Detect MIP symmetry using dejavu; Perform orbital fixing and lexical reduction

cpp/CMakeLists.txt

@@ -279,6 +279,20 @@ FetchContent_MakeAvailable(pslp)
 set(BUILD_SHARED_LIBS ${BUILD_SHARED_LIBS_SAVED})
 
 
+# dejavu - header-only graph automorphism library for MIP symmetry detection
+# https://github.com/markusa4/dejavu (header-only, skip its CMakeLists.txt)
+FetchContent_Declare(
+  dejavu
+  GIT_REPOSITORY "https://github.com/markusa4/dejavu.git"
+  GIT_TAG "v2.1"
+  GIT_PROGRESS TRUE
+  EXCLUDE_FROM_ALL
+  SYSTEM
+  SOURCE_SUBDIR _nonexistent
+)
+FetchContent_MakeAvailable(dejavu)
+message(STATUS "dejavu (graph automorphism): ${dejavu_SOURCE_DIR}")
+
 include(${rapids-cmake-dir}/cpm/rapids_logger.cmake)
 # generate logging macros
 rapids_cpm_rapids_logger(BUILD_EXPORT_SET cuopt-exports INSTALL_EXPORT_SET cuopt-exports)
@@ -469,6 +483,7 @@ target_include_directories(cuopt PRIVATE
 
 target_include_directories(cuopt SYSTEM PRIVATE
   "${pslp_SOURCE_DIR}/include"
+  "${dejavu_SOURCE_DIR}"
 )
 
 target_include_directories(cuopt

cpp/src/branch_and_bound/branch_and_bound.cpp

@@ -8,6 +8,7 @@
 #include <branch_and_bound/branch_and_bound.hpp>
 #include <branch_and_bound/mip_node.hpp>
 #include <branch_and_bound/pseudo_costs.hpp>
+#include <branch_and_bound/symmetry.hpp>
 
 #include <cuts/cuts.hpp>
 #include <mip_heuristics/presolve/conflict_graph/clique_table.cuh>
@@ -248,11 +249,13 @@ branch_and_bound_t<i_t, f_t>::branch_and_bound_t(
   const simplex_solver_settings_t<i_t, f_t>& solver_settings,
   f_t start_time,
   const probing_implied_bound_t<i_t, f_t>& probing_implied_bound,
-  std::shared_ptr<detail::clique_table_t<i_t, f_t>> clique_table)
+  std::shared_ptr<detail::clique_table_t<i_t, f_t>> clique_table,
+  mip_symmetry_t<i_t, f_t>* symmetry)
   : original_problem_(user_problem),
     settings_(solver_settings),
     probing_implied_bound_(probing_implied_bound),
     clique_table_(std::move(clique_table)),
+    symmetry_(symmetry),
     original_lp_(user_problem.handle_ptr, 1, 1, 1),
     Arow_(1, 1, 0),
     incumbent_(1),
@@ -1388,6 +1391,163 @@ dual::status_t branch_and_bound_t<i_t, f_t>::solve_node_lp(
   worker->leaf_edge_norms  = edge_norms_;
 
   if (feasible) {
+
+
+    // Perform orbital fixing
+    if (symmetry_ != nullptr) {
+      // First get the set of variables that have been branched down and branched up on
+      std::vector<i_t> branched_zero;
+      std::vector<i_t> branched_one;
+      branched_zero.reserve(node_ptr->depth);
+      branched_one.reserve(node_ptr->depth);
+      mip_node_t<i_t, f_t>* node = node_ptr;
+      while (node != nullptr && node->branch_var >= 0) {
+        if (node->branch_var_upper == 0.0) {
+          branched_zero.push_back(node->branch_var);
+          symmetry_->marked_b0[node->branch_var] = 1;
+        } else if (node->branch_var_lower == 1.0) {
+          branched_one.push_back(node->branch_var);
+          symmetry_->marked_b1[node->branch_var] = 1;
+        } else {
+          assert(false); // Unexpected non-binary variable. Only binaries supported in symmetry handling.
+        }
+        node = node->parent;
+      }
+
+      {
+        for (i_t j = 0; j < symmetry_->num_original_vars; j++) {
+          if (var_types_[j] == variable_type_t::CONTINUOUS) continue;
+          if (symmetry_->marked_b1[j] == 0 && worker->leaf_problem.lower[j] == 1.0) {
+            symmetry_->f1.push_back(j);
+            symmetry_->marked_f1[j] = 1;
+          }
+          if (symmetry_->marked_b0[j] == 0 && worker->leaf_problem.upper[j] == 0.0) {
+            symmetry_->f0.push_back(j);
+            symmetry_->marked_f0[j] = 1;
+          }
+        }
+
+        // Compute Stab(G, B1) and its orbits
+        std::vector<i_t> new_base;
+        new_base.reserve(symmetry_->num_original_vars);
+        for (i_t j: branched_one) {
+          new_base.push_back(j);
+          symmetry_->marked_variables[j] = 1;
+        }
+        for (i_t j = 0; j < symmetry_->num_original_vars; j++) {
+          if (symmetry_->marked_variables[j] == 0) {
+            new_base.push_back(j);
+          }
+        }
+        for (i_t j: branched_one) {
+          symmetry_->marked_variables[j] = 0;
+        }
+
+        symmetry_->schreier->set_base(new_base);
+
+        dejavu::groups::orbit orb;
+        orb.initialize(symmetry_->domain_size);
+        symmetry_->schreier->get_stabilizer_orbit(static_cast<int>(branched_one.size()), orb);
+
+        for (i_t v : branched_one) {
+          symmetry_->orbit_has_b1[orb.find_orbit(v)] = 1;
+        }
+
+        for (i_t v : branched_zero) {
+          symmetry_->orbit_has_b0[orb.find_orbit(v)] = 1;
+        }
+
+        for (i_t v: symmetry_->continuous_variables) {
+          symmetry_->orbit_has_continuous[orb.find_orbit(v)] = 1;
+        }
+
+        for (i_t v: symmetry_->f0) {
+          symmetry_->orbit_has_f0[orb.find_orbit(v)] = 1;
+        }
+
+        for (i_t v: symmetry_->f1) {
+          symmetry_->orbit_has_f1[orb.find_orbit(v)] = 1;
+        }
+
+        std::vector<i_t> fix_zero; // The set L0 of variables that can be fixed to 0
+        std::vector<i_t> fix_one;  // The set L1 of variables that can be fixed to 1
+
+        for (i_t j = 0; j < symmetry_->num_original_vars; j++) {
+          i_t o = orb.find_orbit(j);
+          if (orb.orbit_size(o) < 2) continue;
+
+          if (symmetry_->orbit_has_b1[o] == 1 || symmetry_->orbit_has_continuous[o] == 1) {
+            // The orbit contains variables in B1 or continuous variables
+            // So we can't fix any variables in this orbit to 0
+            continue;
+          }
+
+          if (symmetry_->orbit_has_b0[o] == 1 || symmetry_->orbit_has_f0[o] == 1) {
+            // The orbit of this variable contains variables in B0 or F0
+            // So we can fix this variable to zero (provided its not already in B0 or F0)
+            if (symmetry_->marked_b0[j] == 0 && symmetry_->marked_f0[j] == 0) {
+              fix_zero.push_back(j);
+            }
+          }
+
+          if (symmetry_->orbit_has_f1[o] == 1) {
+            // The orbit of this variable contains variables in F1
+            // So we can fix this variable to one (provided its not already in F1)
+            if (symmetry_->marked_f1[j] == 0) {
+              fix_one.push_back(j);
+            }
+          }
+        }
+
+        // Restore the work arrays
+        for (i_t v: branched_one) {
+          symmetry_->orbit_has_b1[orb.find_orbit(v)] = 0;
+          symmetry_->marked_b1[v] = 0;
+        }
+
+        for (i_t v: branched_zero) {
+          symmetry_->orbit_has_b0[orb.find_orbit(v)] = 0;
+          symmetry_->marked_b0[v] = 0;
+        }
+
+        for (i_t v: symmetry_->continuous_variables) {
+          symmetry_->orbit_has_continuous[orb.find_orbit(v)] = 0;
+        }
+
+        for (i_t v: symmetry_->f0) {
+          symmetry_->orbit_has_f0[orb.find_orbit(v)] = 0;
+          symmetry_->marked_f0[v] = 0;
+        }
+
+        for (i_t v: symmetry_->f1) {
+          symmetry_->orbit_has_f1[orb.find_orbit(v)] = 0;
+          symmetry_->marked_f1[v] = 0;
+        }
+
+        symmetry_->f0.clear();
+        symmetry_->f1.clear();
+
+        settings_.log.printf(
+          "Orbital fixing at node %d: fixing %d variables to 0 and %d variables to 1\n",
+          node_ptr->node_id,
+          fix_zero.size(),
+          fix_one.size());
+        // Finally fix the variables in L0 and L1
+        for (i_t v: fix_zero) {
+          settings_.log.printf("Orbital fixing at node %d: fixing variable %d to 0\n", node_ptr->node_id, v);
+          worker->leaf_problem.lower[v] = 0.0;
+          worker->leaf_problem.upper[v] = 0.0;
+        }
+        for (i_t v: fix_one) {
+          settings_.log.printf("Orbital fixing at node %d: fixing variable %d to 1\n", node_ptr->node_id, v);
+          worker->leaf_problem.lower[v] = 1.0;
+          worker->leaf_problem.upper[v] = 1.0;
+        }
+      }
+    }
+
+
+
     i_t node_iter     = 0;
     f_t lp_start_time = tic();
 

cpp/src/branch_and_bound/branch_and_bound.hpp

@@ -47,6 +47,9 @@ struct clique_table_t;
 
 namespace cuopt::linear_programming::dual_simplex {
 
+template <typename i_t, typename f_t>
+struct mip_symmetry_t;
+
 enum class mip_status_t {
   OPTIMAL    = 0,  // The optimal integer solution was found
   UNBOUNDED  = 1,  // The problem is unbounded
@@ -80,7 +83,8 @@ class branch_and_bound_t {
                      const simplex_solver_settings_t<i_t, f_t>& solver_settings,
                      f_t start_time,
                      const probing_implied_bound_t<i_t, f_t>& probing_implied_bound,
-                     std::shared_ptr<detail::clique_table_t<i_t, f_t>> clique_table = nullptr);
+                     std::shared_ptr<detail::clique_table_t<i_t, f_t>> clique_table = nullptr,
+                     mip_symmetry_t<i_t, f_t>* symmetry = nullptr);
 
   // Set an initial guess based on the user_problem. This should be called before solve.
   void set_initial_guess(const std::vector<f_t>& user_guess) { guess_ = user_guess; }
@@ -162,6 +166,7 @@ class branch_and_bound_t {
   const simplex_solver_settings_t<i_t, f_t> settings_;
   const probing_implied_bound_t<i_t, f_t>& probing_implied_bound_;
   std::shared_ptr<detail::clique_table_t<i_t, f_t>> clique_table_;
+  mip_symmetry_t<i_t, f_t>* symmetry_;
   std::future<std::shared_ptr<detail::clique_table_t<i_t, f_t>>> clique_table_future_;
   std::atomic<bool> signal_extend_cliques_{false};