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Detect when MIP objectives must move in discrete steps. Tighten the dual bound using this info. #1239

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Detect when MIP objectives must move in discrete steps. Tighten the dual bound using this info. #1239

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1 change: 1 addition & 0 deletions cpp/include/cuopt/linear_programming/constants.h
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Original file line number Diff line number Diff line change
Expand Up @@ -68,6 +68,7 @@
#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_OBJECTIVE_STEP "mip_objective_step"
#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"
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1 change: 1 addition & 0 deletions cpp/include/cuopt/linear_programming/mip/solver_settings.hpp
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Expand Up @@ -98,6 +98,7 @@ class mip_solver_settings_t {
i_t implied_bound_cuts = -1;
i_t strong_chvatal_gomory_cuts = -1;
i_t reduced_cost_strengthening = -1;
i_t objective_step = 1; // 0 = disable objective step tightening, 1 = enable
f_t cut_change_threshold = -1.0;
f_t cut_min_orthogonality = 0.5;
i_t mip_batch_pdlp_strong_branching{
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22 changes: 19 additions & 3 deletions cpp/src/branch_and_bound/branch_and_bound.cpp
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Expand Up @@ -1227,7 +1227,13 @@ std::pair<node_status_t, rounding_direction_t> branch_and_bound_t<i_t, f_t>::upd
policy.graphviz(search_tree, node_ptr, "lower bound", leaf_obj);
policy.update_pseudo_costs(node_ptr, leaf_obj);
node_ptr->lower_bound = leaf_obj;
if (original_lp_.objective_is_integral) {
if (original_lp_.objective_step.has_step()) {
f_t step = original_lp_.objective_step.step_size;
f_t bias = original_lp_.objective_step.bias;
// Round up to next value on the lattice: k * step + bias >= leaf_obj
f_t k = std::ceil((leaf_obj - bias) / step - settings_.integer_tol);
node_ptr->lower_bound = k * step + bias;
} else if (original_lp_.objective_is_integral) {
node_ptr->lower_bound = std::ceil(leaf_obj - settings_.integer_tol);
Comment on lines +1230 to 1237
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@coderabbitai coderabbitai Bot May 19, 2026

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⚠️ Potential issue | 🟠 Major | ⚡ Quick win

Fathom against the tightened node bound, not the raw LP objective.

After Lines 1230-1237, node_ptr->lower_bound may already be snapped up to the incumbent lattice value, but the branch/fathom check still uses leaf_obj. That keeps branching nodes that cannot produce a strictly improving integer solution anymore (for example, UB = 2, step = 0.5, leaf_obj = 1.7 snaps to LB = 2.0 and still branches here). Drive this decision from the tightened bound instead.

Also applies to: 1247-1273

🤖 Prompt for AI Agents 
Verify each finding against current code. Fix only still-valid issues, skip the
rest with a brief reason, keep changes minimal, and validate.

In `@cpp/src/branch_and_bound/branch_and_bound.cpp` around lines 1230 - 1237, The
code computes a tightened lattice-aware lower bound into node_ptr->lower_bound
(inside the original_lp_.objective_step/objective_is_integral branches) but the
subsequent fathom/branch decision still uses leaf_obj; update the branch/fathom
comparisons to use node_ptr->lower_bound instead of leaf_obj so decisions are
driven by the tightened bound (replace occurrences of leaf_obj in the
fathom/branch checks near the first block and also in the similar logic in the
1247-1273 section); ensure you keep the same tolerance logic
(settings_.integer_tol) and the existing comparison direction when swapping to
node_ptr->lower_bound.

}
policy.on_optimal_callback(leaf_solution.x, leaf_obj);
Expand Down Expand Up @@ -1345,8 +1351,18 @@ dual::status_t branch_and_bound_t<i_t, f_t>::solve_node_lp(
lp_settings.concurrent_halt = &node_concurrent_halt_;
lp_settings.set_log(false);
f_t cutoff = upper_bound_.load();
if (original_lp_.objective_is_integral) {
lp_settings.cut_off = std::ceil(cutoff - settings_.integer_tol) + settings_.dual_tol;
if (original_lp_.objective_step.has_step()) {
f_t step = original_lp_.objective_step.step_size;
f_t bias = original_lp_.objective_step.bias;
// Any improving feasible solution must have objective <= cutoff - step.
f_t k = std::floor((cutoff - bias) / step + settings_.integer_tol);
lp_settings.cut_off = (k - 1) * step + bias + settings_.dual_tol;
} else if (original_lp_.objective_is_integral) {
// If the objective is integral, any feasible solution should produce an upper bound that is
// (approximately) integral. We add a small tolerance and floor this value to get an integer,
// we then subtract 1, to stop simplex on problems that cannot improve the primal objective.
lp_settings.cut_off =
std::floor(cutoff + settings_.integer_tol) - 1 + settings_.dual_tol;
Comment on lines +1354 to +1365
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@coderabbitai coderabbitai Bot May 19, 2026

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⚠️ Potential issue | 🟠 Major | ⚡ Quick win

The cutoff formula drops one attainable value when cutoff is off-lattice.

(floor((cutoff - bias) / step + tol) - 1) * step + bias is only correct when cutoff is already on the objective lattice. If the incumbent is between lattice points—or just slightly below one because upper_bound_ stores the raw compute_objective(...) sum—you skip the next improving objective as well. The same off-by-one exists in the integral fallback.

Possible fix 
   if (original_lp_.objective_step.has_step()) {
     f_t step = original_lp_.objective_step.step_size;
     f_t bias = original_lp_.objective_step.bias;
-    // Any improving feasible solution must have objective <= cutoff - step.
-    f_t k               = std::floor((cutoff - bias) / step + settings_.integer_tol);
+    // Largest lattice value strictly below `cutoff`.
+    f_t k               = std::ceil((cutoff - bias) / step - settings_.integer_tol);
     lp_settings.cut_off = (k - 1) * step + bias + settings_.dual_tol;
   } else if (original_lp_.objective_is_integral) {
-    lp_settings.cut_off =
-      std::floor(cutoff + settings_.integer_tol) - 1 + settings_.dual_tol;
+    lp_settings.cut_off =
+      std::ceil(cutoff - settings_.integer_tol) - 1 + settings_.dual_tol;
   } else {
🤖 Prompt for AI Agents 
Verify each finding against current code. Fix only still-valid issues, skip the
rest with a brief reason, keep changes minimal, and validate.

In `@cpp/src/branch_and_bound/branch_and_bound.cpp` around lines 1354 - 1365, The
current cutoff computation in the objective_step and integral branches subtracts
an extra 1 (via (k - 1) and -1) which drops the next attainable lattice value
when cutoff is off-lattice; to fix, compute the lattice index k =
std::floor((cutoff - bias) / step + settings_.integer_tol) (for objective_step)
and use lp_settings.cut_off = k * step + bias + settings_.dual_tol (remove the
"-1" adjustment), and in the original_lp_.objective_is_integral fallback use
lp_settings.cut_off = std::floor(cutoff + settings_.integer_tol) +
settings_.dual_tol (remove the "-1"); update code around
original_lp_.objective_step, lp_settings.cut_off, settings_.integer_tol,
settings_.dual_tol, original_lp_.objective_is_integral and k accordingly.

} else {
lp_settings.cut_off = cutoff + settings_.dual_tol;
}
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1 change: 1 addition & 0 deletions cpp/src/dual_simplex/presolve.cpp
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Expand Up @@ -577,6 +577,7 @@ void convert_user_problem(const user_problem_t<i_t, f_t>& user_problem,
problem.obj_scale = user_problem.obj_scale;
problem.obj_constant = user_problem.obj_constant;
problem.objective_is_integral = user_problem.objective_is_integral;
problem.objective_step = user_problem.objective_step;
problem.rhs = user_problem.rhs;
problem.lower = user_problem.lower;
problem.upper = user_problem.upper;
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1 change: 1 addition & 0 deletions cpp/src/dual_simplex/presolve.hpp
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Expand Up @@ -49,6 +49,7 @@ struct lp_problem_t {
f_t obj_constant;
f_t obj_scale; // 1.0 for min, -1.0 for max
bool objective_is_integral{false};
objective_step_t<f_t> objective_step;

void write_mps(const std::string& path) const
{
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11 changes: 11 additions & 0 deletions cpp/src/dual_simplex/user_problem.hpp
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Expand Up @@ -23,6 +23,16 @@ enum class variable_type_t : int8_t {
INTEGER = 2,
};

// The objective function takes values on a lattice: k * step_size + bias
// for integer k. A step_size of 0 means no lattice structure is known.
template <typename f_t>
struct objective_step_t {
f_t step_size{0};
f_t bias{0};

bool has_step() const { return step_size > 0; }
};

template <typename i_t, typename f_t>
struct user_problem_t {
user_problem_t(raft::handle_t const* handle_ptr_)
Expand All @@ -48,6 +58,7 @@ struct user_problem_t {
f_t obj_constant;
f_t obj_scale; // positive for min, netagive for max
bool objective_is_integral{false};
objective_step_t<f_t> objective_step;
std::vector<variable_type_t> var_types;
std::vector<i_t> Q_offsets;
std::vector<i_t> Q_indices;
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1 change: 1 addition & 0 deletions cpp/src/math_optimization/solver_settings.cu
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Expand Up @@ -135,6 +135,7 @@ solver_settings_t<i_t, f_t>::solver_settings_t() : pdlp_settings(), mip_settings
{CUOPT_MIP_IMPLIED_BOUND_CUTS, &mip_settings.implied_bound_cuts, -1, 1, -1},
{CUOPT_MIP_STRONG_CHVATAL_GOMORY_CUTS, &mip_settings.strong_chvatal_gomory_cuts, -1, 1, -1},
{CUOPT_MIP_REDUCED_COST_STRENGTHENING, &mip_settings.reduced_cost_strengthening, -1, std::numeric_limits<i_t>::max(), -1},
{CUOPT_MIP_OBJECTIVE_STEP, &mip_settings.objective_step, 0, 1, 1},
{CUOPT_NUM_GPUS, &pdlp_settings.num_gpus, 1, 2, 1},
{CUOPT_NUM_GPUS, &mip_settings.num_gpus, 1, 2, 1},
{CUOPT_MIP_BATCH_PDLP_STRONG_BRANCHING, &mip_settings.mip_batch_pdlp_strong_branching, 0, 2, 0},
Expand Down
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