Propagate the bounds from the parent to the child nodes

cpp/src/dual_simplex/CMakeLists.txt

@@ -17,6 +17,7 @@ set(DUAL_SIMPLEX_SRC_FILES
   ${CMAKE_CURRENT_SOURCE_DIR}/phase1.cpp
   ${CMAKE_CURRENT_SOURCE_DIR}/phase2.cpp
   ${CMAKE_CURRENT_SOURCE_DIR}/presolve.cpp
+  ${CMAKE_CURRENT_SOURCE_DIR}/bounds_strengthening.cpp
   ${CMAKE_CURRENT_SOURCE_DIR}/primal.cpp
   ${CMAKE_CURRENT_SOURCE_DIR}/pseudo_costs.cpp
   ${CMAKE_CURRENT_SOURCE_DIR}/right_looking_lu.cpp

cpp/src/dual_simplex/bounds_strengthening.cpp

@@ -0,0 +1,290 @@
+/* clang-format off */
+/*
+ * SPDX-FileCopyrightText: Copyright (c) 2025, NVIDIA CORPORATION & AFFILIATES. All rights reserved.
+ * SPDX-License-Identifier: Apache-2.0
+ */
+/* clang-format on */
+
+#include <dual_simplex/bounds_strengthening.hpp>
+
+#include <algorithm>
+#include <cmath>
+
+namespace cuopt::linear_programming::dual_simplex {
+
+template <typename f_t>
+static inline f_t update_lb(f_t curr_lb, f_t coeff, f_t delta_min_act, f_t delta_max_act)
+{
+  auto comp_bnd = (coeff < 0.) ? delta_min_act / coeff : delta_max_act / coeff;
+  return std::max(curr_lb, comp_bnd);
+}
+
+template <typename f_t>
+static inline f_t update_ub(f_t curr_ub, f_t coeff, f_t delta_min_act, f_t delta_max_act)
+{
+  auto comp_bnd = (coeff < 0.) ? delta_max_act / coeff : delta_min_act / coeff;
+  return std::min(curr_ub, comp_bnd);
+}
+
+template <typename i_t, typename f_t>
+static inline bool check_infeasibility(f_t min_a, f_t max_a, f_t cnst_lb, f_t cnst_ub, f_t eps)
+{
+  return (min_a > cnst_ub + eps) || (max_a < cnst_lb - eps);
+}
+
+#define DEBUG_BOUND_STRENGTHENING 0
+
+template <typename i_t, typename f_t>
+void print_bounds_stats(const std::vector<f_t>& lower,
+                        const std::vector<f_t>& upper,
+                        const simplex_solver_settings_t<i_t, f_t>& settings,
+                        const std::string msg)
+{
+#if DEBUG_BOUND_STRENGTHENING
+  f_t lb_norm = 0.0;
+  f_t ub_norm = 0.0;
+
+  i_t sz = lower.size();
+  for (i_t i = 0; i < sz; ++i) {
+    if (std::isfinite(lower[i])) { lb_norm += abs(lower[i]); }
+    if (std::isfinite(upper[i])) { ub_norm += abs(upper[i]); }
+  }
+  settings.log.printf("%s :: lb norm %e, ub norm %e\n", msg.c_str(), lb_norm, ub_norm);
+#endif
+}
+
+template <typename i_t, typename f_t>
+bounds_strengthening_t<i_t, f_t>::bounds_strengthening_t(
+  const lp_problem_t<i_t, f_t>& problem,
+  const csr_matrix_t<i_t, f_t>& Arow,
+  const std::vector<char>& row_sense,
+  const std::vector<variable_type_t>& var_types)
+  : bounds_changed(problem.num_cols, false),
+    A(problem.A),
+    Arow(Arow),
+    var_types(var_types),
+    delta_min_activity(problem.num_rows),
+    delta_max_activity(problem.num_rows),
+    constraint_lb(problem.num_rows),
+    constraint_ub(problem.num_rows)
+{
+  const bool is_row_sense_empty = row_sense.empty();
+  if (is_row_sense_empty) {
+    std::copy(problem.rhs.begin(), problem.rhs.end(), constraint_lb.begin());
+    std::copy(problem.rhs.begin(), problem.rhs.end(), constraint_ub.begin());
+  } else {
+    //  Set the constraint bounds
+    for (i_t i = 0; i < problem.num_rows; ++i) {
+      if (row_sense[i] == 'E') {
+        constraint_lb[i] = problem.rhs[i];
+        constraint_ub[i] = problem.rhs[i];
+      } else if (row_sense[i] == 'L') {
+        constraint_ub[i] = problem.rhs[i];
+        constraint_lb[i] = -inf;
+      } else {
+        constraint_lb[i] = problem.rhs[i];
+        constraint_ub[i] = inf;
+      }
+    }
+  }
+}
+
+template <typename i_t, typename f_t>
+bool bounds_strengthening_t<i_t, f_t>::bounds_strengthening(
+  std::vector<f_t>& lower_bounds,
+  std::vector<f_t>& upper_bounds,
+  const simplex_solver_settings_t<i_t, f_t>& settings)
+{
+  const i_t m = A.m;
+  const i_t n = A.n;
+
+  std::vector<bool> constraint_changed(m, true);
+  std::vector<bool> variable_changed(n, false);
+  std::vector<bool> constraint_changed_next(m, false);
+
+  if (!bounds_changed.empty()) {
+    std::fill(constraint_changed.begin(), constraint_changed.end(), false);
+    for (i_t i = 0; i < n; ++i) {
+      if (bounds_changed[i]) {
+        const i_t row_start = A.col_start[i];
+        const i_t row_end   = A.col_start[i + 1];
+        for (i_t p = row_start; p < row_end; ++p) {
+          const i_t j           = A.i[p];
+          constraint_changed[j] = true;
+        }
+      }
+    }
+  }
+
+  lower = lower_bounds;
+  upper = upper_bounds;
+  print_bounds_stats(lower, upper, settings, "Initial bounds");
+
+  i_t iter             = 0;
+  const i_t iter_limit = 10;
+  while (iter < iter_limit) {
+    for (i_t i = 0; i < m; ++i) {
+      if (!constraint_changed[i]) { continue; }
+      const i_t row_start = Arow.row_start[i];
+      const i_t row_end   = Arow.row_start[i + 1];
+
+      f_t min_a = 0.0;
+      f_t max_a = 0.0;
+      for (i_t p = row_start; p < row_end; ++p) {
+        const i_t j    = Arow.j[p];
+        const f_t a_ij = Arow.x[p];
+
+        variable_changed[j] = true;
+        if (a_ij > 0) {
+          min_a += a_ij * lower[j];
+          max_a += a_ij * upper[j];
+        } else if (a_ij < 0) {
+          min_a += a_ij * upper[j];
+          max_a += a_ij * lower[j];
+        }
+        if (upper[j] == inf && a_ij > 0) { max_a = inf; }
+        if (lower[j] == -inf && a_ij < 0) { max_a = inf; }
+
+        if (lower[j] == -inf && a_ij > 0) { min_a = -inf; }
+        if (upper[j] == inf && a_ij < 0) { min_a = -inf; }
+      }
+
+      f_t cnst_lb = constraint_lb[i];
+      f_t cnst_ub = constraint_ub[i];
+      bool is_infeasible =
+        check_infeasibility<i_t, f_t>(min_a, max_a, cnst_lb, cnst_ub, settings.primal_tol);
+      if (is_infeasible) {
+        settings.log.printf(
+          "Iter:: %d, Infeasible constraint %d, cnst_lb %e, cnst_ub %e, min_a %e, max_a %e\n",
+          iter,
+          i,
+          cnst_lb,
+          cnst_ub,
+          min_a,
+          max_a);
+        return false;
+      }
+
+      delta_min_activity[i] = cnst_ub - min_a;
+      delta_max_activity[i] = cnst_lb - max_a;
+    }
+
+    i_t num_bounds_changed = 0;
+
+    for (i_t k = 0; k < n; ++k) {
+      if (!variable_changed[k]) { continue; }
+      f_t old_lb = lower[k];
+      f_t old_ub = upper[k];
+
+      f_t new_lb = old_lb;
+      f_t new_ub = old_ub;
+
+      const i_t row_start = A.col_start[k];
+      const i_t row_end   = A.col_start[k + 1];
+      for (i_t p = row_start; p < row_end; ++p) {
+        const i_t i = A.i[p];
+
+        if (!constraint_changed[i]) { continue; }
+        const f_t a_ik = A.x[p];
+
+        f_t delta_min_act = delta_min_activity[i];
+        f_t delta_max_act = delta_max_activity[i];
+
+        delta_min_act += (a_ik < 0) ? a_ik * old_ub : a_ik * old_lb;
+        delta_max_act += (a_ik > 0) ? a_ik * old_ub : a_ik * old_lb;
+
+        new_lb = std::max(new_lb, update_lb(old_lb, a_ik, delta_min_act, delta_max_act));
+        new_ub = std::min(new_ub, update_ub(old_ub, a_ik, delta_min_act, delta_max_act));
+      }
+
+      // Integer rounding
+      if (!var_types.empty() &&
+          (var_types[k] == variable_type_t::INTEGER || var_types[k] == variable_type_t::BINARY)) {
+        new_lb = std::ceil(new_lb - settings.integer_tol);
+        new_ub = std::floor(new_ub + settings.integer_tol);
+      }
+
+      bool lb_updated = std::abs(new_lb - old_lb) > 1e3 * settings.primal_tol;
+      bool ub_updated = std::abs(new_ub - old_ub) > 1e3 * settings.primal_tol;
+
+      new_lb = std::max(new_lb, lower_bounds[k]);
+      new_ub = std::min(new_ub, upper_bounds[k]);
+
+      if (new_lb > new_ub + 1e-6) {
+        settings.log.printf(
+          "Iter:: %d, Infeasible variable after update %d, %e > %e\n", iter, k, new_lb, new_ub);
+        return false;
+      }
+      if (new_lb != old_lb || new_ub != old_ub) {
+        for (i_t p = row_start; p < row_end; ++p) {
+          const i_t i                = A.i[p];
+          constraint_changed_next[i] = true;
+        }
+      }
+
+      lower[k] = std::min(new_lb, new_ub);
+      upper[k] = std::max(new_lb, new_ub);
+
+      bool bounds_changed = lb_updated || ub_updated;
+      if (bounds_changed) { num_bounds_changed++; }
+    }
+
+    if (num_bounds_changed == 0) { break; }
+
+    std::swap(constraint_changed, constraint_changed_next);
+    std::fill(constraint_changed_next.begin(), constraint_changed_next.end(), false);
+    std::fill(variable_changed.begin(), variable_changed.end(), false);
+
+    iter++;
+  }
+
+  // settings.log.printf("Total strengthened variables %d\n", total_strengthened_variables);
+
+#if DEBUG_BOUND_STRENGTHENING
+  f_t lb_change      = 0.0;
+  f_t ub_change      = 0.0;
+  int num_lb_changed = 0;
+  int num_ub_changed = 0;
+
+  for (i_t i = 0; i < n; ++i) {
+    if (lower[i] > problem.lower[i] + settings.primal_tol ||
+        (!std::isfinite(problem.lower[i]) && std::isfinite(lower[i]))) {
+      num_lb_changed++;
+      lb_change +=
+        std::isfinite(problem.lower[i])
+          ? (lower[i] - problem.lower[i]) / (1e-6 + std::max(abs(lower[i]), abs(problem.lower[i])))
+          : 1.0;
+    }
+    if (upper[i] < problem.upper[i] - settings.primal_tol ||
+        (!std::isfinite(problem.upper[i]) && std::isfinite(upper[i]))) {
+      num_ub_changed++;
+      ub_change +=
+        std::isfinite(problem.upper[i])
+          ? (problem.upper[i] - upper[i]) / (1e-6 + std::max(abs(problem.upper[i]), abs(upper[i])))
+          : 1.0;
+    }
+  }
+
+  if (num_lb_changed > 0 || num_ub_changed > 0) {
+    settings.log.printf(
+      "lb change %e, ub change %e, num lb changed %d, num ub changed %d, iter %d\n",
+      100 * lb_change / std::max(1, num_lb_changed),
+      100 * ub_change / std::max(1, num_ub_changed),
+      num_lb_changed,
+      num_ub_changed,
+      iter);
+  }
+  print_bounds_stats(lower, upper, settings, "Final bounds");
+#endif
+
+  lower_bounds = lower;
+  upper_bounds = upper;
+
+  return true;
+}
+
+#ifdef DUAL_SIMPLEX_INSTANTIATE_DOUBLE
+template class bounds_strengthening_t<int, double>;
+#endif
+
+}  // namespace cuopt::linear_programming::dual_simplex

cpp/src/dual_simplex/bounds_strengthening.hpp

@@ -0,0 +1,42 @@
+/* clang-format off */
+/*
+ * SPDX-FileCopyrightText: Copyright (c) 2025, NVIDIA CORPORATION & AFFILIATES. All rights reserved.
+ * SPDX-License-Identifier: Apache-2.0
+ */
+/* clang-format on */
+
+#pragma once
+
+#include <dual_simplex/presolve.hpp>
+
+namespace cuopt::linear_programming::dual_simplex {
+
+template <typename i_t, typename f_t>
+class bounds_strengthening_t {
+ public:
+  // For pure LP bounds strengthening, var_types should be defaulted (i.e. left empty)
+  bounds_strengthening_t(const lp_problem_t<i_t, f_t>& problem,
+                         const csr_matrix_t<i_t, f_t>& Arow,
+                         const std::vector<char>& row_sense,
+                         const std::vector<variable_type_t>& var_types);
+
+  bool bounds_strengthening(std::vector<f_t>& lower_bounds,
+                            std::vector<f_t>& upper_bounds,
+                            const simplex_solver_settings_t<i_t, f_t>& settings);
+
+  std::vector<bool> bounds_changed;
+
+ private:
+  const csc_matrix_t<i_t, f_t>& A;
+  const csr_matrix_t<i_t, f_t>& Arow;
+  const std::vector<variable_type_t>& var_types;
+
+  std::vector<f_t> lower;
+  std::vector<f_t> upper;
+
+  std::vector<f_t> delta_min_activity;
+  std::vector<f_t> delta_max_activity;
+  std::vector<f_t> constraint_lb;
+  std::vector<f_t> constraint_ub;
+};
+}  // namespace cuopt::linear_programming::dual_simplex