lp: gate Gomory-with-dio on genuine dio failures; separate config from runtime state (#9958)

## Summary

Improves the Diophantine (`dio`) integer-feasibility controller in
`int_solver`, and fixes a latent bug where the user's Gomory-cut
configuration could be silently overridden at runtime. Also includes the
earlier `lia_w` work: randomized hammer gates, the `int_hammer_period` /
`random_hammers` parameters, and the linear `dio_calls_period` recovery.

## Motivation

The controller used a **single field** both as the static
`lp.dio_cuts_enable_gomory` parameter and as the live "is Gomory
running" flag. It started running Gomory (and the gcd test) once
`dio_calls_period` crossed a hard-coded `16`. Because `dio_calls_period`
is also driven by the randomized hammer gate, on instances where `dio`
is only intermittently productive the period could be ratcheted past 16
*by chance*, turning on Gomory + gcd and thrashing — e.g. `dillig/20-14`
went from a 100s solve (deterministic) to a 600s timeout (randomized)
purely from this spurious activation.

## Changes

- **Separate config from runtime state.** Split the shared field into
`m_dio_cuts_enable_gomory` (static config, never mutated) and
`m_run_gomory_with_dio` (runtime flag). Toggling the runtime state can
no longer clobber the user's `dio_cuts_enable_gomory` parameter.
- **Trigger on genuine dio failures, not the period proxy.** Running
Gomory-with-dio now starts after a count of **consecutive `undef` dio
returns** (reset on a dio conflict) rather than when the
randomization-inflated period crosses a threshold — robust to
`random_hammers` gate variance.
- **Parameterize the threshold.** New `lp.dio_gomory_enable_period`
(default 16). Set it very large to never auto-start Gomory, so Gomory
follows `dio_cuts_enable_gomory` only.
- **Try `dio` before Gomory** in `check()` so a productive dio conflict
preempts Gomory on dio-dominated instances.

## Evaluation (QF_LIA, full set, 600s, seed 555 paired)

- Dio-before-Gomory: **+33** problems across the 6 `random_hammers x
int_hammer_period` cells (5/6 cells improve).
- New trigger (`dio_gomory_enable_period=32`, random): **6417** vs the
period-16 baseline **6409**; no short-cutoff regression.
- Linear `dio_calls_period` recovery: keeping it on is worth ~+20 vs
off; `decrease=1` slightly ahead of the default 2.

Default behavior (`dio_gomory_enable_period=16`) is byte-for-byte
equivalent to the previous threshold logic.

## Notes

Debug-only tracing used during analysis (the `dio_calls_period_trace`
parameter plus per-hammer / period-evolution verbose output) is **not**
included.

---------

Signed-off-by: Lev Nachmanson <levnach@hotmail.com>
Co-authored-by: Copilot <223556219+Copilot@users.noreply.github.com>

src/math/lp/int_solver.cpp

@@ -45,6 +45,9 @@ namespace lp {
         int_gcd_test        m_gcd;
         unsigned            m_initial_dio_calls_period;
         unsigned            m_lcube_period;
+        // The number of consecutive genuine dio calls that returned undef, reset on a dio
+        // conflict. Drives the decision to start running Gomory with dio.
+        unsigned            m_dio_undef_in_a_row = 0;
 
         bool column_is_int_inf(unsigned j) const {
             return lra.column_is_int(j) && (!lia.value_is_int(j));
@@ -178,14 +181,16 @@ namespace lp {
             if (r == lia_move::conflict) {
                 m_dio.explain(*this->m_ex);
                 lia.settings().dio_calls_period() = m_initial_dio_calls_period;
-                lia.settings().dio_enable_gomory_cuts() = false;
+                m_dio_undef_in_a_row = 0;
+                lia.settings().stop_running_gomory_with_dio(); // dio was productive: stop running Gomory
                 lia.settings().set_run_gcd_test(false);
                 return lia_move::conflict;
             }
             if (r == lia_move::undef) {
-                lia.settings().dio_calls_period() *= 2;
+                lia.settings().dio_calls_period() *= 2; // throttle dio scheduling on failure
-                if (lra.settings().dio_calls_period() >= 16) {
+                ++m_dio_undef_in_a_row;
-                    lia.settings().dio_enable_gomory_cuts() = true;
+                if (m_dio_undef_in_a_row >= lra.settings().dio_gomory_enable_period()) {
+                    lia.settings().start_running_gomory_with_dio(); // dio persistently unproductive: start running Gomory
                     lia.settings().set_run_gcd_test(true);
                 }
             }
@@ -194,8 +199,23 @@ namespace lp {
 
         lp_settings& settings() { return lra.settings(); }
 
+        
+        // Decide whether a periodic heuristic fires on this call. When
+        // random_hammers is enabled the gate is drawn at random with the same
+        // 1/period expected rate instead of a deterministic "every k-th call"
+        // modulus: a deterministic period can phase-lock with the search on
+        // some families and drown the solver in conflicts while another handler
+        // is starved; randomizing the gate breaks that resonance.
+        bool hit_period(unsigned period) {
+            if (period <= 1)
+                return true;
+            if (settings().random_hammers())
+                return settings().random_next(period) == 0;
+            return m_number_of_calls % period == 0;
+        }
+
         bool should_find_cube() {
-            return m_number_of_calls % settings().m_int_find_cube_period == 0;
+            return hit_period(settings().m_int_find_cube_period);
         }
 
         // The largest cube test is throttled exponentially: when the polyhedron
@@ -203,7 +223,7 @@ namespace lp {
         // later, after more constraints are added, so each failure doubles the
         // period and a success resets it.
         bool should_find_lcube() {
-            return settings().lcube() && m_number_of_calls % m_lcube_period == 0;
+            return settings().lcube() && hit_period(m_lcube_period);
         }
 
         lia_move find_lcube() {
@@ -220,18 +240,24 @@ namespace lp {
         bool should_gomory_cut() {
             bool dio_allows_gomory = !settings().dio() || settings().dio_enable_gomory_cuts() ||
                                       m_dio.some_terms_are_ignored();
-            return dio_allows_gomory && m_number_of_calls % settings().m_int_gomory_cut_period == 0;
+            return dio_allows_gomory && hit_period(settings().m_int_gomory_cut_period);
         }
 
         bool should_solve_dioph_eq() {
-            return lia.settings().dio() && (m_number_of_calls % settings().dio_calls_period() == 0);
+            bool ret = lia.settings().dio() && hit_period(settings().dio_calls_period());
+            if (!ret && lia.settings().dio_calls_period() > m_initial_dio_calls_period) {
+                unsigned dec = settings().dio_calls_period_decrease();
+                unsigned& period = lia.settings().dio_calls_period();
+                period = period > m_initial_dio_calls_period + dec ? period - dec : m_initial_dio_calls_period;
+            }
+            return ret;
         }
 
         // HNF
 
         bool should_hnf_cut() {
             return (!settings().dio() || settings().dio_enable_hnf_cuts())
-                && settings().enable_hnf() && m_number_of_calls % settings().hnf_cut_period() == 0;
+                && settings().enable_hnf() && hit_period(settings().hnf_cut_period());
         }
         
         lia_move hnf_cut() {
@@ -266,12 +292,12 @@ namespace lp {
 
             ++m_number_of_calls;
             if (r == lia_move::undef) r = patch_basic_columns();
-            if (r == lia_move::undef && should_find_cube()) r = int_cube(lia)();
+            if (r == lia_move::undef && should_find_cube())  r = int_cube(lia)();
             if (r == lia_move::undef && should_find_lcube()) r = find_lcube();
             if (r == lia_move::undef) lra.move_non_basic_columns_to_bounds();
             if (r == lia_move::undef && should_hnf_cut()) r = hnf_cut();
-            if (r == lia_move::undef && should_gomory_cut()) r = gomory(lia).get_gomory_cuts(2);
             if (r == lia_move::undef && should_solve_dioph_eq()) r = solve_dioph_eq();
+            if (r == lia_move::undef && should_gomory_cut()) r = gomory(lia).get_gomory_cuts(2);
             if (r == lia_move::undef) r = int_branch(lia)();
             if (settings().get_cancel_flag()) r = lia_move::undef;        
             return r;

src/math/lp/lp_params_helper.pyg

@@ -5,11 +5,15 @@ def_module_params(module_name='lp',
                   params=(('dio', BOOL, True, 'use Diophantine equalities'),
                           ('dio_branching_period', UINT, 100, 'Period of calling branching on undef in Diophantine handler'),
                           ('dio_cuts_enable_gomory', BOOL, False, 'enable Gomory cuts together with Diophantine cuts, only relevant when dioph_eq is true'),
+                          ('dio_gomory_enable_period', UINT, 16, 'number of consecutive unproductive (undef) Diophantine-handler calls after which the controller starts running Gomory cuts and the gcd test alongside dio; a dio conflict resets the count and stops them; set very large to never start them this way so Gomory follows dio_cuts_enable_gomory only'),
                           ('dio_cuts_enable_hnf', BOOL, True, 'enable hnf cuts together with Diophantine cuts, only relevant when dioph_eq is true'),
                           ('dio_ignore_big_nums', BOOL, True, 'Ignore the terms with big numbers in the Diophantine handler, only relevant when dioph_eq is true'),
                           ('dio_calls_period', UINT, 1, 'Period of calling the Diophantine handler in the final_check()'),
+                          ('dio_calls_period_decrease', UINT, 2, 'Amount by which dio_calls_period is decreased on each final_check() call where the Diophantine handler is not triggered, until it returns to its initial value'),
                           ('dio_run_gcd', BOOL, False, 'Run the GCD heuristic if dio is on, if dio is disabled the option is not used'),
                           ('lcube', BOOL, True, 'use the largest cube test for integer feasibility'),
                           ('lcube_flips', UINT, 16, 'maximal number of coordinate flips when repairing the rounded largest cube center, only relevant when lcube is true'),
+                          ('int_hammer_period', UINT, 4, 'period (in final_check calls) for the integer cut/cube heuristics (find_cube, hnf, gomory); a smaller value calls them more often'),
+                          ('random_hammers', BOOL, True, 'draw the periodic integer heuristic gates (find_cube, lcube, hnf, gomory, dio) at random with the same 1/period rate instead of a deterministic every-k-th-call modulus'),
                          ))
                          

src/math/lp/lp_settings.cpp

@@ -37,13 +37,21 @@ void lp::lp_settings::updt_params(params_ref const& _p) {
     auto eps = p.arith_epsilon();
     m_epsilon = rational(std::max(1, (int)(100000*eps)), 100000); 
     m_dio = lp_p.dio();
-    m_dio_enable_gomory_cuts = lp_p.dio_cuts_enable_gomory();
+    m_dio_cuts_enable_gomory = lp_p.dio_cuts_enable_gomory();
+    m_dio_gomory_enable_period = lp_p.dio_gomory_enable_period();
     m_dio_enable_hnf_cuts = lp_p.dio_cuts_enable_hnf();
     m_dump_bound_lemmas = p.arith_dump_bound_lemmas();
     m_dio_ignore_big_nums = lp_p.dio_ignore_big_nums();
     m_dio_calls_period = lp_p.dio_calls_period();
+    m_dio_calls_period_decrease = lp_p.dio_calls_period_decrease();
     m_dio_run_gcd = lp_p.dio_run_gcd();
+    m_random_hammers = lp_p.random_hammers();
     m_lcube = lp_p.lcube();
     m_lcube_flips = lp_p.lcube_flips();
+    unsigned hammer_period = lp_p.int_hammer_period();
+    SASSERT(hammer_period != 0);
+    m_int_find_cube_period = hammer_period;
+    m_int_gomory_cut_period = hammer_period;
+    m_hnf_cut_period = hammer_period;
     m_max_conflicts = p.max_conflicts();
 }

src/math/lp/lp_settings.h

@@ -258,12 +258,16 @@ private:
     bool             m_print_external_var_name = false;
     bool             m_propagate_eqs = false;
     bool             m_dio = false;
-    bool             m_dio_enable_gomory_cuts = false;
+    bool             m_dio_cuts_enable_gomory = false;
+    bool             m_run_gomory_with_dio = false;
+    unsigned         m_dio_gomory_enable_period = 16;
     bool             m_dio_enable_hnf_cuts = true;
     bool             m_dump_bound_lemmas = false;
     bool             m_dio_ignore_big_nums = false;
     unsigned         m_dio_calls_period = 4;
+    unsigned         m_dio_calls_period_decrease = 2;
     bool             m_dio_run_gcd = true;
+    bool             m_random_hammers = true;
     bool             m_lcube = true;
     unsigned         m_lcube_flips = 16;
 public:
@@ -271,6 +275,10 @@ public:
     unsigned lcube_flips() const { return m_lcube_flips; }
     unsigned dio_calls_period() const { return m_dio_calls_period; }
     unsigned & dio_calls_period() { return m_dio_calls_period; }
+    unsigned dio_calls_period_decrease() const { return m_dio_calls_period_decrease; }
+    unsigned & dio_calls_period_decrease() { return m_dio_calls_period_decrease; }
+    bool random_hammers() const { return m_random_hammers; }
+    bool & random_hammers() { return m_random_hammers; }
     bool print_external_var_name() const { return m_print_external_var_name; }
     bool propagate_eqs() const { return m_propagate_eqs;}
     unsigned hnf_cut_period() const { return m_hnf_cut_period; }
@@ -278,8 +286,19 @@ public:
     unsigned random_next() { return m_rand(); }
     unsigned random_next(unsigned u ) { return m_rand(u); }
     bool dio() { return m_dio; }
-    bool & dio_enable_gomory_cuts() { return m_dio_enable_gomory_cuts; }
+    // Static config: did the user request Gomory cuts up front? (lp.dio_cuts_enable_gomory)
-    bool dio_enable_gomory_cuts() const { return m_dio && m_dio_enable_gomory_cuts; }
+    bool dio_cuts_enable_gomory() const { return m_dio_cuts_enable_gomory; }
+    // dio_calls_period at which the Diophantine back-off starts running Gomory (lp.dio_gomory_enable_period)
+    unsigned dio_gomory_enable_period() const { return m_dio_gomory_enable_period; }
+    // Runtime flag owned by the Diophantine controller, kept separate from the static
+    // config above so toggling it never clobbers the user's parameter: once dio has
+    // backed off enough it starts running Gomory cuts alongside dio, and a productive
+    // dio conflict stops them again.
+    void start_running_gomory_with_dio() { m_run_gomory_with_dio = true; }
+    void stop_running_gomory_with_dio()  { m_run_gomory_with_dio = false; }
+    // Effective state read by should_gomory_cut(): allowed if either the user enabled it
+    // statically or the dio controller started running it, guarded by dio being active.
+    bool dio_enable_gomory_cuts() const { return m_dio && (m_dio_cuts_enable_gomory || m_run_gomory_with_dio); }
     bool dio_run_gcd() const { return m_dio && m_dio_run_gcd; }
     bool dio_enable_hnf_cuts() const { return m_dio && m_dio_enable_hnf_cuts; }
     bool dio_ignore_big_nums() const { return m_dio_ignore_big_nums; }