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https://github.com/Z3Prover/z3
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fix bug in bound simplification in Gomory for mixed integer linear cuts, enable fixed variable redution after bugfix, add notes that rewriting bounds does not work
Signed-off-by: Nikolaj Bjorner <nbjorner@microsoft.com>
This commit is contained in:
Nikolaj Bjorner
parent
aa9c7912dc
commit
3de5af3cb0
5 changed files with 121 additions and 261 deletions
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@ -32,7 +32,6 @@ class create_cut {
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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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int_solver& lia;
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mpq m_lcm_den = { mpq(1) };
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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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@ -131,120 +130,7 @@ class create_cut {
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// conflict 0 >= k where k is positive
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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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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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auto const& [a, v] = pol[0];
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lp_assert(is_int(v));
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if (a.is_pos()) { // we have av >= 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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// 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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else {
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m_lcm_den = denominator(m_k);
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for (auto const& [c, v] : pol)
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m_lcm_den = lcm(m_lcm_den, denominator(c));
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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 & [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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#if 0
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unsigned j = 0, i = 0;
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for (auto & [c, v] : pol) {
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if (lia.is_fixed(v)) {
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push_explanation(column_lower_bound_constraint(v));
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push_explanation(column_upper_bound_constraint(v));
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m_k -= c;
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IF_VERBOSE(0, verbose_stream() << "got fixed " << v << "\n");
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}
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else
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pol[j++] = pol[i];
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++i;
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}
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pol.shrink(j);
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#endif
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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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return std::string("x") + std::to_string(j);
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@ -359,12 +245,12 @@ public:
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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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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 << "\n";);
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lp_assert(m_f.is_pos() && (get_value(m_inf_col).x - m_f).is_int());
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bool some_int_columns = false;
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#if SMALL_CUTS
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m_abs_max = 0;
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for (const auto & p : m_row) {
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@ -408,13 +294,7 @@ public:
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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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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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simplify_inequality();
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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_detail", dump_cut_and_constraints_as_smt_lemma(tout);
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@ -423,6 +303,91 @@ public:
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return lia_move::cut;
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}
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// TODO: use this also for HNF cuts?
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mpq m_lcm_den = { mpq(1) };
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void simplify_inequality() {
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auto 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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SASSERT(!lia.m_upper);
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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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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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auto const& [a, v] = pol[0];
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lp_assert(is_int(v));
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if (a.is_pos()) { // we have av >= 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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// 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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else {
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m_lcm_den = denominator(m_k);
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for (auto const& [c, v] : pol)
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m_lcm_den = lcm(m_lcm_den, denominator(c));
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lp_assert(m_lcm_den.is_pos());
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bool int_row = true;
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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 & [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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int_row &= is_int(v);
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}
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m_k *= m_lcm_den;
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}
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unsigned j = 0, i = 0;
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for (auto & [c, v] : pol) {
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if (lia.is_fixed(v)) {
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push_explanation(column_lower_bound_constraint(v));
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push_explanation(column_upper_bound_constraint(v));
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m_k -= c * lower_bound(v).x;
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}
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else
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pol[j++] = pol[i];
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++i;
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}
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pol.shrink(j);
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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 (!int_row)
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g = gcd(g, m_k);
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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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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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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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