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fix bug in bound simplification in Gomory for mixed integer linear cu…
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…ts, enable fixed variable redution after bugfix, add notes that rewriting bounds does not work

Signed-off-by: Nikolaj Bjorner <[email protected]>
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@NikolajBjorner
NikolajBjorner committed Nov 10, 2023
1 parent aa9c791 commit 3de5af3
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Showing 5 changed files with 121 additions and 261 deletions.
209 changes: 87 additions & 122 deletions src/math/lp/gomory.cpp
View file
Original file line number Diff line number Diff line change
Expand Up @@ -32,7 +32,6 @@ class create_cut {
unsigned m_inf_col; // a basis column which has to be an integer but has a non integral value
const row_strip<mpq>& m_row;
int_solver& lia;
mpq m_lcm_den = { mpq(1) };
mpq m_f;
mpq m_one_minus_f;
mpq m_fj;
Expand Down Expand Up @@ -131,120 +130,7 @@ class create_cut {
// conflict 0 >= k where k is positive
return lia_move::conflict;
}

void divd(mpq& r, mpq const& d) {
r /= d;
if (!r.is_int())
r = ceil(r);
}

bool can_divide_by(vector<std::pair<mpq, lpvar>> const& p, mpq const& d) {
mpq lhs(0), rhs(m_k);
mpq max_c(abs(m_k));
for (auto const& [c, v] : p) {
auto c1 = c;
max_c = std::max(max_c, abs(c1));
divd(c1, d);
if (c1 == 0)
return false;
VERIFY(lia.get_value(v).y == 0);
lhs += c1 * lia.get_value(v).x;
}
if (max_c == 1)
return false;
divd(rhs, d);
return lhs < rhs;
}

void adjust_term_and_k_for_some_ints_case_gomory() {
lp_assert(!m_t.is_empty());
// k = 1 + sum of m_t at bounds
lar_term t = lia.lra.unfold_nested_subterms(m_t);
auto pol = t.coeffs_as_vector();
m_t.clear();
if (pol.size() == 1) {
TRACE("gomory_cut_detail", tout << "pol.size() is 1" << std::endl;);
auto const& [a, v] = pol[0];
lp_assert(is_int(v));
if (a.is_pos()) { // we have av >= k
divd(m_k, a);
m_t.add_monomial(mpq(1), v);
}
else {
// av >= k
// a/-a*v >= k / - a
// -v >= k / - a
// -v >= ceil(k / -a)
divd(m_k, -a);
m_t.add_monomial(-mpq(1), v);
}
}
else {
m_lcm_den = denominator(m_k);
for (auto const& [c, v] : pol)
m_lcm_den = lcm(m_lcm_den, denominator(c));
lp_assert(m_lcm_den.is_pos());
TRACE("gomory_cut_detail", tout << "pol.size() > 1 den: " << m_lcm_den << std::endl;);
if (!m_lcm_den.is_one()) {
// normalize coefficients of integer parameters to be integers.
for (auto & [c,v]: pol) {
c *= m_lcm_den;
SASSERT(!is_int(v) || c.is_int());
}
m_k *= m_lcm_den;
}
#if 0
unsigned j = 0, i = 0;
for (auto & [c, v] : pol) {
if (lia.is_fixed(v)) {
push_explanation(column_lower_bound_constraint(v));
push_explanation(column_upper_bound_constraint(v));
m_k -= c;
IF_VERBOSE(0, verbose_stream() << "got fixed " << v << "\n");
}
else
pol[j++] = pol[i];
++i;
}
pol.shrink(j);
#endif

// gcd reduction is loss-less:
mpq g(1);
for (const auto & [c, v] : pol)
g = gcd(g, c);

if (g != 1) {
for (auto & [c, v] : pol)
c /= g;
divd(m_k, g);
}

#if 0
// TODO: create self-contained rounding mode to weaken cuts
// whose cofficients are considered too large
// (larger than bounds from the input)
mpq min_c = abs(m_k);
for (const auto & [c, v] : pol)
min_c = std::min(min_c, abs(c));

if (min_c > 1 && can_divide_by(pol, min_c)) {
for (auto& [c, v] : pol)
divd(c, min_c);
divd(m_k, min_c);
}
#endif

for (const auto & [c, v]: pol)
m_t.add_monomial(c, v);
VERIFY(m_t.size() > 0);
}

TRACE("gomory_cut_detail", tout << "k = " << m_k << std::endl;);
lp_assert(m_k.is_int());


}

std::string var_name(unsigned j) const {
return std::string("x") + std::to_string(j);
Expand Down Expand Up @@ -359,12 +245,12 @@ class create_cut {
// gomory will be t >= k and the current solution has a property t < k
m_k = 1;
m_t.clear();
bool some_int_columns = false;
mpq m_f = fractional_part(get_value(m_inf_col));
TRACE("gomory_cut_detail", tout << "m_f: " << m_f << ", ";
tout << "1 - m_f: " << 1 - m_f << ", get_value(m_inf_col).x - m_f = " << get_value(m_inf_col).x - m_f << "\n";);
lp_assert(m_f.is_pos() && (get_value(m_inf_col).x - m_f).is_int());

bool some_int_columns = false;
#if SMALL_CUTS
m_abs_max = 0;
for (const auto & p : m_row) {
Expand Down Expand Up @@ -408,13 +294,7 @@ class create_cut {
if (m_t.is_empty())
return report_conflict_from_gomory_cut();
if (some_int_columns)
adjust_term_and_k_for_some_ints_case_gomory();
if (!lia.current_solution_is_inf_on_cut()) {
m_ex->clear();
m_t.clear();
m_k = 1;
return lia_move::undef;
}
simplify_inequality();
lp_assert(lia.current_solution_is_inf_on_cut()); // checks that indices are columns
TRACE("gomory_cut", print_linear_combination_of_column_indices_only(m_t.coeffs_as_vector(), tout << "gomory cut: "); tout << " >= " << m_k << std::endl;);
TRACE("gomory_cut_detail", dump_cut_and_constraints_as_smt_lemma(tout);
Expand All @@ -423,6 +303,91 @@ class create_cut {
return lia_move::cut;
}

// TODO: use this also for HNF cuts?
mpq m_lcm_den = { mpq(1) };

void simplify_inequality() {

auto divd = [](mpq& r, mpq const& d) {
r /= d;
if (!r.is_int())
r = ceil(r);
};
SASSERT(!lia.m_upper);
lp_assert(!m_t.is_empty());
// k = 1 + sum of m_t at bounds
lar_term t = lia.lra.unfold_nested_subterms(m_t);
auto pol = t.coeffs_as_vector();
m_t.clear();
if (pol.size() == 1) {
TRACE("gomory_cut_detail", tout << "pol.size() is 1" << std::endl;);
auto const& [a, v] = pol[0];
lp_assert(is_int(v));
if (a.is_pos()) { // we have av >= k
divd(m_k, a);
m_t.add_monomial(mpq(1), v);
}
else {
// av >= k
// a/-a*v >= k / - a
// -v >= k / - a
// -v >= ceil(k / -a)
divd(m_k, -a);
m_t.add_monomial(-mpq(1), v);
}
}
else {
m_lcm_den = denominator(m_k);
for (auto const& [c, v] : pol)
m_lcm_den = lcm(m_lcm_den, denominator(c));
lp_assert(m_lcm_den.is_pos());
bool int_row = true;
TRACE("gomory_cut_detail", tout << "pol.size() > 1 den: " << m_lcm_den << std::endl;);
if (!m_lcm_den.is_one()) {
// normalize coefficients of integer parameters to be integers.
for (auto & [c,v]: pol) {
c *= m_lcm_den;
SASSERT(!is_int(v) || c.is_int());
int_row &= is_int(v);
}
m_k *= m_lcm_den;
}
unsigned j = 0, i = 0;
for (auto & [c, v] : pol) {
if (lia.is_fixed(v)) {
push_explanation(column_lower_bound_constraint(v));
push_explanation(column_upper_bound_constraint(v));
m_k -= c * lower_bound(v).x;
}
else
pol[j++] = pol[i];
++i;
}
pol.shrink(j);

// gcd reduction is loss-less:
mpq g(1);
for (const auto & [c, v] : pol)
g = gcd(g, c);
if (!int_row)
g = gcd(g, m_k);

if (g != 1) {
for (auto & [c, v] : pol)
c /= g;
divd(m_k, g);
}

for (const auto & [c, v]: pol)
m_t.add_monomial(c, v);
VERIFY(m_t.size() > 0);
}

TRACE("gomory_cut_detail", tout << "k = " << m_k << std::endl;);
lp_assert(m_k.is_int());
}


create_cut(lar_term & t, mpq & k, explanation* ex, unsigned basic_inf_int_j, const row_strip<mpq>& row, int_solver& lia) :
m_t(t),
m_k(k),
Expand Down
40 changes: 16 additions & 24 deletions src/math/lp/hnf_cutter.cpp
View file
Original file line number Diff line number Diff line change
Expand Up @@ -83,31 +83,29 @@ namespace lp {
// consider return from here if b[i] is not an integer and return i
}
}

vector<mpq> hnf_cutter::create_b(const svector<unsigned> & basis_rows) {
if (basis_rows.size() == m_right_sides.size())
return m_right_sides;
vector<mpq> b;
for (unsigned i : basis_rows) {
b.push_back(m_right_sides[i]);
}
for (unsigned i : basis_rows)
b.push_back(m_right_sides[i]);
return b;
}

int hnf_cutter::find_cut_row_index(const vector<mpq> & b) {
int ret = -1;
int n = 0;
for (int i = 0; i < static_cast<int>(b.size()); i++) {
if (is_integer(b[i])) continue;
if (n == 0 ) {
if (is_integer(b[i]))
continue;
if (n == 0) {
lp_assert(ret == -1);
n = 1;
ret = i;
} else {
if (m_settings.random_next() % (++n) == 0) {
ret = i;
}
}
else if (m_settings.random_next() % (++n) == 0)
ret = i;
}
return ret;
}
Expand Down Expand Up @@ -240,10 +238,7 @@ branch y_i >= ceil(y0_i) is impossible.
}

bool hnf_cutter::hnf_has_var_with_non_integral_value() const {
for (unsigned j : vars())
if (!lia.get_value(j).is_int())
return true;
return false;
return any_of(vars(), [&](unsigned j) { return !lia.get_value(j).is_int(); });
}

bool hnf_cutter::init_terms_for_hnf_cut() {
Expand All @@ -252,17 +247,15 @@ branch y_i >= ceil(y0_i) is impossible.
try_add_term_to_A_for_hnf(tv::term(i));
return hnf_has_var_with_non_integral_value();
}

lia_move hnf_cutter::make_hnf_cut() {
if (!init_terms_for_hnf_cut()) {
if (!init_terms_for_hnf_cut())
return lia_move::undef;
}
lia.settings().stats().m_hnf_cutter_calls++;
TRACE("hnf_cut", tout << "settings().stats().m_hnf_cutter_calls = " << lia.settings().stats().m_hnf_cutter_calls << "\n";
for (u_dependency* d : constraints_for_explanation()) {
for (auto ci : lra.flatten(d))
lra.constraints().display(tout, ci);
}
for (u_dependency* d : constraints_for_explanation())
for (auto ci : lra.flatten(d))
lra.constraints().display(tout, ci);
tout << lra.constraints();
);
#ifdef Z3DEBUG
Expand All @@ -273,14 +266,14 @@ branch y_i >= ceil(y0_i) is impossible.
, x0
#endif
);

if (r == lia_move::cut) {
TRACE("hnf_cut",
lra.print_term(lia.m_t, tout << "cut:");
tout << " <= " << lia.m_k << std::endl;
for (auto* dep : constraints_for_explanation())
for (auto ci : lra.flatten(dep))
lra.constraints().display(tout, ci);
lra.constraints().display(tout, ci);
);
lp_assert(lia.current_solution_is_inf_on_cut());
lia.settings().stats().m_hnf_cuts++;
Expand All @@ -291,5 +284,4 @@ branch y_i >= ceil(y0_i) is impossible.
}
return r;
}

}
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