mirror of
https://github.com/Z3Prover/z3
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342 lines
12 KiB
C++
342 lines
12 KiB
C++
/*++
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Copyright (c) 2017 Microsoft Corporation
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Module Name:
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<name>
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Abstract:
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<abstract>
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Author:
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Nikolaj Bjorner (nbjorner)
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Lev Nachmanson (levnach)
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Revision History:
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--*/
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#include "util/lp/gomory.h"
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#include "util/lp/int_solver.h"
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#include "util/lp/lar_solver.h"
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#include "util/lp/lp_utils.h"
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namespace lp {
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class gomory::imp {
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lar_term & m_t; // the term to return in the cut
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mpq & m_k; // the right side of the cut
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explanation& m_ex; // the conflict explanation
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unsigned m_inf_col; // a basis column which has to be an integer but has a non integral value
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const row_strip<mpq>& m_row;
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const int_solver& m_int_solver;
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mpq m_lcm_den;
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mpq m_f;
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mpq m_one_minus_f;
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mpq m_fj;
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mpq m_one_minus_fj;
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const impq & get_value(unsigned j) const { return m_int_solver.get_value(j); }
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bool is_real(unsigned j) const { return m_int_solver.is_real(j); }
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bool at_lower(unsigned j) const { return m_int_solver.at_lower(j); }
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bool at_upper(unsigned j) const { return m_int_solver.at_upper(j); }
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const impq & lower_bound(unsigned j) const { return m_int_solver.lower_bound(j); }
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const impq & upper_bound(unsigned j) const { return m_int_solver.upper_bound(j); }
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constraint_index column_lower_bound_constraint(unsigned j) const { return m_int_solver.column_lower_bound_constraint(j); }
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constraint_index column_upper_bound_constraint(unsigned j) const { return m_int_solver.column_upper_bound_constraint(j); }
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bool column_is_fixed(unsigned j) const { return m_int_solver.m_lar_solver->column_is_fixed(j); }
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void int_case_in_gomory_cut(unsigned j) {
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lp_assert(is_int(j) && m_fj.is_pos());
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TRACE("gomory_cut_detail",
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tout << " k = " << m_k;
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tout << ", fj: " << m_fj << ", ";
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tout << (at_lower(j)?"at_lower":"at_upper")<< std::endl;
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);
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mpq new_a;
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if (at_lower(j)) {
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new_a = m_fj <= m_one_minus_f ? m_fj / m_one_minus_f : ((1 - m_fj) / m_f);
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lp_assert(new_a.is_pos());
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m_k.addmul(new_a, lower_bound(j).x);
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m_ex.push_justification(column_lower_bound_constraint(j));
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}
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else {
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lp_assert(at_upper(j));
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// the upper terms are inverted: therefore we have the minus
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new_a = - (m_fj <= m_f ? m_fj / m_f : ((1 - m_fj) / m_one_minus_f));
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lp_assert(new_a.is_neg());
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m_k.addmul(new_a, upper_bound(j).x);
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m_ex.push_justification(column_upper_bound_constraint(j));
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}
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m_t.add_monomial(new_a, j);
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m_lcm_den = lcm(m_lcm_den, denominator(new_a));
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TRACE("gomory_cut_detail", tout << "v" << j << " new_a = " << new_a << ", k = " << m_k << ", m_lcm_den = " << m_lcm_den << "\n";);
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}
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void real_case_in_gomory_cut(const mpq & a, unsigned j) {
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TRACE("gomory_cut_detail_real", tout << "real\n";);
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mpq new_a;
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if (at_lower(j)) {
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if (a.is_pos()) {
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new_a = a / m_one_minus_f;
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}
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else {
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new_a = - a / m_f;
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}
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m_k.addmul(new_a, lower_bound(j).x); // is it a faster operation than
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// k += lower_bound(j).x * new_a;
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m_ex.push_justification(column_lower_bound_constraint(j));
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}
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else {
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lp_assert(at_upper(j));
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if (a.is_pos()) {
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new_a = - a / m_f;
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}
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else {
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new_a = a / m_one_minus_f;
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}
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m_k.addmul(new_a, upper_bound(j).x); // k += upper_bound(j).x * new_a;
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m_ex.push_justification(column_upper_bound_constraint(j));
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}
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TRACE("gomory_cut_detail_real", tout << a << "*v" << j << " k: " << m_k << "\n";);
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m_t.add_monomial(new_a, j);
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}
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lia_move report_conflict_from_gomory_cut() {
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lp_assert(m_k.is_pos());
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// conflict 0 >= k where k is positive
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m_k.neg(); // returning 0 <= -k
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return lia_move::conflict;
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}
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void adjust_term_and_k_for_some_ints_case_gomory() {
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lp_assert(!m_t.is_empty());
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// k = 1 + sum of m_t at bounds
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auto pol = m_t.coeffs_as_vector();
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m_t.clear();
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if (pol.size() == 1) {
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TRACE("gomory_cut_detail", tout << "pol.size() is 1" << std::endl;);
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unsigned v = pol[0].second;
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lp_assert(is_int(v));
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const mpq& a = pol[0].first;
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m_k /= a;
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if (a.is_pos()) { // we have av >= k
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if (!m_k.is_int())
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m_k = ceil(m_k);
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// switch size
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m_t.add_monomial(- mpq(1), v);
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m_k.neg();
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} else {
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if (!m_k.is_int())
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m_k = floor(m_k);
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m_t.add_monomial(mpq(1), v);
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}
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} else {
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m_lcm_den = lcm(m_lcm_den, denominator(m_k));
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lp_assert(m_lcm_den.is_pos());
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TRACE("gomory_cut_detail", tout << "pol.size() > 1 den: " << m_lcm_den << std::endl;);
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if (!m_lcm_den.is_one()) {
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// normalize coefficients of integer parameters to be integers.
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for (auto & pi: pol) {
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pi.first *= m_lcm_den;
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SASSERT(!is_int(pi.second) || pi.first.is_int());
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}
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m_k *= m_lcm_den;
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}
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// negate everything to return -pol <= -m_k
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for (const auto & pi: pol) {
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TRACE("gomory_cut", tout << pi.first << "* " << "v" << pi.second << "\n";);
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m_t.add_monomial(-pi.first, pi.second);
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}
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m_k.neg();
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}
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TRACE("gomory_cut_detail", tout << "k = " << m_k << std::endl;);
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lp_assert(m_k.is_int());
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}
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std::string var_name(unsigned j) const {
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return std::string("x") + std::to_string(j);
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}
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std::ostream& dump_coeff_val(std::ostream & out, const mpq & a) const {
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if (a.is_int()) {
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out << a;
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}
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else if ( a >= zero_of_type<mpq>())
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out << "(/ " << numerator(a) << " " << denominator(a) << ")";
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else {
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out << "(- ( / " << numerator(-a) << " " << denominator(-a) << "))";
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}
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return out;
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}
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template <typename T>
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void dump_coeff(std::ostream & out, const T& c) const {
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out << "( * ";
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dump_coeff_val(out, c.coeff());
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out << " " << var_name(c.var()) << ")";
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}
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std::ostream& dump_row_coefficients(std::ostream & out) const {
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mpq lc(1);
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for (const auto& p : m_row) {
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lc = lcm(lc, denominator(p.coeff()));
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}
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for (const auto& p : m_row) {
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dump_coeff_val(out << " (* ", p.coeff()*lc) << " " << var_name(p.var()) << ")";
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}
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return out;
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}
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void dump_the_row(std::ostream& out) const {
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out << "; the row, excluding fixed vars\n";
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out << "(assert ( = ( +";
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dump_row_coefficients(out) << ") 0))\n";
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}
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void dump_declaration(std::ostream& out, unsigned v) const {
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out << "(declare-const " << var_name(v) << (is_int(v) ? " Int" : " Real") << ")\n";
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}
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void dump_declarations(std::ostream& out) const {
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// for a column j the var name is vj
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for (const auto & p : m_row) {
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dump_declaration(out, p.var());
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}
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for (const auto& p : m_t) {
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unsigned v = p.var();
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if (m_int_solver.m_lar_solver->is_term(v)) {
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dump_declaration(out, v);
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}
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}
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}
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void dump_lower_bound_expl(std::ostream & out, unsigned j) const {
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out << "(assert (>= " << var_name(j) << " " << lower_bound(j).x << "))\n";
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}
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void dump_upper_bound_expl(std::ostream & out, unsigned j) const {
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out << "(assert (<= " << var_name(j) << " " << upper_bound(j).x << "))\n";
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}
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void dump_explanations(std::ostream& out) const {
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for (const auto & p : m_row) {
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unsigned j = p.var();
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if (j == m_inf_col || (!is_real(j) && p.coeff().is_int())) {
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continue;
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}
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else if (at_lower(j)) {
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dump_lower_bound_expl(out, j);
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} else {
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lp_assert(at_upper(j));
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dump_upper_bound_expl(out, j);
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}
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}
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}
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std::ostream& dump_term_coefficients(std::ostream & out) const {
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for (const auto& p : m_t) {
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dump_coeff(out, p);
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}
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return out;
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}
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std::ostream& dump_term_sum(std::ostream & out) const {
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return dump_term_coefficients(out << "(+ ") << ")";
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}
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std::ostream& dump_term_le_k(std::ostream & out) const {
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return dump_term_sum(out << "(<= ") << " " << m_k << ")";
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}
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void dump_the_cut_assert(std::ostream & out) const {
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dump_term_le_k(out << "(assert (not ") << "))\n";
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}
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void dump_cut_and_constraints_as_smt_lemma(std::ostream& out) const {
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dump_declarations(out);
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dump_the_row(out);
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dump_explanations(out);
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dump_the_cut_assert(out);
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out << "(check-sat)\n";
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}
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public:
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lia_move create_cut() {
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TRACE("gomory_cut",
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tout << "applying cut at:\n"; print_linear_combination_of_column_indices_only(m_row, tout); tout << std::endl;
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for (auto & p : m_row) {
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m_int_solver.m_lar_solver->m_mpq_lar_core_solver.m_r_solver.print_column_info(p.var(), tout);
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}
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tout << "inf_col = " << m_inf_col << std::endl;
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);
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// gomory will be t <= k and the current solution has a property t > k
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m_k = 1;
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m_t.clear();
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mpq m_lcm_den(1);
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bool some_int_columns = false;
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mpq m_f = fractional_part(get_value(m_inf_col));
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TRACE("gomory_cut_detail", tout << "m_f: " << m_f << ", ";
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tout << "1 - m_f: " << 1 - m_f << ", get_value(m_inf_col).x - m_f = " << get_value(m_inf_col).x - m_f;);
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lp_assert(m_f.is_pos() && (get_value(m_inf_col).x - m_f).is_int());
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mpq one_min_m_f = 1 - m_f;
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for (const auto & p : m_row) {
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unsigned j = p.var();
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if (j == m_inf_col) {
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lp_assert(p.coeff() == one_of_type<mpq>());
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TRACE("gomory_cut_detail", tout << "seeing basic var";);
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continue;
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}
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// use -p.coeff() to make the format compatible with the format used in: Integrating Simplex with DPLL(T)
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if (is_real(j)) {
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real_case_in_gomory_cut(- p.coeff(), j);
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} else {
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if (p.coeff().is_int()) {
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// m_fj will be zero and no monomial will be added
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continue;
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}
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some_int_columns = true;
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m_fj = fractional_part(-p.coeff());
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m_one_minus_fj = 1 - m_fj;
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int_case_in_gomory_cut(j);
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}
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}
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if (m_t.is_empty())
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return report_conflict_from_gomory_cut();
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if (some_int_columns)
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adjust_term_and_k_for_some_ints_case_gomory();
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lp_assert(m_int_solver.current_solution_is_inf_on_cut());
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TRACE("gomory_cut_detail", dump_cut_and_constraints_as_smt_lemma(tout););
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m_int_solver.m_lar_solver->subs_term_columns(m_t);
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TRACE("gomory_cut", print_linear_combination_of_column_indices_only(m_t, tout << "gomory cut:"); tout << " <= " << m_k << std::endl;);
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return lia_move::cut;
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}
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imp(lar_term & t, mpq & k, explanation& ex, unsigned basic_inf_int_j, const row_strip<mpq>& row, const int_solver& int_slv ) :
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m_t(t),
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m_k(k),
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m_ex(ex),
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m_inf_col(basic_inf_int_j),
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m_row(row),
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m_int_solver(int_slv),
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m_lcm_den(1),
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m_f(fractional_part(get_value(basic_inf_int_j).x)),
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m_one_minus_f(1 - m_f) {}
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};
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lia_move gomory::create_cut() {
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return m_imp->create_cut();
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}
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gomory::gomory(lar_term & t, mpq & k, explanation& ex, unsigned basic_inf_int_j, const row_strip<mpq>& row, const int_solver& s) {
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m_imp = alloc(imp, t, k, ex, basic_inf_int_j, row, s);
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}
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gomory::~gomory() { dealloc(m_imp); }
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}
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