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https://github.com/Z3Prover/z3
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Gomory cut / branch and bound improvements
Improve fairness of cut generation by switching to find_infeasible_int_var with cascading priorities, allow stronger cuts by inlining terms.
This commit is contained in:
Nikolaj Bjorner
parent
9f0b3cdc25
commit
3d99ed9dd4
5 changed files with 230 additions and 100 deletions
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@ -31,7 +31,7 @@ class create_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& lia;
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int_solver& lia;
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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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@ -133,26 +133,50 @@ class create_cut {
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return lia_move::conflict;
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}
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void divd(mpq& r, mpq const& d) {
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r /= d;
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if (!r.is_int())
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r = ceil(r);
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}
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bool can_divide_by(vector<std::pair<mpq, lpvar>> const& p, mpq const& d) {
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mpq lhs(0), rhs(m_k);
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mpq max_c(abs(m_k));
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for (auto const& [c, v] : p) {
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auto c1 = c;
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max_c = std::max(max_c, abs(c1));
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divd(c1, d);
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if (c1 == 0)
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return false;
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VERIFY(lia.get_value(v).y == 0);
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lhs += c1 * lia.get_value(v).x;
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}
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if (max_c == 1)
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return false;
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divd(rhs, d);
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return lhs < rhs;
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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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lar_term t = lia.lra.unfold_nested_subterms(m_t);
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auto pol = 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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auto const& [a, v] = pol[0];
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lp_assert(is_int(v));
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const mpq& a = pol[0].first;
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if (a.is_pos()) { // we have av >= k
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m_k /= a;
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if (!m_k.is_int())
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m_k = ceil(m_k);
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divd(m_k, a);
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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_k /= -a;
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if (!m_k.is_int())
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m_k = ceil(m_k);
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// av >= k
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// a/-a*v >= k / - a
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// -v >= k / - a
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// -v >= ceil(k / -a)
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divd(m_k, -a);
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m_t.add_monomial(-mpq(1), v);
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}
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}
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@ -162,17 +186,48 @@ class create_cut {
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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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for (auto & [c,v]: pol) {
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c *= m_lcm_den;
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SASSERT(!is_int(v) || c.is_int());
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}
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m_k *= m_lcm_den;
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}
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for (const auto & pi: pol)
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m_t.add_monomial(pi.first, pi.second);
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// gcd reduction is loss-less:
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mpq g(1);
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for (const auto & [c, v] : pol)
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g = gcd(g, c);
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if (g != 1) {
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for (auto & [c, v] : pol)
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c /= g;
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divd(m_k, g);
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}
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#if 0
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// TODO: create self-contained rounding mode to weaken cuts
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// whose cofficients are considered too large
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// (larger than bounds from the input)
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mpq min_c = abs(m_k);
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for (const auto & [c, v] : pol)
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min_c = std::min(min_c, abs(c));
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if (min_c > 1 && can_divide_by(pol, min_c)) {
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for (auto& [c, v] : pol)
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divd(c, min_c);
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divd(m_k, min_c);
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}
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#endif
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for (const auto & [c, v]: pol)
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m_t.add_monomial(c, v);
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VERIFY(m_t.size() > 0);
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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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@ -191,10 +246,9 @@ class create_cut {
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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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out << "(* ";
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dump_coeff_val(out, c.coeff());
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auto t = lia.lra.column2tv(c.column());
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out << " " << var_name(t.id()) << ")";
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out << " " << var_name(c.column().index()) << ")";
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}
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std::ostream& dump_row_coefficients(std::ostream & out) const {
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@ -208,7 +262,7 @@ class create_cut {
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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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out << "(assert (= (+";
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dump_row_coefficients(out) << ") 0))\n";
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}
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@ -259,12 +313,12 @@ class create_cut {
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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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std::ostream& dump_term_ge_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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dump_term_ge_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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@ -310,7 +364,6 @@ public:
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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\n";);
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continue;
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}
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@ -341,13 +394,21 @@ public:
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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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TRACE("gomory_cut_detail", dump_cut_and_constraints_as_smt_lemma(tout););
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if (!lia.current_solution_is_inf_on_cut()) {
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m_ex->clear();
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m_t.clear();
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m_k = 1;
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return lia_move::undef;
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}
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lp_assert(lia.current_solution_is_inf_on_cut()); // checks that indices are columns
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TRACE("gomory_cut", print_linear_combination_of_column_indices_only(m_t.coeffs_as_vector(), tout << "gomory cut:"); tout << " <= " << m_k << std::endl;);
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TRACE("gomory_cut", print_linear_combination_of_column_indices_only(m_t.coeffs_as_vector(), tout << "gomory cut: "); tout << " >= " << m_k << std::endl;);
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TRACE("gomory_cut_detail", dump_cut_and_constraints_as_smt_lemma(tout);
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lia.lra.display(tout));
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lia.settings().stats().m_gomory_cuts++;
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return lia_move::cut;
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}
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create_cut(lar_term & t, mpq & k, explanation* ex, unsigned basic_inf_int_j, const row_strip<mpq>& row, const int_solver& lia) :
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create_cut(lar_term & t, mpq & k, explanation* ex, unsigned basic_inf_int_j, const row_strip<mpq>& row, int_solver& lia) :
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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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@ -385,22 +446,26 @@ int gomory::find_basic_var() {
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int result = -1;
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unsigned min_row_size = UINT_MAX;
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#if 0
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result = lia.select_int_infeasible_var();
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#if 1
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result = lia.select_int_infeasible_var(true);
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if (result == -1)
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return result;
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TRACE("gomory_cut", tout << "row: " << result << "\n");
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const row_strip<mpq>& row = lra.get_row(lia.row_of_basic_column(result));
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if (is_gomory_cut_target(row))
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return result;
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result = -1;
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UNREACHABLE();
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#endif
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for (unsigned j : lra.r_basis()) {
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if (!lia.column_is_int_inf(j))
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continue;
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const row_strip<mpq>& row = lra.get_row(lia.row_of_basic_column(j));
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TRACE("gomory_cut", tout << "try j" << j << "\n");
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if (!is_gomory_cut_target(row))
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continue;
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IF_VERBOSE(20, lia.display_row_info(verbose_stream(), lia.row_of_basic_column(j)));
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@ -417,7 +482,6 @@ int gomory::find_basic_var() {
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}
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lia_move gomory::operator()() {
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lra.move_non_basic_columns_to_bounds();
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int j = find_basic_var();
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if (j == -1)
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return lia_move::undef;
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@ -426,6 +490,7 @@ lia_move gomory::operator()() {
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SASSERT(lra.row_is_correct(r));
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SASSERT(is_gomory_cut_target(row));
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lia.m_upper = false;
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lia.m_cut_vars.push_back(j);
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return cut(lia.m_t, lia.m_k, lia.m_ex, j, row);
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}
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