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Gomory cut / branch and bound improvements
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Improve fairness of cut generation by switching to find_infeasible_int_var with cascading priorities, allow stronger cuts by inlining terms.
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@NikolajBjorner
NikolajBjorner committed Nov 7, 2023
1 parent 9f0b3cd commit 3d99ed9
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Showing 5 changed files with 226 additions and 96 deletions.
123 changes: 94 additions & 29 deletions src/math/lp/gomory.cpp
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Original file line number Diff line number Diff line change
Expand Up @@ -31,7 +31,7 @@ class create_cut {
explanation* m_ex; // the conflict explanation
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;
const int_solver& lia;
int_solver& lia;
mpq m_lcm_den;
mpq m_f;
mpq m_one_minus_f;
Expand Down Expand Up @@ -133,26 +133,50 @@ class create_cut {
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
auto pol = m_t.coeffs_as_vector();
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;);
unsigned v = pol[0].second;
auto const& [a, v] = pol[0];
lp_assert(is_int(v));
const mpq& a = pol[0].first;
if (a.is_pos()) { // we have av >= k
m_k /= a;
if (!m_k.is_int())
m_k = ceil(m_k);
divd(m_k, a);
m_t.add_monomial(mpq(1), v);
}
else {
m_k /= -a;
if (!m_k.is_int())
m_k = ceil(m_k);
// 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);
}
}
Expand All @@ -162,17 +186,48 @@ class create_cut {
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 & pi: pol) {
pi.first *= m_lcm_den;
SASSERT(!is_int(pi.second) || pi.first.is_int());
for (auto & [c,v]: pol) {
c *= m_lcm_den;
SASSERT(!is_int(v) || c.is_int());
}
m_k *= m_lcm_den;
}
for (const auto & pi: pol)
m_t.add_monomial(pi.first, pi.second);

// 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 {
Expand All @@ -191,10 +246,9 @@ class create_cut {

template <typename T>
void dump_coeff(std::ostream & out, const T& c) const {
out << "( * ";
out << "(* ";
dump_coeff_val(out, c.coeff());
auto t = lia.lra.column2tv(c.column());
out << " " << var_name(t.id()) << ")";
out << " " << var_name(c.column().index()) << ")";
}

std::ostream& dump_row_coefficients(std::ostream & out) const {
Expand All @@ -208,7 +262,7 @@ class create_cut {

void dump_the_row(std::ostream& out) const {
out << "; the row, excluding fixed vars\n";
out << "(assert ( = ( +";
out << "(assert (= (+";
dump_row_coefficients(out) << ") 0))\n";
}

Expand Down Expand Up @@ -259,12 +313,12 @@ class create_cut {
return dump_term_coefficients(out << "(+ ") << ")";
}

std::ostream& dump_term_le_k(std::ostream & out) const {
return dump_term_sum(out << "(<= ") << " " << m_k << ")";
std::ostream& dump_term_ge_k(std::ostream & out) const {
return dump_term_sum(out << "(>= ") << " " << m_k << ")";
}

void dump_the_cut_assert(std::ostream & out) const {
dump_term_le_k(out << "(assert (not ") << "))\n";
dump_term_ge_k(out << "(assert (not ") << "))\n";
}

void dump_cut_and_constraints_as_smt_lemma(std::ostream& out) const {
Expand Down Expand Up @@ -310,7 +364,6 @@ class create_cut {
unsigned j = p.var();
if (j == m_inf_col) {
lp_assert(p.coeff() == one_of_type<mpq>());
TRACE("gomory_cut_detail", tout << "seeing basic var\n";);
continue;
}

Expand Down Expand Up @@ -341,13 +394,21 @@ class create_cut {
return report_conflict_from_gomory_cut();
if (some_int_columns)
adjust_term_and_k_for_some_ints_case_gomory();
TRACE("gomory_cut_detail", dump_cut_and_constraints_as_smt_lemma(tout););
if (!lia.current_solution_is_inf_on_cut()) {
m_ex->clear();
m_t.clear();
m_k = 1;
return lia_move::undef;
}
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", 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);
lia.lra.display(tout));
lia.settings().stats().m_gomory_cuts++;
return lia_move::cut;
}

create_cut(lar_term & t, mpq & k, explanation* ex, unsigned basic_inf_int_j, const row_strip<mpq>& row, const int_solver& lia) :
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),
m_ex(ex),
Expand Down Expand Up @@ -385,22 +446,26 @@ int gomory::find_basic_var() {
int result = -1;
unsigned min_row_size = UINT_MAX;

#if 0
result = lia.select_int_infeasible_var();
#if 1
result = lia.select_int_infeasible_var(true);

if (result == -1)
return result;

TRACE("gomory_cut", tout << "row: " << result << "\n");
const row_strip<mpq>& row = lra.get_row(lia.row_of_basic_column(result));
if (is_gomory_cut_target(row))
return result;
result = -1;

UNREACHABLE();
#endif

for (unsigned j : lra.r_basis()) {
if (!lia.column_is_int_inf(j))
continue;
const row_strip<mpq>& row = lra.get_row(lia.row_of_basic_column(j));
TRACE("gomory_cut", tout << "try j" << j << "\n");
if (!is_gomory_cut_target(row))
continue;
IF_VERBOSE(20, lia.display_row_info(verbose_stream(), lia.row_of_basic_column(j)));
Expand All @@ -417,7 +482,6 @@ int gomory::find_basic_var() {
}

lia_move gomory::operator()() {
lra.move_non_basic_columns_to_bounds();
int j = find_basic_var();
if (j == -1)
return lia_move::undef;
Expand All @@ -426,6 +490,7 @@ lia_move gomory::operator()() {
SASSERT(lra.row_is_correct(r));
SASSERT(is_gomory_cut_target(row));
lia.m_upper = false;
lia.m_cut_vars.push_back(j);
return cut(lia.m_t, lia.m_k, lia.m_ex, j, row);
}

Expand Down
4 changes: 2 additions & 2 deletions src/math/lp/int_branch.cpp
View file
Original file line number Diff line number Diff line change
Expand Up @@ -52,8 +52,8 @@ lia_move int_branch::create_branch_on_column(int j) {

int int_branch::find_inf_int_base_column() {

#if 0
return lia.select_int_infeasible_var();
#if 1
return lia.select_int_infeasible_var(false);
#endif

int result = -1;
Expand Down

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