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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

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Signed-off-by: Nikolaj Bjorner <nbjorner@microsoft.com>
This commit is contained in:
Nikolaj Bjorner 2023-11-10 16:38:55 +01:00
parent aa9c7912dc
commit 3de5af3cb0
5 changed files with 121 additions and 261 deletions
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209
src/math/lp/gomory.cpp
View file

@ -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;
@ -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);
@ -359,12 +245,12 @@ public:
// 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) {
@ -408,13 +294,7 @@ public:
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);
@ -423,6 +303,91 @@ public:
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),

40
src/math/lp/hnf_cutter.cpp
View file

@ -83,14 +83,13 @@ 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;
}
@ -98,16 +97,15 @@ namespace lp {
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;
}
@ -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() {
@ -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
@ -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++;
@ -291,5 +284,4 @@ branch y_i >= ceil(y0_i) is impossible.
}
return r;
}
}

116
src/math/lp/int_solver.cpp
View file

@ -197,11 +197,14 @@ namespace lp {
if (r == lia_move::undef && should_find_cube()) r = int_cube(*this)();
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
if (r == lia_move::undef && should_gomory_cut()) r = local_gomory(2);
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)();
@ -711,6 +714,8 @@ namespace lp {
return;
#if 0
// in-processing simplification can go here, such as bounds improvements.
if (!lra.is_feasible()) {
@ -728,113 +733,9 @@ namespace lp {
if (has_inf_int())
local_gomory(5);
#if 0
stopwatch sw;
explanation exp1, exp2;
//
// tighten integer bounds
// It is a weak method as it ownly strengthens bounds if
// variables are already at one of the to-be discovered bounds.
//
sw.start();
unsigned changes = 0;
auto const& constraints = lra.constraints();
auto print_var = [this](lpvar j) {
if (lra.column_corresponds_to_term(j)) {
std::stringstream strm;
lra.print_column_info(j, strm);
return strm.str();
}
else
return std::string("j") + std::to_string(j);
};
unsigned start = random();
unsigned num_checks = 0;
for (lpvar j0 = 0; j0 < lra.column_count(); ++j0) {
lpvar j = (j0 + start) % lra.column_count();
if (num_checks > 1000)
break;
if (is_fixed(j))
continue;
if (!lra.column_is_int(j))
continue;
rational value = get_value(j).x;
bool tight_lower = false, tight_upper = false;
u_dependency* dep;
if (!value.is_int())
continue;
bool at_up = at_upper(j);
if (!at_lower(j)) {
++num_checks;
lra.push();
auto k = lp::lconstraint_kind::LE;
lra.update_column_type_and_bound(j, k, (value - 1).to_mpq(), nullptr);
lra.find_feasible_solution();
if (!lra.is_feasible()) {
tight_upper = true;
++changes;
lra.get_infeasibility_explanation(exp1);
#if 0
display_column(std::cout, j);
std::cout << print_var(j) << " >= " << value << "\n";
unsigned i = 0;
for (auto p : exp1) {
std::cout << "(" << p.ci() << ")";
constraints.display(std::cout, print_var, p.ci());
if (++i < exp1.size())
std::cout << " ";
}
#endif
}
lra.pop(1);
if (tight_upper) {
dep = nullptr;
for (auto& cc : exp1)
dep = lra.join_deps(dep, constraints[cc.ci()].dep());
lra.update_column_type_and_bound(j, lp::lconstraint_kind::GE, value.to_mpq(), dep);
}
}
if (!at_up) {
++num_checks;
lra.push();
auto k = lp::lconstraint_kind::GE;
lra.update_column_type_and_bound(j, k, (value + 1).to_mpq(), nullptr);
lra.find_feasible_solution();
if (!lra.is_feasible()) {
tight_lower = true;
++changes;
lra.get_infeasibility_explanation(exp1);
#if 0
display_column(std::cout, j);
std::cout << print_var(j) << " <= " << value << "\n";
unsigned i = 0;
for (auto p : exp1) {
std::cout << "(" << p.ci() << ")";
constraints.display(std::cout, print_var, p.ci());
if (++i < exp1.size())
std::cout << " ";
}
#endif
}
lra.pop(1);
if (tight_lower) {
dep = nullptr;
for (auto& cc : exp1)
dep = lra.join_deps(dep, constraints[cc.ci()].dep());
lra.update_column_type_and_bound(j, lp::lconstraint_kind::LE, value.to_mpq(), dep);
}
}
}
sw.stop();
std::cout << "changes " << changes << " columns " << lra.column_count() << " time: " << sw.get_seconds() << "\n";
std::cout.flush();
//
// identify equalities
//
@ -948,7 +849,8 @@ namespace lp {
#endif
}
lia_move int_solver::local_gomory(unsigned num_cuts) {
lia_move int_solver::local_cut(unsigned num_cuts, std::function<lia_move(void)>& cut_fn) {
struct ex { explanation m_ex; lar_term m_term; mpq m_k; bool m_is_upper; };
vector<ex> cuts;
@ -956,7 +858,7 @@ namespace lp {
m_ex->clear();
m_t.clear();
m_k.reset();
auto r = gomory(*this)();
auto r = cut_fn();
if (r != lia_move::cut)
break;
cuts.push_back({ *m_ex, m_t, m_k, is_upper() });

6
src/math/lp/int_solver.h
View file

@ -68,7 +68,7 @@ class int_solver {
hnf_cutter m_hnf_cutter;
unsigned m_hnf_cut_period;
unsigned_vector m_cut_vars; // variables that should not be selected for cuts
vector<equality> m_equalities;
public:
int_solver(lar_solver& lp);
@ -111,8 +111,8 @@ private:
bool has_upper(unsigned j) const;
unsigned row_of_basic_column(unsigned j) const;
bool cut_indices_are_columns() const;
lia_move local_gomory(unsigned num_cuts);
lia_move local_cut(unsigned num_cuts, std::function<lia_move(void)>& cut_fn);
public:
std::ostream& display_column(std::ostream & out, unsigned j) const;
u_dependency* column_upper_bound_constraint(unsigned j) const;

11
src/smt/theory_lra.cpp
View file

@ -1784,14 +1784,15 @@ public:
expr_ref atom(m);
t = coeffs2app(coeffs, rational::zero(), is_int);
if (lower_bound) {
if (lower_bound)
atom = a.mk_ge(t, a.mk_numeral(offset, is_int));
}
else {
atom = a.mk_le(t, a.mk_numeral(offset, is_int));
}
else
atom = a.mk_le(t, a.mk_numeral(offset, is_int));
// ctx().get_rewriter()(atom);
// Note: it is not safe to rewrite atom because the rewriter can
// destroy structure, such as (div x 24) >= 0 becomes x >= 0 and the internal variable
// corresponding to (div x 24) is not constrained.
TRACE("arith", tout << t << ": " << atom << "\n";
lp().print_term(term, tout << "bound atom: ") << (lower_bound?" >= ":" <= ") << k << "\n";);
ctx().internalize(atom, true);