solver.m_column_types[j] ) {
|
|
case column_type::fixed:
|
|
case column_type::boxed:
|
|
case column_type::lower_bound:
|
|
return mpq_solver.m_lower_bounds[j] == get_value(j);
|
|
default:
|
|
return false;
|
|
}
|
|
}
|
|
|
|
bool int_solver::at_upper(unsigned j) const {
|
|
auto & mpq_solver = lrac.m_r_solver;
|
|
switch (mpq_solver.m_column_types[j] ) {
|
|
case column_type::fixed:
|
|
case column_type::boxed:
|
|
case column_type::upper_bound:
|
|
return mpq_solver.m_upper_bounds[j] == get_value(j);
|
|
default:
|
|
return false;
|
|
}
|
|
}
|
|
|
|
std::ostream & int_solver::display_row(std::ostream & out, lp::row_strip<rational> const & row) const {
|
|
bool first = true;
|
|
auto & rslv = lrac.m_r_solver;
|
|
for (const auto &c : row) {
|
|
if (is_fixed(c.var())) {
|
|
if (!get_value(c.var()).is_zero()) {
|
|
impq val = get_value(c.var()) * c.coeff();
|
|
if (!first && val.is_pos())
|
|
out << "+";
|
|
if (val.y.is_zero())
|
|
out << val.x << " ";
|
|
else
|
|
out << val << " ";
|
|
}
|
|
first = false;
|
|
continue;
|
|
}
|
|
if (c.coeff().is_one()) {
|
|
if (!first)
|
|
out << "+";
|
|
}
|
|
else if (c.coeff().is_minus_one())
|
|
out << "-";
|
|
else {
|
|
if (c.coeff().is_pos() && !first)
|
|
out << "+";
|
|
if (c.coeff().is_big())
|
|
out << " b*";
|
|
else
|
|
out << c.coeff();
|
|
}
|
|
out << rslv.column_name(c.var()) << " ";
|
|
first = false;
|
|
}
|
|
out << "\n";
|
|
for (const auto &c : row) {
|
|
if (is_fixed(c.var()))
|
|
continue;
|
|
rslv.print_column_info(c.var(), out);
|
|
if (is_base(c.var()))
|
|
out << "j" << c.var() << " base\n";
|
|
}
|
|
return out;
|
|
}
|
|
|
|
std::ostream& int_solver::display_row_info(std::ostream & out, unsigned row_index) const {
|
|
auto & rslv = lrac.m_r_solver;
|
|
auto const& row = rslv.m_A.m_rows[row_index];
|
|
return display_row(out, row);
|
|
}
|
|
|
|
bool int_solver::shift_var(unsigned j, unsigned range) {
|
|
if (is_fixed(j) || is_base(j))
|
|
return false;
|
|
if (settings().get_cancel_flag())
|
|
return false;
|
|
bool inf_l = false, inf_u = false;
|
|
impq l, u;
|
|
mpq m;
|
|
if (!get_freedom_interval_for_column(j, inf_l, l, inf_u, u, m))
|
|
return false;
|
|
if (settings().get_cancel_flag())
|
|
return false;
|
|
const impq & x = get_value(j);
|
|
// x, the value of j column, might be shifted on a multiple of m
|
|
|
|
if (inf_l && inf_u) {
|
|
impq new_val = m * impq(random() % (range + 1)) + x;
|
|
lra.set_value_for_nbasic_column(j, new_val);
|
|
return true;
|
|
}
|
|
if (column_is_int(j)) {
|
|
if (!inf_l)
|
|
l = impq(ceil(l));
|
|
if (!inf_u)
|
|
u = impq(floor(u));
|
|
}
|
|
if (!inf_l && !inf_u && l >= u)
|
|
return false;
|
|
|
|
|
|
if (inf_u) {
|
|
SASSERT(!inf_l);
|
|
impq new_val = x + m * impq(random() % (range + 1));
|
|
lra.set_value_for_nbasic_column(j, new_val);
|
|
return true;
|
|
}
|
|
|
|
if (inf_l) {
|
|
SASSERT(!inf_u);
|
|
impq new_val = x - m * impq(random() % (range + 1));
|
|
lra.set_value_for_nbasic_column(j, new_val);
|
|
return true;
|
|
}
|
|
|
|
SASSERT(!inf_l && !inf_u);
|
|
// The shift has to be a multiple of m: let us look for s, such that the shift is m*s.
|
|
// We have new_val = x+m*s <= u, so m*s <= u-x and, finally, s <= floor((u- x)/m) = a
|
|
// The symmetric reasoning gives us s >= ceil((l-x)/m) = b
|
|
// We randomly pick s in the segment [b, a]
|
|
mpq a = floor((u - x) / m);
|
|
mpq b = ceil((l - x) / m);
|
|
mpq r = a - b;
|
|
if (!r.is_pos())
|
|
return false;
|
|
TRACE("int_solver", tout << "a = " << a << ", b = " << b << ", r = " << r<< ", m = " << m << "\n";);
|
|
if (r < mpq(range))
|
|
range = static_cast<unsigned>(r.get_uint64());
|
|
|
|
mpq s = b + mpq(random() % (range + 1));
|
|
impq new_val = x + m * impq(s);
|
|
TRACE("int_solver", tout << "new_val = " << new_val << "\n";);
|
|
SASSERT(l <= new_val && new_val <= u);
|
|
lra.set_value_for_nbasic_column(j, new_val);
|
|
return true;
|
|
}
|
|
|
|
|
|
int int_solver::select_int_infeasible_var(bool check_bounded) {
|
|
int r_small_box = -1;
|
|
int r_small_value = -1;
|
|
int r_any_value = -1;
|
|
unsigned n_small_box = 1;
|
|
unsigned n_small_value = 1;
|
|
unsigned n_any_value = 1;
|
|
mpq range;
|
|
mpq new_range;
|
|
mpq small_value(1024);
|
|
lar_core_solver & lcs = lra.m_mpq_lar_core_solver;
|
|
unsigned prev_usage = 0;
|
|
|
|
auto check_bounded_fn = [&](unsigned j) {
|
|
if (!check_bounded)
|
|
return true;
|
|
auto const& row = lra.get_row(row_of_basic_column(j));
|
|
for (const auto & p : row) {
|
|
unsigned j = p.var();
|
|
if (!is_base(j) && (!at_bound(j) || !is_zero(get_value(j).y)))
|
|
return false;
|
|
}
|
|
return true;
|
|
};
|
|
|
|
auto add_column = [&](bool improved, int& result, unsigned& n, unsigned j) {
|
|
if (result == -1)
|
|
result = j;
|
|
else if (improved && ((random() % (++n)) == 0))
|
|
result = j;
|
|
};
|
|
|
|
for (unsigned j : lra.r_basis()) {
|
|
if (!column_is_int_inf(j))
|
|
continue;
|
|
if (!check_bounded_fn(j))
|
|
continue;
|
|
if (m_cut_vars.contains(j))
|
|
continue;
|
|
|
|
SASSERT(!is_fixed(j));
|
|
|
|
unsigned usage = lra.usage_in_terms(j);
|
|
if (is_boxed(j) && (new_range = lcs.m_r_upper_bounds()[j].x - lcs.m_r_lower_bounds()[j].x - rational(2*usage)) <= small_value) {
|
|
|
|
bool improved = new_range <= range || r_small_box == -1;
|
|
if (improved)
|
|
range = new_range;
|
|
add_column(improved, r_small_box, n_small_box, j);
|
|
continue;
|
|
}
|
|
impq const& value = get_value(j);
|
|
if (abs(value.x) < small_value ||
|
|
(has_upper(j) && small_value > upper_bound(j).x - value.x) ||
|
|
(has_lower(j) && small_value > value.x - lower_bound(j).x)) {
|
|
TRACE("gomory_cut", tout << "small j" << j << "\n");
|
|
add_column(true, r_small_value, n_small_value, j);
|
|
continue;
|
|
}
|
|
TRACE("gomory_cut", tout << "any j" << j << "\n");
|
|
add_column(usage >= prev_usage, r_any_value, n_any_value, j);
|
|
if (usage > prev_usage)
|
|
prev_usage = usage;
|
|
}
|
|
|
|
if (r_small_box != -1 && (random() % 3 != 0))
|
|
return r_small_box;
|
|
if (r_small_value != -1 && (random() % 3) != 0)
|
|
return r_small_value;
|
|
if (r_any_value != -1)
|
|
return r_any_value;
|
|
if (r_small_box != -1)
|
|
return r_small_box;
|
|
return r_small_value;
|
|
}
|
|
|
|
void int_solver::simplify(std::function<bool(unsigned)>& is_root) {
|
|
|
|
return;
|
|
|
|
// in-processing simplification can go here, such as bounds improvements.
|
|
|
|
if (!lra.is_feasible()) {
|
|
lra.find_feasible_solution();
|
|
if (!lra.is_feasible())
|
|
return;
|
|
}
|
|
|
|
|
|
lp::explanation exp;
|
|
m_ex = &exp;
|
|
m_t.clear();
|
|
m_k.reset();
|
|
|
|
if (has_inf_int())
|
|
local_gomory(5);
|
|
|
|
#if 0
|
|
stopwatch sw;
|
|
explanation exp1, exp2;
|
|
|
|
//
|
|
// tighten integer bounds
|
|
// It is a weak method as it ownly strengthens bounds if
|
|
// variables are already at one of the to-be discovered bounds.
|
|
//
|
|
sw.start();
|
|
unsigned changes = 0;
|
|
auto const& constraints = lra.constraints();
|
|
auto print_var = [this](lpvar j) {
|
|
if (lra.column_corresponds_to_term(j)) {
|
|
std::stringstream strm;
|
|
lra.print_column_info(j, strm);
|
|
return strm.str();
|
|
}
|
|
else
|
|
return std::string("j") + std::to_string(j);
|
|
};
|
|
unsigned start = random();
|
|
unsigned num_checks = 0;
|
|
for (lpvar j0 = 0; j0 < lra.column_count(); ++j0) {
|
|
lpvar j = (j0 + start) % lra.column_count();
|
|
|
|
if (num_checks > 1000)
|
|
break;
|
|
if (is_fixed(j))
|
|
continue;
|
|
if (!lra.column_is_int(j))
|
|
continue;
|
|
rational value = get_value(j).x;
|
|
bool tight_lower = false, tight_upper = false;
|
|
u_dependency* dep;
|
|
|
|
if (!value.is_int())
|
|
continue;
|
|
|
|
bool at_up = at_upper(j);
|
|
|
|
if (!at_lower(j)) {
|
|
++num_checks;
|
|
lra.push();
|
|
auto k = lp::lconstraint_kind::LE;
|
|
lra.update_column_type_and_bound(j, k, (value - 1).to_mpq(), nullptr);
|
|
lra.find_feasible_solution();
|
|
if (!lra.is_feasible()) {
|
|
tight_upper = true;
|
|
++changes;
|
|
lra.get_infeasibility_explanation(exp1);
|
|
#if 0
|
|
display_column(std::cout, j);
|
|
std::cout << print_var(j) << " >= " << value << "\n";
|
|
unsigned i = 0;
|
|
for (auto p : exp1) {
|
|
std::cout << "(" << p.ci() << ")";
|
|
constraints.display(std::cout, print_var, p.ci());
|
|
if (++i < exp1.size())
|
|
std::cout << " ";
|
|
}
|
|
#endif
|
|
}
|
|
lra.pop(1);
|
|
if (tight_upper) {
|
|
dep = nullptr;
|
|
for (auto& cc : exp1)
|
|
dep = lra.join_deps(dep, constraints[cc.ci()].dep());
|
|
lra.update_column_type_and_bound(j, lp::lconstraint_kind::GE, value.to_mpq(), dep);
|
|
}
|
|
}
|
|
|
|
if (!at_up) {
|
|
++num_checks;
|
|
lra.push();
|
|
auto k = lp::lconstraint_kind::GE;
|
|
lra.update_column_type_and_bound(j, k, (value + 1).to_mpq(), nullptr);
|
|
lra.find_feasible_solution();
|
|
if (!lra.is_feasible()) {
|
|
tight_lower = true;
|
|
++changes;
|
|
lra.get_infeasibility_explanation(exp1);
|
|
#if 0
|
|
display_column(std::cout, j);
|
|
std::cout << print_var(j) << " <= " << value << "\n";
|
|
unsigned i = 0;
|
|
for (auto p : exp1) {
|
|
std::cout << "(" << p.ci() << ")";
|
|
constraints.display(std::cout, print_var, p.ci());
|
|
if (++i < exp1.size())
|
|
std::cout << " ";
|
|
}
|
|
#endif
|
|
}
|
|
lra.pop(1);
|
|
if (tight_lower) {
|
|
dep = nullptr;
|
|
for (auto& cc : exp1)
|
|
dep = lra.join_deps(dep, constraints[cc.ci()].dep());
|
|
lra.update_column_type_and_bound(j, lp::lconstraint_kind::LE, value.to_mpq(), dep);
|
|
}
|
|
}
|
|
}
|
|
sw.stop();
|
|
std::cout << "changes " << changes << " columns " << lra.column_count() << " time: " << sw.get_seconds() << "\n";
|
|
std::cout.flush();
|
|
|
|
//
|
|
// identify equalities
|
|
//
|
|
|
|
m_equalities.reset();
|
|
map<rational, unsigned_vector, rational::hash_proc, rational::eq_proc> value2roots;
|
|
|
|
vector<std::pair<lp::mpq, unsigned>> coeffs;
|
|
coeffs.push_back({-rational::one(), 0});
|
|
coeffs.push_back({rational::one(), 0});
|
|
|
|
num_checks = 0;
|
|
|
|
// make sure values are sampled with respect to the same state of the Simplex.
|
|
vector<rational> values;
|
|
for (lpvar j = 0; j < lra.column_count(); ++j)
|
|
values.push_back(get_value(j).x);
|
|
|
|
sw.reset();
|
|
sw.start();
|
|
start = random();
|
|
for (lpvar j0 = 0; j0 < lra.column_count(); ++j0) {
|
|
lpvar j = (j0 + start) % lra.column_count();
|
|
if (is_fixed(j))
|
|
continue;
|
|
if (!lra.column_is_int(j))
|
|
continue;
|
|
if (!is_root(j))
|
|
continue;
|
|
rational value = values[j];
|
|
if (!value2roots.contains(value)) {
|
|
unsigned_vector vec;
|
|
vec.push_back(j);
|
|
value2roots.insert(value, vec);
|
|
continue;
|
|
}
|
|
auto& roots = value2roots.find(value);
|
|
bool has_eq = false;
|
|
//
|
|
// Super inefficient check. There are better ways.
|
|
// 1. call into equality finder:
|
|
// the cheap equality finder can also be used.
|
|
// 2. value sweeping:
|
|
// update partitions of values based on feasible tableaus
|
|
// instead of having just the values vector use the values
|
|
// collected when the find_feasible_solution succeeds with
|
|
// a new assignment.
|
|
// 3. a more expensive equality finder:
|
|
// use the tableau to extract equalities from tight rows.
|
|
// If x = y is implied, there is a set of rows that link x and y
|
|
// and such that the variables are at their bounds.
|
|
// 4. retain information between calls:
|
|
// If simplification is invoked at the same backtracking level (or above)
|
|
// form the previous call and it is established that x <= y (but not x == y), then no need to
|
|
// recheck the inequality x <= y.
|
|
for (auto k : roots) {
|
|
bool le = false, ge = false;
|
|
u_dependency* dep = nullptr;
|
|
lra.push();
|
|
coeffs[0].second = j;
|
|
coeffs[1].second = k;
|
|
lp::lpvar term_index = lra.add_term(coeffs, UINT_MAX);
|
|
term_index = lra.map_term_index_to_column_index(term_index);
|
|
lra.push();
|
|
lra.update_column_type_and_bound(term_index, lp::lconstraint_kind::GE, mpq(1), nullptr);
|
|
lra.find_feasible_solution();
|
|
if (!lra.is_feasible()) {
|
|
lra.get_infeasibility_explanation(exp1);
|
|
le = true;
|
|
}
|
|
lra.pop(1);
|
|
++num_checks;
|
|
if (le) {
|
|
lra.push();
|
|
lra.update_column_type_and_bound(term_index, lp::lconstraint_kind::LE, mpq(-1), nullptr);
|
|
lra.find_feasible_solution();
|
|
if (!lra.is_feasible()) {
|
|
lra.get_infeasibility_explanation(exp2);
|
|
exp1.add_expl(exp2);
|
|
ge = true;
|
|
}
|
|
lra.pop(1);
|
|
++num_checks;
|
|
}
|
|
lra.pop(1);
|
|
if (le && ge) {
|
|
has_eq = true;
|
|
m_equalities.push_back({j, k, exp1});
|
|
break;
|
|
}
|
|
// artificial throttle.
|
|
if (num_checks > 10000)
|
|
break;
|
|
}
|
|
if (!has_eq)
|
|
roots.push_back(j);
|
|
|
|
// artificial throttle.
|
|
if (num_checks > 10000)
|
|
break;
|
|
}
|
|
|
|
sw.stop();
|
|
std::cout << "equalities " << m_equalities.size() << " num checks " << num_checks << " time: " << sw.get_seconds() << "\n";
|
|
std::cout.flush();
|
|
|
|
//
|
|
// Cuts? Eg. for 0-1 variables or bounded integers?
|
|
//
|
|
|
|
#endif
|
|
}
|
|
|
|
lia_move int_solver::local_gomory(unsigned num_cuts) {
|
|
|
|
struct ex { explanation m_ex; lar_term m_term; mpq m_k; bool m_is_upper; };
|
|
vector<ex> cuts;
|
|
for (unsigned i = 0; i < num_cuts && has_inf_int() && !settings().get_cancel_flag(); ++i) {
|
|
m_ex->clear();
|
|
m_t.clear();
|
|
m_k.reset();
|
|
auto r = gomory(*this)();
|
|
if (r != lia_move::cut)
|
|
break;
|
|
cuts.push_back({ *m_ex, m_t, m_k, is_upper() });
|
|
}
|
|
m_cut_vars.reset();
|
|
|
|
auto is_small_cut = [&](ex const& cut) {
|
|
return all_of(cut.m_term, [&](auto ci) { return ci.coeff().is_small(); });
|
|
};
|
|
|
|
auto add_cut = [&](ex const& cut) {
|
|
u_dependency* dep = nullptr;
|
|
for (auto c : cut.m_ex)
|
|
dep = lra.join_deps(lra.dep_manager().mk_leaf(c.ci()), dep);
|
|
lp::lpvar term_index = lra.add_term(cut.m_term.coeffs_as_vector(), UINT_MAX);
|
|
term_index = lra.map_term_index_to_column_index(term_index);
|
|
lra.update_column_type_and_bound(term_index,
|
|
cut.m_is_upper ? lp::lconstraint_kind::LE : lp::lconstraint_kind::GE,
|
|
cut.m_k, dep);
|
|
};
|
|
|
|
auto _check_feasible = [&](void) {
|
|
auto st = lra.find_feasible_solution();
|
|
if (!lra.is_feasible()) {
|
|
lra.get_infeasibility_explanation(*m_ex);
|
|
return false;
|
|
}
|
|
return true;
|
|
};
|
|
|
|
bool has_small = false, has_large = false;
|
|
|
|
for (auto const& cut : cuts) {
|
|
if (!is_small_cut(cut)) {
|
|
has_large = true;
|
|
continue;
|
|
}
|
|
has_small = true;
|
|
add_cut(cut);
|
|
}
|
|
|
|
if (has_large) {
|
|
lra.push();
|
|
|
|
for (auto const& cut : cuts)
|
|
if (!is_small_cut(cut))
|
|
add_cut(cut);
|
|
|
|
bool feas = _check_feasible();
|
|
lra.pop(1);
|
|
|
|
if (!feas)
|
|
return lia_move::conflict;
|
|
|
|
}
|
|
|
|
if (!_check_feasible())
|
|
return lia_move::conflict;
|
|
|
|
|
|
m_ex->clear();
|
|
m_t.clear();
|
|
m_k.reset();
|
|
if (!has_inf_int())
|
|
return lia_move::sat;
|
|
|
|
if (has_small || has_large)
|
|
return lia_move::continue_with_check;
|
|
|
|
lra.move_non_basic_columns_to_bounds();
|
|
return lia_move::undef;
|
|
}
|
|
|
|
|
|
|
|
}
|