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a simple version of choosing a column for gomory cut

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This commit is contained in:
Lev Nachmanson 2023-12-04 15:06:50 -10:00
parent f98b42ae42
commit fc23a498c4
6 changed files with 90 additions and 96 deletions
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64
src/math/lp/gomory.cpp
View file

@ -409,73 +409,15 @@ lia_move gomory::cut(lar_term & t, mpq & k, explanation* ex, unsigned basic_inf_
create_cut cc(t, k, ex, basic_inf_int_j, row, lia);
return cc.cut();
}
bool gomory::is_gomory_cut_target(const row_strip<mpq>& row) {
// All non base variables must be at their bounds and assigned to rationals (that is, infinitesimals are not allowed).
unsigned j;
for (const auto & p : row) {
j = p.var();
if (!lia.is_base(j) && (!lia.at_bound(j) || !is_zero(lia.get_value(j).y))) {
TRACE("gomory_cut", tout << "row is not gomory cut target:\n";
lia.display_column(tout, j);
tout << "infinitesimal: " << !is_zero(lia.get_value(j).y) << "\n";);
return false;
}
}
return true;
}
int gomory::find_basic_var() {
unsigned n = 0;
int result = -1;
unsigned min_row_size = UINT_MAX;
#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)));
// Prefer smaller row size
if (min_row_size == UINT_MAX ||
2*row.size() < min_row_size ||
(4*row.size() < 5*min_row_size && lia.random() % (++n) == 0)) {
result = j;
n = 1;
min_row_size = std::min(min_row_size, row.size());
}
}
return result;
}
lia_move gomory::operator()() {
int j = find_basic_var();
if (j == -1)
return lia_move::undef;
lia_move gomory::get_cut(lpvar j) {
unsigned r = lia.row_of_basic_column(j);
const row_strip<mpq>& row = lra.get_row(r);
SASSERT(lra.row_is_correct(r));
SASSERT(is_gomory_cut_target(row));
SASSERT(lia.is_gomory_cut_target(j));
lia.m_upper = false;
lia.m_cut_vars.push_back(j);
return cut(lia.m_t, lia.m_k, lia.m_ex, j, row);
return cut(lia.m_t, lia.m_k, lia.m_ex, j, row);
}

4
src/math/lp/gomory.h
View file

@ -27,11 +27,9 @@ namespace lp {
class gomory {
class int_solver& lia;
class lar_solver& lra;
int find_basic_var();
bool is_gomory_cut_target(const row_strip<mpq>& row);
lia_move cut(lar_term & t, mpq & k, explanation* ex, unsigned basic_inf_int_j, const row_strip<mpq>& row);
public:
gomory(int_solver& lia);
lia_move operator()();
lia_move get_cut(lpvar j);
};
}

2
src/math/lp/int_branch.cpp
View file

@ -53,7 +53,7 @@ lia_move int_branch::create_branch_on_column(int j) {
int int_branch::find_inf_int_base_column() {
#if 1
return lia.select_int_infeasible_var(false);
return lia.select_int_infeasible_var();
#endif
int result = -1;

104
src/math/lp/int_solver.cpp
View file

@ -198,15 +198,9 @@ namespace lp {
if (r == lia_move::undef) lra.move_non_basic_columns_to_bounds();
if (r == lia_move::undef && should_hnf_cut()) r = hnf_cut();
std::function<lia_move(void)> gomory_fn = [&]() { return gomory(*this)(); };
m_cut_vars.reset();
#if 0
if (r == lia_move::undef && should_gomory_cut()) r = gomory(*this)();
#else
std::function<lia_move(lpvar)> gomory_fn = [&](lpvar j) { return gomory(*this).get_cut(j); };
if (r == lia_move::undef && should_gomory_cut()) r = local_cut(2, gomory_fn);
#endif
m_cut_vars.reset();
if (r == lia_move::undef) r = int_branch(*this)();
if (settings().get_cancel_flag()) r = lia_move::undef;
return r;
@ -635,7 +629,7 @@ namespace lp {
}
int int_solver::select_int_infeasible_var(bool check_bounded) {
int int_solver::select_int_infeasible_var() {
int r_small_box = -1;
int r_small_value = -1;
int r_any_value = -1;
@ -648,18 +642,6 @@ namespace lp {
lar_core_solver & lcs = lra.m_mpq_lar_core_solver;
unsigned prev_usage = 0;
auto check_bounded_fn = [&](unsigned j) {
if (!check_bounded)
return true;
auto const& row = lra.get_row(row_of_basic_column(j));
for (const auto & p : row) {
unsigned j = p.var();
if (!is_base(j) && (!at_bound(j) || !is_zero(get_value(j).y)))
return false;
}
return true;
};
auto add_column = [&](bool improved, int& result, unsigned& n, unsigned j) {
if (result == -1)
result = j;
@ -670,9 +652,7 @@ namespace lp {
for (unsigned j : lra.r_basis()) {
if (!column_is_int_inf(j))
continue;
if (!check_bounded_fn(j))
continue;
if (m_cut_vars.contains(j))
if (m_cut_vars.contains(j))
continue;
SASSERT(!is_fixed(j));
@ -849,19 +829,71 @@ namespace lp {
#endif
}
// return the minimal distance from the column value to an integer
mpq get_gomory_score(const int_solver& lia, lpvar j) {
const mpq& val = lia.get_value(j).x;
auto l = val - floor(val);
if (l <= mpq(1, 2))
return l;
return mpq(1) - l;
}
unsigned_vector int_solver::gomory_select_int_infeasible_vars(unsigned num_cuts) {
SASSERT(m_cut_vars.size() == 0&& num_cuts >= 0);
std::list<lpvar> sorted_vars;
std::unordered_map<lpvar, mpq> score;
for (lpvar j : lra.r_basis()) {
if (!column_is_int_inf(j) || !is_gomory_cut_target(j))
continue;
SASSERT(!is_fixed(j));
sorted_vars.push_back(j);
score[j] = get_gomory_score(*this, j);
}
// prefer the columns with the values close to integers
sorted_vars.sort([&](lpvar j, lpvar k) {
auto diff = score[j] - score[k];
if (diff.is_neg())
return true;
if (diff.is_pos())
return false;
return lra.usage_in_terms(j) > lra.usage_in_terms(k);
});
unsigned_vector ret;
unsigned n = static_cast<unsigned>(sorted_vars.size());
lia_move int_solver::local_cut(unsigned num_cuts, std::function<lia_move(void)>& cut_fn) {
while (num_cuts-- && n > 0) {
unsigned k = random() % n;
double k_ratio = k / (double) n;
k_ratio *= k_ratio*k_ratio; // square k_ratio to make it smaller
k = static_cast<unsigned>(std::floor(k_ratio * n));
// these operations move k to the beginning of the indices range
SASSERT(0 <= k && k < n);
auto it = sorted_vars.begin();
while(k--) it++;
ret.push_back(*it);
sorted_vars.erase(it);
n--;
}
return ret;
}
lia_move int_solver::local_cut(unsigned num_cuts, std::function<lia_move(lpvar)>& cut_fn) {
struct ex { explanation m_ex; lar_term m_term; mpq m_k; bool m_is_upper; };
unsigned_vector columns_for_cuts = gomory_select_int_infeasible_vars(num_cuts);
vector<ex> cuts;
for (unsigned i = 0; i < num_cuts && has_inf_int(); ++i) {
for (unsigned j : columns_for_cuts) {
m_ex->clear();
m_t.clear();
m_k.reset();
auto r = cut_fn();
auto r = cut_fn(j);
if (r != lia_move::cut)
break;
continue;
cuts.push_back({ *m_ex, m_t, m_k, is_upper() });
if (settings().get_cancel_flag())
return lia_move::undef;
@ -938,6 +970,22 @@ namespace lp {
return lia_move::undef;
}
bool int_solver::is_gomory_cut_target(lpvar k) {
SASSERT(is_base(k));
// All non base variables must be at their bounds and assigned to rationals (that is, infinitesimals are not allowed).
const row_strip<mpq>& row = lra.get_row(row_of_basic_column(k));
unsigned j;
for (const auto & p : row) {
j = p.var();
if ( k != j && (!at_bound(j) || !is_zero(get_value(j).y))) {
TRACE("gomory_cut", tout << "row is not gomory cut target:\n";
display_column(tout, j);
tout << "infinitesimal: " << !is_zero(get_value(j).y) << "\n";);
return false;
}
}
return true;
}
}

7
src/math/lp/int_solver.h
View file

@ -111,7 +111,7 @@ private:
bool has_upper(unsigned j) const;
unsigned row_of_basic_column(unsigned j) const;
bool cut_indices_are_columns() const;
lia_move local_cut(unsigned num_cuts, std::function<lia_move(void)>& cut_fn);
lia_move local_cut(unsigned num_cuts, std::function<lia_move(lpvar)>& cut_fn);
public:
std::ostream& display_column(std::ostream & out, unsigned j) const;
@ -132,7 +132,8 @@ public:
bool all_columns_are_bounded() const;
lia_move hnf_cut();
int select_int_infeasible_var(bool check_bounded);
int select_int_infeasible_var();
unsigned_vector gomory_select_int_infeasible_vars(unsigned num_cuts);
bool is_gomory_cut_target(lpvar);
};
}

5
src/math/lp/lar_solver.h
View file

@ -532,6 +532,11 @@ public:
inline const impq& get_lower_bound(column_index j) const {
return m_mpq_lar_core_solver.m_r_solver.m_lower_bounds[j];
}
inline mpq bound_span_x(column_index j) const {
return m_mpq_lar_core_solver.m_r_solver.m_upper_bounds[j].x - m_mpq_lar_core_solver.m_r_solver.m_lower_bounds[j].x;
}
bool has_lower_bound(var_index var, u_dependency*& ci, mpq& value, bool& is_strict) const;
bool has_upper_bound(var_index var, u_dependency*& ci, mpq& value, bool& is_strict) const;
bool has_value(var_index var, mpq& value) const;