NVIDIA · rapids-bot · Apr 3, 2026 · Feb 9, 2026 · Feb 9, 2026 · Feb 17, 2026
@@ -20,65 +20,67 @@
 #define CUOPT_INSTANTIATE_INT64  0
 
 /* @brief LP/MIP parameter string constants */
-#define CUOPT_ABSOLUTE_DUAL_TOLERANCE                 "absolute_dual_tolerance"
-#define CUOPT_RELATIVE_DUAL_TOLERANCE                 "relative_dual_tolerance"
-#define CUOPT_ABSOLUTE_PRIMAL_TOLERANCE               "absolute_primal_tolerance"
-#define CUOPT_RELATIVE_PRIMAL_TOLERANCE               "relative_primal_tolerance"
-#define CUOPT_ABSOLUTE_GAP_TOLERANCE                  "absolute_gap_tolerance"
-#define CUOPT_RELATIVE_GAP_TOLERANCE                  "relative_gap_tolerance"
-#define CUOPT_INFEASIBILITY_DETECTION                 "infeasibility_detection"
-#define CUOPT_STRICT_INFEASIBILITY                    "strict_infeasibility"
-#define CUOPT_PRIMAL_INFEASIBLE_TOLERANCE             "primal_infeasible_tolerance"
-#define CUOPT_DUAL_INFEASIBLE_TOLERANCE               "dual_infeasible_tolerance"
-#define CUOPT_ITERATION_LIMIT                         "iteration_limit"
-#define CUOPT_TIME_LIMIT                              "time_limit"
-#define CUOPT_WORK_LIMIT                              "work_limit"
-#define CUOPT_PDLP_SOLVER_MODE                        "pdlp_solver_mode"
-#define CUOPT_METHOD                                  "method"
-#define CUOPT_PER_CONSTRAINT_RESIDUAL                 "per_constraint_residual"
-#define CUOPT_SAVE_BEST_PRIMAL_SO_FAR                 "save_best_primal_so_far"
-#define CUOPT_FIRST_PRIMAL_FEASIBLE                   "first_primal_feasible"
-#define CUOPT_LOG_FILE                                "log_file"
-#define CUOPT_LOG_TO_CONSOLE                          "log_to_console"
-#define CUOPT_CROSSOVER                               "crossover"
-#define CUOPT_FOLDING                                 "folding"
-#define CUOPT_AUGMENTED                               "augmented"
-#define CUOPT_DUALIZE                                 "dualize"
-#define CUOPT_ORDERING                                "ordering"
-#define CUOPT_BARRIER_DUAL_INITIAL_POINT              "barrier_dual_initial_point"
-#define CUOPT_ELIMINATE_DENSE_COLUMNS                 "eliminate_dense_columns"
-#define CUOPT_CUDSS_DETERMINISTIC                     "cudss_deterministic"
-#define CUOPT_PRESOLVE                                "presolve"
-#define CUOPT_DUAL_POSTSOLVE                          "dual_postsolve"
-#define CUOPT_MIP_DETERMINISM_MODE                    "mip_determinism_mode"
-#define CUOPT_MIP_ABSOLUTE_TOLERANCE                  "mip_absolute_tolerance"
-#define CUOPT_MIP_RELATIVE_TOLERANCE                  "mip_relative_tolerance"
-#define CUOPT_MIP_INTEGRALITY_TOLERANCE               "mip_integrality_tolerance"
-#define CUOPT_MIP_ABSOLUTE_GAP                        "mip_absolute_gap"
-#define CUOPT_MIP_RELATIVE_GAP                        "mip_relative_gap"
-#define CUOPT_MIP_HEURISTICS_ONLY                     "mip_heuristics_only"
-#define CUOPT_MIP_SCALING                             "mip_scaling"
-#define CUOPT_MIP_PRESOLVE                            "mip_presolve"
-#define CUOPT_MIP_RELIABILITY_BRANCHING               "mip_reliability_branching"
-#define CUOPT_MIP_CUT_PASSES                          "mip_cut_passes"
-#define CUOPT_MIP_MIXED_INTEGER_ROUNDING_CUTS         "mip_mixed_integer_rounding_cuts"
-#define CUOPT_MIP_MIXED_INTEGER_GOMORY_CUTS           "mip_mixed_integer_gomory_cuts"
-#define CUOPT_MIP_KNAPSACK_CUTS                       "mip_knapsack_cuts"
-#define CUOPT_MIP_IMPLIED_BOUND_CUTS                  "mip_implied_bound_cuts"
-#define CUOPT_MIP_CLIQUE_CUTS                         "mip_clique_cuts"
-#define CUOPT_MIP_STRONG_CHVATAL_GOMORY_CUTS          "mip_strong_chvatal_gomory_cuts"
-#define CUOPT_MIP_REDUCED_COST_STRENGTHENING          "mip_reduced_cost_strengthening"
-#define CUOPT_MIP_CUT_CHANGE_THRESHOLD                "mip_cut_change_threshold"
-#define CUOPT_MIP_CUT_MIN_ORTHOGONALITY               "mip_cut_min_orthogonality"
-#define CUOPT_MIP_BATCH_PDLP_STRONG_BRANCHING         "mip_batch_pdlp_strong_branching"
-#define CUOPT_MIP_STRONG_BRANCHING_SIMPLEX_ITER_LIMIT "mip_strong_branching_simplex_iter_limit"
-#define CUOPT_SOLUTION_FILE                           "solution_file"
-#define CUOPT_NUM_CPU_THREADS                         "num_cpu_threads"
-#define CUOPT_NUM_GPUS                                "num_gpus"
-#define CUOPT_USER_PROBLEM_FILE                       "user_problem_file"
-#define CUOPT_PRESOLVE_FILE                           "presolve_file"
-#define CUOPT_RANDOM_SEED                             "random_seed"
-#define CUOPT_PDLP_PRECISION                          "pdlp_precision"
+#define CUOPT_ABSOLUTE_DUAL_TOLERANCE              "absolute_dual_tolerance"
+#define CUOPT_RELATIVE_DUAL_TOLERANCE              "relative_dual_tolerance"
+#define CUOPT_ABSOLUTE_PRIMAL_TOLERANCE            "absolute_primal_tolerance"
+#define CUOPT_RELATIVE_PRIMAL_TOLERANCE            "relative_primal_tolerance"
+#define CUOPT_ABSOLUTE_GAP_TOLERANCE               "absolute_gap_tolerance"
+#define CUOPT_RELATIVE_GAP_TOLERANCE               "relative_gap_tolerance"
+#define CUOPT_INFEASIBILITY_DETECTION              "infeasibility_detection"
+#define CUOPT_STRICT_INFEASIBILITY                 "strict_infeasibility"
+#define CUOPT_PRIMAL_INFEASIBLE_TOLERANCE          "primal_infeasible_tolerance"
+#define CUOPT_DUAL_INFEASIBLE_TOLERANCE            "dual_infeasible_tolerance"
+#define CUOPT_ITERATION_LIMIT                      "iteration_limit"
+#define CUOPT_TIME_LIMIT                           "time_limit"
+#define CUOPT_WORK_LIMIT                           "work_limit"
+#define CUOPT_PDLP_SOLVER_MODE                     "pdlp_solver_mode"
+#define CUOPT_METHOD                               "method"
+#define CUOPT_PER_CONSTRAINT_RESIDUAL              "per_constraint_residual"
+#define CUOPT_SAVE_BEST_PRIMAL_SO_FAR              "save_best_primal_so_far"
+#define CUOPT_FIRST_PRIMAL_FEASIBLE                "first_primal_feasible"
+#define CUOPT_LOG_FILE                             "log_file"
+#define CUOPT_LOG_TO_CONSOLE                       "log_to_console"
+#define CUOPT_CROSSOVER                            "crossover"
+#define CUOPT_FOLDING                              "folding"
+#define CUOPT_AUGMENTED                            "augmented"
+#define CUOPT_DUALIZE                              "dualize"
+#define CUOPT_ORDERING                             "ordering"
+#define CUOPT_BARRIER_DUAL_INITIAL_POINT           "barrier_dual_initial_point"
+#define CUOPT_ELIMINATE_DENSE_COLUMNS              "eliminate_dense_columns"
+#define CUOPT_CUDSS_DETERMINISTIC                  "cudss_deterministic"
+#define CUOPT_PRESOLVE                             "presolve"
+#define CUOPT_DUAL_POSTSOLVE                       "dual_postsolve"
+#define CUOPT_MIP_DETERMINISM_MODE                 "mip_determinism_mode"
+#define CUOPT_MIP_ABSOLUTE_TOLERANCE               "mip_absolute_tolerance"
+#define CUOPT_MIP_RELATIVE_TOLERANCE               "mip_relative_tolerance"
+#define CUOPT_MIP_INTEGRALITY_TOLERANCE            "mip_integrality_tolerance"
+#define CUOPT_MIP_ABSOLUTE_GAP                     "mip_absolute_gap"
+#define CUOPT_MIP_RELATIVE_GAP                     "mip_relative_gap"
+#define CUOPT_MIP_HEURISTICS_ONLY                  "mip_heuristics_only"
+#define CUOPT_MIP_SCALING                          "mip_scaling"
+#define CUOPT_MIP_PRESOLVE                         "mip_presolve"
+#define CUOPT_MIP_RELIABILITY_BRANCHING            "mip_reliability_branching"
+#define CUOPT_MIP_CUT_PASSES                       "mip_cut_passes"
+#define CUOPT_MIP_MIXED_INTEGER_ROUNDING_CUTS      "mip_mixed_integer_rounding_cuts"
+#define CUOPT_MIP_MIXED_INTEGER_GOMORY_CUTS        "mip_mixed_integer_gomory_cuts"
+#define CUOPT_MIP_KNAPSACK_CUTS                    "mip_knapsack_cuts"
+#define CUOPT_MIP_IMPLIED_BOUND_CUTS               "mip_implied_bound_cuts"
+#define CUOPT_MIP_CLIQUE_CUTS                      "mip_clique_cuts"
+#define CUOPT_MIP_STRONG_CHVATAL_GOMORY_CUTS       "mip_strong_chvatal_gomory_cuts"
+#define CUOPT_MIP_REDUCED_COST_STRENGTHENING       "mip_reduced_cost_strengthening"
+#define CUOPT_MIP_CUT_CHANGE_THRESHOLD             "mip_cut_change_threshold"
+#define CUOPT_MIP_CUT_MIN_ORTHOGONALITY            "mip_cut_min_orthogonality"
+#define CUOPT_MIP_BATCH_PDLP_STRONG_BRANCHING      "mip_batch_pdlp_strong_branching"
+#define CUOPT_MIP_BATCH_PDLP_RELIABILITY_BRANCHING "mip_batch_pdlp_reliability_branching"
+#define CUOPT_MIP_STRONG_BRANCHING_SIMPLEX_ITERATION_LIMIT \
+  "mip_strong_branching_simplex_iteration_limit"
+#define CUOPT_SOLUTION_FILE     "solution_file"
+#define CUOPT_NUM_CPU_THREADS   "num_cpu_threads"
+#define CUOPT_NUM_GPUS          "num_gpus"
+#define CUOPT_USER_PROBLEM_FILE "user_problem_file"
+#define CUOPT_PRESOLVE_FILE     "presolve_file"
+#define CUOPT_RANDOM_SEED       "random_seed"
+#define CUOPT_PDLP_PRECISION    "pdlp_precision"
 
 /* @brief MIP determinism mode constants */
 #define CUOPT_MODE_OPPORTUNISTIC 0

@@ -95,11 +95,14 @@ class mip_solver_settings_t {
   i_t knapsack_cuts             = -1;
   i_t clique_cuts               = -1;
   i_t implied_bound_cuts        = -1;
-  i_t strong_chvatal_gomory_cuts               = -1;
-  i_t reduced_cost_strengthening               = -1;
-  f_t cut_change_threshold                     = -1.0;
-  f_t cut_min_orthogonality                    = 0.5;
-  i_t mip_batch_pdlp_strong_branching          = 0;
+  i_t strong_chvatal_gomory_cuts = -1;
+  i_t reduced_cost_strengthening = -1;
+  f_t cut_change_threshold       = -1.0;
+  f_t cut_min_orthogonality      = 0.5;
+  i_t mip_batch_pdlp_strong_branching{
+    0};  // 0 = DS only, 1 = cooperative DS + PDLP, 2 = batch PDLP only
+  i_t mip_batch_pdlp_reliability_branching{
+    0};  // 0 = DS only, 1 = cooperative DS + PDLP, 2 = batch PDLP only
   i_t strong_branching_simplex_iteration_limit = -1;
   i_t num_gpus                                 = 1;
   bool log_to_console                          = true;

@@ -18,6 +18,8 @@
 
 #include <atomic>
 
+#include <cuda/std/span>
+
 namespace cuopt::linear_programming {
 
 // Forward declare solver_settings_t for friend class
@@ -162,6 +164,12 @@ class pdlp_solver_settings_t {
    * @param[in] initial_primal_weight Initial primal weight.
    */
   void set_initial_primal_weight(f_t initial_primal_weight);
+  /**
+   * @brief Set an initial pdlp iteration.
+   *
+   * @param[in] initial_pdlp_iteration Initial pdlp iteration.
+   */
+  void set_initial_pdlp_iteration(i_t initial_pdlp_iteration);
 
   /**
    * @brief Set the pdlp warm start data. This allows to restart PDLP with a
@@ -228,6 +236,8 @@ class pdlp_solver_settings_t {
   std::optional<f_t> get_initial_step_size() const;
   // TODO batch mode: tmp
   std::optional<f_t> get_initial_primal_weight() const;
+  // TODO batch mode: tmp
+  std::optional<i_t> get_initial_pdlp_iteration() const;
 
   const rmm::device_uvector<f_t>& get_initial_primal_solution() const;
   const rmm::device_uvector<f_t>& get_initial_dual_solution() const;
@@ -280,6 +290,8 @@ class pdlp_solver_settings_t {
   bool inside_mip{false};
   // For concurrent termination
   std::atomic<int>* concurrent_halt{nullptr};
+  // Shared strong branching solved flags for cooperative DS + PDLP
+  cuda::std::span<std::atomic<int>> shared_sb_solved;
   static constexpr f_t minimal_absolute_tolerance = 1.0e-12;
   pdlp_hyper_params::pdlp_hyper_params_t hyper_params;
   // Holds the information of new variable lower and upper bounds for each climber in the format:
@@ -288,6 +300,12 @@ class pdlp_solver_settings_t {
   // concurrently i.e. if new_bounds.size() == 2, then 2 versions of the problem with updated bounds
   // will be solved concurrently
   std::vector<std::tuple<i_t, f_t, f_t>> new_bounds;
+  // By default to save memory and speed we don't store and copy each climber's primal and dual
+  // solutions We only retrieve termination statistics and the objective values
+  bool generate_batch_primal_dual_solution{false};
+  // Used to force batch PDLP to solve a subbatch of the problems at a time
+  // The 0 default value will make the solver use its heuristic to determine the subbatch size
+  i_t sub_batch_size{0};
-  // By default to save memory and speed we don't store and copy each climber's primal and dual
-  // solutions We only retrieve termination statistics and the objective values
-  bool generate_batch_primal_dual_solution{false};
-  // Used to force batch PDLP to solve a subbatch of the problems at a time
-  // The 0 default value will make the solver use its heuristic to determine the subbatch size
-  i_t sub_batch_size{0};
+  // By default to save memory and speed we don't store and copy each climber's primal and dual
+  // solutions We only retrieve termination statistics and the objective values
+  bool generate_batch_primal_dual_solution{true};
+  // Used to force batch PDLP to solve a subbatch of the problems at a time
+  // The 0 default value will make the solver use its heuristic to determine the subbatch size
+  i_t sub_batch_size{0};
-  // By default to save memory and speed we don't store and copy each climber's primal and dual
-  // solutions We only retrieve termination statistics and the objective values
-  bool generate_batch_primal_dual_solution{false};
-  // Used to force batch PDLP to solve a subbatch of the problems at a time
-  // The 0 default value will make the solver use its heuristic to determine the subbatch size
-  i_t sub_batch_size{0};
+  // By default to save memory and speed we don't store and copy each climber's primal and dual
+  // solutions We only retrieve termination statistics and the objective values
+  bool generate_batch_primal_dual_solution{true};
+  // Used to force batch PDLP to solve a subbatch of the problems at a time
+  // The 0 default value will make the solver use its heuristic to determine the subbatch size
+  i_t sub_batch_size{0};
 
  private:
   /** Initial primal solution */
@@ -300,6 +318,9 @@ class pdlp_solver_settings_t {
   /** Initial primal weight */
   // TODO batch mode: tmp
   std::optional<f_t> initial_primal_weight_;
+  /** Initial pdlp iteration */
+  // TODO batch mode: tmp
+  std::optional<i_t> initial_pdlp_iteration_;
   /** GPU-backed warm start data (device_uvector), used by C++ API and local GPU solves */
   pdlp_warm_start_data_t<i_t, f_t> pdlp_warm_start_data_;
   /** Warm start data as spans over external memory, used by Cython/Python interface */

@@ -846,7 +846,9 @@ branch_variable_t<i_t> branch_and_bound_t<i_t, f_t>::variable_selection(
                                                      settings_,
                                                      upper_bound_,
                                                      worker_pool_.num_idle_workers(),
-                                                     log);
+                                                     log,
+                                                     new_slacks_,
+                                                     original_lp_);
       } else {
         branch_var = pc_.variable_selection(fractional, solution, log);
       }
@@ -2503,10 +2505,10 @@ mip_status_t branch_and_bound_t<i_t, f_t>::solve(mip_solution_t<i_t, f_t>& solut
   original_lp_.A.transpose(pc_.AT);
   {
     raft::common::nvtx::range scope_sb("BB::strong_branching");
-    strong_branching<i_t, f_t>(original_problem_,
-                               original_lp_,
+    strong_branching<i_t, f_t>(original_lp_,
                                settings_,
                                exploration_stats_.start_time,
+                               new_slacks_,
                                var_types_,
                                root_relax_soln_,
                                fractional,