diff --git a/examples/python/single_machine_scheduling_with_setup_release_due_dates_sat.py b/examples/python/single_machine_scheduling_with_setup_release_due_dates_sat.py
index 65b1602631..8e048c0969 100644
--- a/examples/python/single_machine_scheduling_with_setup_release_due_dates_sat.py
+++ b/examples/python/single_machine_scheduling_with_setup_release_due_dates_sat.py
@@ -27,7 +27,7 @@ _OUTPUT_PROTO = flags.DEFINE_string(
 )
 _PARAMS = flags.DEFINE_string(
     "params",
-    "num_search_workers:16,log_search_progress:true,max_time_in_seconds:45",
+    "num_search_workers:16,log_search_progress:false,max_time_in_seconds:45",
     "Sat solver parameters.",
 )
 _PREPROCESS = flags.DEFINE_bool(
@@ -503,6 +503,7 @@ def single_machine_scheduling():
     if parameters:
         text_format.Parse(parameters, solver.parameters)
     solution_printer = SolutionPrinter()
+    solver.best_bound_callback = lambda a : print(f"New objective lower bound: {a}")
     solver.solve(model, solution_printer)
     for job_id in all_jobs:
         print(
diff --git a/ortools/java/com/google/ortools/sat/CpSolver.java b/ortools/java/com/google/ortools/sat/CpSolver.java
index 704bcbdd63..d5f67fbf7b 100644
--- a/ortools/java/com/google/ortools/sat/CpSolver.java
+++ b/ortools/java/com/google/ortools/sat/CpSolver.java
@@ -30,6 +30,7 @@ public final class CpSolver {
   public CpSolver() {
     this.solveParameters = SatParameters.newBuilder();
     this.logCallback = null;
+    this.bestBoundCallback = null;
     this.solveWrapper = null;
   }
 
@@ -52,6 +53,9 @@ public final class CpSolver {
     if (logCallback != null) {
       solveWrapper.addLogCallback(logCallback);
     }
+    if (bestBoundCallback != null) {
+      solveWrapper.addBestBoundCallback(bestBoundCallback);
+    }
 
     solveResponse = solveWrapper.solve(model.model());
 
@@ -201,5 +205,6 @@ public final class CpSolver {
   private CpSolverResponse solveResponse;
   private final SatParameters.Builder solveParameters;
   private Consumer<String> logCallback;
+  private Consumer<Double> bestBoundCallback;
   private SolveWrapper solveWrapper;
 }
diff --git a/ortools/sat/cp_model_checker.cc b/ortools/sat/cp_model_checker.cc
index 35a0a9a9eb..d7e7ca75b5 100644
--- a/ortools/sat/cp_model_checker.cc
+++ b/ortools/sat/cp_model_checker.cc
@@ -28,7 +28,6 @@
 #include "absl/log/check.h"
 #include "absl/meta/type_traits.h"
 #include "absl/strings/str_cat.h"
-#include "absl/strings/string_view.h"
 #include "absl/types/span.h"
 #include "ortools/base/logging.h"
 #include "ortools/port/proto_utils.h"
diff --git a/ortools/sat/cp_model_solver.cc b/ortools/sat/cp_model_solver.cc
index 7e974b5b1d..8a6e3ba340 100644
--- a/ortools/sat/cp_model_solver.cc
+++ b/ortools/sat/cp_model_solver.cc
@@ -1088,6 +1088,7 @@ struct SolutionObservers {
   std::vector<std::function<void(const CpSolverResponse& response)>> observers;
   std::vector<std::function<std::string(const CpSolverResponse& response)>>
       log_callbacks;
+  std::vector<std::function<void(double)>> best_bound_callbacks;
 };
 
 std::function<void(Model*)> NewFeasibleSolutionObserver(
@@ -1105,6 +1106,14 @@ std::function<void(Model*)> NewFeasibleSolutionLogCallback(
   };
 }
 
+std::function<void(Model*)> NewBestBoundCallback(
+    const std::function<void(double)>& callback) {
+  return [=](Model* model) {
+    model->GetOrCreate<SolutionObservers>()->best_bound_callbacks.push_back(
+        callback);
+  };
+}
+
 #if !defined(__PORTABLE_PLATFORM__)
 // TODO(user): Support it on android.
 std::function<SatParameters(Model*)> NewSatParameters(
@@ -4185,6 +4194,12 @@ CpSolverResponse SolveCpModel(const CpModelProto& model_proto, Model* model) {
     shared_response_manager->AddLogCallback(callback);
   }
 
+  const auto& best_bound_callbacks =
+      model->GetOrCreate<SolutionObservers>()->best_bound_callbacks;
+  for (const auto& callback : best_bound_callbacks) {
+    shared_response_manager->AddBestBoundCallback(callback);
+  }
+
   // Make sure everything stops when we have a first solution if requested.
   if (params.stop_after_first_solution()) {
     shared_response_manager->AddSolutionCallback(
diff --git a/ortools/sat/cp_model_solver.h b/ortools/sat/cp_model_solver.h
index c29b468b6b..24fd56cee2 100644
--- a/ortools/sat/cp_model_solver.h
+++ b/ortools/sat/cp_model_solver.h
@@ -103,6 +103,15 @@ std::function<void(Model*)> NewFeasibleSolutionLogCallback(
     const std::function<std::string(const CpSolverResponse& response)>&
         callback);
 
+/** Creates a callbacks that will be called on each new best objective bound
+ *  found.
+ *
+ * Note that adding a callback is not free since some computation will be done
+ * before this is called, and it will only be called on optimization models.
+ */
+std::function<void(Model*)> NewBestBoundCallback(
+    const std::function<void(double)>& callback);
+
 /**
  * Creates parameters for the solver, which you can add to the model with
  * \code
diff --git a/ortools/sat/csharp/CpSolver.cs b/ortools/sat/csharp/CpSolver.cs
index 51203daf66..bdf763b4b2 100644
--- a/ortools/sat/csharp/CpSolver.cs
+++ b/ortools/sat/csharp/CpSolver.cs
@@ -41,6 +41,10 @@ public class CpSolver
         {
             solve_wrapper_.AddLogCallbackFromClass(log_callback_);
         }
+        if (best_bound_callback_ is not null)
+        {
+            solve_wrapper_.AddBestBoundCallbackFromClass(best_bound_callback_);
+        }
         if (cb is not null)
         {
             solve_wrapper_.AddSolutionCallback(cb);
@@ -141,6 +145,11 @@ public class CpSolver
         log_callback_ = new LogCallbackDelegate(del);
     }
 
+    public void SetBestBoundCallback(DoubleToVoidDelegate del)
+    {
+        best_bound_callback_ = new BestBoundCallbackDelegate(del);
+    }
+
     public CpSolverResponse Response
     {
         get {
@@ -283,6 +292,7 @@ public class CpSolver
 
     private CpSolverResponse response_;
     private LogCallback log_callback_;
+    private BestBoundCallback best_bound_callback_;
     private string string_parameters_;
     private SolveWrapper solve_wrapper_;
     private Queue<Term> terms_;
@@ -303,4 +313,19 @@ class LogCallbackDelegate : LogCallback
     private StringToVoidDelegate delegate_;
 }
 
+class BestBoundCallbackDelegate : BestBoundCallback
+{
+    public BestBoundCallbackDelegate(DoubleToVoidDelegate del)
+    {
+        this.delegate_ = del;
+    }
+
+    public override void NewBestBound(double bound)
+    {
+        delegate_(bound);
+    }
+
+    private DoubleToVoidDelegate delegate_;
+}
+
 } // namespace Google.OrTools.Sat
diff --git a/ortools/sat/csharp/sat.i b/ortools/sat/csharp/sat.i
index 1f3dedeffd..ff8c09f0df 100644
--- a/ortools/sat/csharp/sat.i
+++ b/ortools/sat/csharp/sat.i
@@ -39,6 +39,8 @@ using Google.OrTools.Util;
 %typemap(csimports) operations_research::sat::SolveWrapper %{
 // Used to wrap log callbacks (std::function<void(const std::string&>)
 public delegate void StringToVoidDelegate(string message);
+// Used to wrap best bound callbacks (std::function<void(double>)
+public delegate void DoubleToVoidDelegate(double bound);
 %}
 
 PROTO_INPUT(operations_research::sat::CpModelProto,
@@ -82,8 +84,16 @@ JAGGED_MATRIX_AS_CSHARP_ARRAY(int64_t, int64_t, long, Int64VectorVector);
 %unignore operations_research::sat::LogCallback::~LogCallback;
 %unignore operations_research::sat::LogCallback::NewMessage;
 
+// Temporary wrapper class for the DoubleToVoidDelegate.
+%feature("director") operations_research::sat::BestBoundCallback;
+%unignore operations_research::sat::BestBoundCallback;
+%unignore operations_research::sat::BestBoundCallback::~BestBoundCallback;
+%unignore operations_research::sat::BestBoundCallback::NewBestBound;
+
+
 // Wrap the SolveWrapper class.
 %unignore operations_research::sat::SolveWrapper;
+%unignore operations_research::sat::SolveWrapper::AddBestBoundCallbackFromClass;
 %unignore operations_research::sat::SolveWrapper::AddLogCallbackFromClass;
 %unignore operations_research::sat::SolveWrapper::AddSolutionCallback;
 %unignore operations_research::sat::SolveWrapper::ClearSolutionCallback;
diff --git a/ortools/sat/integer_search.cc b/ortools/sat/integer_search.cc
index 7d3d9fcd33..f95de4c846 100644
--- a/ortools/sat/integer_search.cc
+++ b/ortools/sat/integer_search.cc
@@ -256,33 +256,34 @@ std::function<BooleanOrIntegerLiteral()> LpPseudoCostHeuristic(Model* model) {
       // average, it is good anyway?
       if (!is_reliable && is_integer) continue;
 
-      // For Booleans, for some reason it seems the up-branch first work better?
-      if (lb == 0 && ub == 1) {
-        const double score = pseudo_costs->LpPseudoCost(var, lp_value);
-        if (score > best_score) {
-          const LiteralIndex index = encoder->GetAssociatedLiteral(
-              IntegerLiteral::GreaterOrEqual(var, 1));
-          if (index != kNoLiteralIndex) {
-            best_score = score;
-            decision = BooleanOrIntegerLiteral(Literal(index));
-          }
-        }
-      }
-
       // There are some corner cases if we are at the bound. Note that it is
       // important to be in sync with the SplitAroundLpValue() below.
       double down_fractionality = lp_value - std::floor(lp_value);
-      if (lp_value >= ToDouble(ub)) down_fractionality = 1.0;
-      if (lp_value <= ToDouble(lb)) down_fractionality = 0.0;
-      const double score = pseudo_costs->LpPseudoCost(var, down_fractionality);
+      IntegerValue down_target = IntegerValue(std::floor(lp_value));
+      if (lp_value >= ToDouble(ub)) {
+        down_fractionality = 1.0;
+        down_target = ub - 1;
+      } else if (lp_value <= ToDouble(lb)) {
+        down_fractionality = 0.0;
+        down_target = lb;
+      }
+      const auto [down_score, up_score] =
+          pseudo_costs->LpPseudoCost(var, down_fractionality);
+      const double score = pseudo_costs->CombineScores(down_score, up_score);
 
       // We delay to subsequent heuristic if the score is 0.0.
       if (score > best_score) {
         best_score = score;
 
-        // This choose <= value if possible.
-        decision = BooleanOrIntegerLiteral(SplitAroundGivenValue(
-            var, IntegerValue(std::floor(lp_value)), model));
+        // This direction works better than the inverse in the benchs. But
+        // always branching up seems even better. TODO(user): investigate.
+        if (down_score > up_score) {
+          decision = BooleanOrIntegerLiteral(
+              IntegerLiteral::LowerOrEqual(var, down_target));
+        } else {
+          decision = BooleanOrIntegerLiteral(
+              IntegerLiteral::GreaterOrEqual(var, down_target + 1));
+        }
       }
     }
     return decision;
diff --git a/ortools/sat/java/sat.i b/ortools/sat/java/sat.i
index 1f0e32731c..e2c6cad058 100644
--- a/ortools/sat/java/sat.i
+++ b/ortools/sat/java/sat.i
@@ -115,6 +115,40 @@ PROTO2_RETURN(operations_research::sat::CpSolverResponse,
 %typemap(jstype) std::function<void(const std::string&)> "java.util.function.Consumer<String>" // Type used in the Proxy class.
 %typemap(javain) std::function<void(const std::string&)> "$javainput" // passing the Callback to JNI java class.
 
+%typemap(in) std::function<void(double)> %{
+  // $input will be deleted once this function return.
+  // So we create a JNI global reference to keep it alive.
+  jobject $input_object = jenv->NewGlobalRef($input);
+  // and we wrap it in a GlobalRefGuard object which will call the
+  // JNI global reference deleter to avoid leak at destruction.
+  JavaVM* jvm;
+  jenv->GetJavaVM(&jvm);
+  auto $input_guard = std::make_shared<GlobalRefGuard>(jvm, $input_object);
+
+  jclass $input_object_class = jenv->GetObjectClass($input);
+  if (nullptr == $input_object_class) return $null;
+  jmethodID $input_method_id = jenv->GetMethodID(
+    $input_object_class, "accept", "(Ljava/lang/Double;)V");
+  assert($input_method_id != nullptr);
+
+  // When the lambda will be destroyed, input_guard's destructor will be called.
+  $1 = [jvm, $input_object, $input_method_id, $input_guard](
+      double bound) -> void {
+        JNIEnv *jenv = NULL;
+        JavaVMAttachArgs args;
+        args.version = JNI_VERSION_1_2;
+        args.name = NULL;
+        args.group = NULL;
+        jvm->AttachCurrentThread((void**)&jenv, &args);
+        jenv->CallVoidMethod($input_object, $input_method_id, bound);
+        jvm->DetachCurrentThread();
+  };
+%}
+%typemap(jni) std::function<void(double)> "jobject" // Type used in the JNI.java.
+%typemap(jtype) std::function<void(double)> "java.util.function.Consumer<Double>" // Type used in the JNI.java.
+%typemap(jstype) std::function<void(double)> "java.util.function.Consumer<Double>" // Type used in the Proxy class.
+%typemap(javain) std::function<void(double)> "$javainput" // passing the Callback to JNI java class.
+
 %ignoreall
 
 %unignore operations_research;
@@ -122,6 +156,7 @@ PROTO2_RETURN(operations_research::sat::CpSolverResponse,
 
 // Wrap the SolveWrapper class.
 %unignore operations_research::sat::SolveWrapper;
+%rename (addBestBoundCallback) operations_research::sat::SolveWrapper::AddBestBoundCallback;
 %rename (addLogCallback) operations_research::sat::SolveWrapper::AddLogCallback;
 %rename (addSolutionCallback) operations_research::sat::SolveWrapper::AddSolutionCallback;
 %rename (clearSolutionCallback) operations_research::sat::SolveWrapper::ClearSolutionCallback;
diff --git a/ortools/sat/presolve_context.cc b/ortools/sat/presolve_context.cc
index a9fef9c255..5a60479798 100644
--- a/ortools/sat/presolve_context.cc
+++ b/ortools/sat/presolve_context.cc
@@ -1484,22 +1484,21 @@ bool PresolveContext::CanonicalizeEncoding(int* ref, int64_t* value) {
   return true;
 }
 
-bool PresolveContext::InsertVarValueEncoding(int literal, int ref,
+bool PresolveContext::InsertVarValueEncoding(int literal, int var,
                                              int64_t value) {
-  if (!CanonicalizeEncoding(&ref, &value) || !DomainOf(ref).Contains(value)) {
+  if (!CanonicalizeEncoding(&var, &value) || !DomainOf(var).Contains(value)) {
     return SetLiteralToFalse(literal);
   }
   literal = GetLiteralRepresentative(literal);
-  InsertVarValueEncodingInternal(literal, ref, value, /*add_constraints=*/true);
+  InsertVarValueEncodingInternal(literal, var, value, /*add_constraints=*/true);
 
   if (hint_is_loaded_) {
     const int bool_var = PositiveRef(literal);
-    const int int_var = PositiveRef(ref);
-    if (!hint_has_value_[bool_var] && hint_has_value_[int_var]) {
-      const int64_t int_value = RefIsPositive(ref) ? value : -value;
-      const int64_t hint_value = hint_[int_var] == int_value ? 1 : 0;
+    DCHECK(RefIsPositive(var));
+    if (!hint_has_value_[bool_var] && hint_has_value_[var]) {
+      const int64_t bool_value = hint_[var] == value ? 1 : 0;
       hint_has_value_[bool_var] = true;
-      hint_[bool_var] = RefIsPositive(literal) ? hint_value : 1 - hint_value;
+      hint_[bool_var] = RefIsPositive(literal) ? bool_value : 1 - bool_value;
     }
   }
   return true;
diff --git a/ortools/sat/presolve_context.h b/ortools/sat/presolve_context.h
index d81532f929..7b8b8240d3 100644
--- a/ortools/sat/presolve_context.h
+++ b/ortools/sat/presolve_context.h
@@ -365,7 +365,7 @@ class PresolveContext {
   // Clears the "rules" statistics.
   void ClearStats();
 
-  // Inserts the given literal to encode ref == value.
+  // Inserts the given literal to encode var == value.
   // If an encoding already exists, it adds the two implications between
   // the previous encoding and the new encoding.
   //
@@ -376,9 +376,9 @@ class PresolveContext {
   // Returns false if the model become UNSAT.
   //
   // TODO(user): This function is not always correct if
-  // !context->DomainOf(ref).contains(value), we could make it correct but it
+  // !context->DomainOf(var).contains(value), we could make it correct but it
   // might be a bit expansive to do so. For now we just have a DCHECK().
-  bool InsertVarValueEncoding(int literal, int ref, int64_t value);
+  bool InsertVarValueEncoding(int literal, int var, int64_t value);
 
   // Gets the associated literal if it is already created. Otherwise
   // create it, add the corresponding constraints and returns it.
diff --git a/ortools/sat/pseudo_costs.cc b/ortools/sat/pseudo_costs.cc
index 92d4ac95ea..79a17e58de 100644
--- a/ortools/sat/pseudo_costs.cc
+++ b/ortools/sat/pseudo_costs.cc
@@ -18,6 +18,7 @@
 #include <limits>
 #include <string>
 #include <tuple>
+#include <utility>
 #include <vector>
 
 #include "absl/log/check.h"
@@ -38,7 +39,7 @@ namespace operations_research {
 namespace sat {
 
 // We prefer the product to combine the cost of two branches.
-double PseudoCosts::CombineCosts(double down_branch, double up_branch) const {
+double PseudoCosts::CombineScores(double down_branch, double up_branch) const {
   if (true) {
     return std::max(1e-6, down_branch) * std::max(1e-6, up_branch);
   } else {
@@ -96,10 +97,10 @@ void PseudoCosts::BeforeTakingDecision(Literal decision) {
   bound_changes_ = GetBoundChanges(decision);
 }
 
-double PseudoCosts::LpPseudoCost(IntegerVariable var,
-                                 double down_fractionality) const {
+std::pair<double, double> PseudoCosts::LpPseudoCost(
+    IntegerVariable var, double down_fractionality) const {
   const int max_index = std::max(var.value(), NegationOf(var).value());
-  if (max_index >= average_unit_objective_increase_.size()) return 0.0;
+  if (max_index >= average_unit_objective_increase_.size()) return {0.0, 0.0};
 
   const double up_fractionality = 1.0 - down_fractionality;
   const double up_branch =
@@ -107,7 +108,7 @@ double PseudoCosts::LpPseudoCost(IntegerVariable var,
   const double down_branch =
       down_fractionality *
       average_unit_objective_increase_[NegationOf(var)].CurrentAverage();
-  return CombineCosts(down_branch, up_branch);
+  return {down_branch, up_branch};
 }
 
 void PseudoCosts::UpdateBoolPseudoCosts(absl::Span<const Literal> reason,
@@ -132,7 +133,7 @@ double PseudoCosts::BoolPseudoCost(Literal lit, double lp_value) const {
   const double down_branch =
       down_fractionality *
       lit_pseudo_costs_[lit.NegatedIndex()].CurrentAverage();
-  return CombineCosts(down_branch, up_branch);
+  return CombineScores(down_branch, up_branch);
 }
 
 int PseudoCosts::LpReliability(IntegerVariable var) const {
@@ -204,7 +205,7 @@ void PseudoCosts::AfterTakingDecision(bool conflict) {
                           pseudo_costs_[negative_var].NumRecords();
     if (count >= parameters_.pseudo_cost_reliability_threshold()) {
       scores_[positive_var] =
-          CombineCosts(GetCost(positive_var), GetCost(negative_var));
+          CombineScores(GetCost(positive_var), GetCost(negative_var));
       if (!is_relevant_[positive_var]) {
         is_relevant_[positive_var] = true;
         relevant_variables_.push_back(positive_var);
diff --git a/ortools/sat/pseudo_costs.h b/ortools/sat/pseudo_costs.h
index b5b950f4cf..a7b8c0447c 100644
--- a/ortools/sat/pseudo_costs.h
+++ b/ortools/sat/pseudo_costs.h
@@ -61,8 +61,11 @@ class PseudoCosts {
   }
 
   // Alternative pseudo-costs. This relies on the LP more heavily and is more
-  // in line with what a MIP solver would do.
-  double LpPseudoCost(IntegerVariable var, double down_fractionality) const;
+  // in line with what a MIP solver would do. Return the (down, up) costs which
+  // can be combined with CombineScores();
+  double CombineScores(double down_branch, double up_branch) const;
+  std::pair<double, double> LpPseudoCost(IntegerVariable var,
+                                         double down_fractionality) const;
 
   // Returns the pseudo cost "reliability".
   int LpReliability(IntegerVariable var) const;
@@ -83,8 +86,6 @@ class PseudoCosts {
   std::vector<VariableBoundChange> GetBoundChanges(Literal decision);
 
  private:
-  double CombineCosts(double down_branch, double up_branch) const;
-
   // Returns the current objective info.
   struct ObjectiveInfo {
     std::string DebugString() const;
diff --git a/ortools/sat/python/cp_model.py b/ortools/sat/python/cp_model.py
index f09baffbce..9ba1854330 100644
--- a/ortools/sat/python/cp_model.py
+++ b/ortools/sat/python/cp_model.py
@@ -3132,6 +3132,7 @@ class CpSolver:
             sat_parameters_pb2.SatParameters()
         )
         self.log_callback: Optional[Callable[[str], None]] = None
+        self.best_bound_callback: Optional[Callable[[double], None]] = None
         self.__solve_wrapper: Optional[swig_helper.SolveWrapper] = None
         self.__lock: threading.Lock = threading.Lock()
 
@@ -3151,6 +3152,9 @@ class CpSolver:
         if self.log_callback is not None:
             self.__solve_wrapper.add_log_callback(self.log_callback)
 
+        if self.best_bound_callback is not None:
+            self.__solve_wrapper.add_best_bound_callback(self.best_bound_callback)
+
         solution: cp_model_pb2.CpSolverResponse = self.__solve_wrapper.solve(
             model.proto
         )
diff --git a/ortools/sat/python/swig_helper.cc b/ortools/sat/python/swig_helper.cc
index 1a581f0919..5f225cb954 100644
--- a/ortools/sat/python/swig_helper.cc
+++ b/ortools/sat/python/swig_helper.cc
@@ -93,6 +93,8 @@ PYBIND11_MODULE(swig_helper, m) {
       .def("add_solution_callback", &SolveWrapper::AddSolutionCallback,
            arg("callback"))
       .def("clear_solution_callback", &SolveWrapper::ClearSolutionCallback)
+      .def("add_best_bound_callback", &SolveWrapper::AddBestBoundCallback,
+           arg("best_bound_callback"))
       .def("set_parameters", &SolveWrapper::SetParameters, arg("parameters"))
       .def("solve",
            [](SolveWrapper* solve_wrapper,
diff --git a/ortools/sat/swig_helper.cc b/ortools/sat/swig_helper.cc
index 63b664eedd..8488320642 100644
--- a/ortools/sat/swig_helper.cc
+++ b/ortools/sat/swig_helper.cc
@@ -140,6 +140,18 @@ void SolveWrapper::AddLogCallbackFromClass(LogCallback* log_callback) {
       });
 }
 
+void SolveWrapper::AddBestBoundCallback(
+    std::function<void(double)> best_bound_callback) {
+  if (best_bound_callback != nullptr) {
+    model_.Add(NewBestBoundCallback(best_bound_callback));
+  }
+}
+
+void SolveWrapper::AddBestBoundCallbackFromClass(BestBoundCallback* callback) {
+  model_.Add(NewBestBoundCallback(
+      [callback](double bound) { callback->NewBestBound(bound); }));
+}
+
 operations_research::sat::CpSolverResponse SolveWrapper::Solve(
     const operations_research::sat::CpModelProto& model_proto) {
   FixFlagsAndEnvironmentForSwig();
diff --git a/ortools/sat/swig_helper.h b/ortools/sat/swig_helper.h
index b46135c1b0..e9821b620d 100644
--- a/ortools/sat/swig_helper.h
+++ b/ortools/sat/swig_helper.h
@@ -88,6 +88,11 @@ class LogCallback {
   virtual ~LogCallback() = default;
   virtual void NewMessage(const std::string& message) = 0;
 };
+class BestBoundCallback {
+ public:
+  virtual ~BestBoundCallback() = default;
+  virtual void NewBestBound(double bound) = 0;
+};
 
 // This class is not meant to be reused after one solve.
 class SolveWrapper {
@@ -108,9 +113,11 @@ class SolveWrapper {
   void AddSolutionCallback(const SolutionCallback& callback);
   void ClearSolutionCallback(const SolutionCallback& callback);
   void AddLogCallback(std::function<void(const std::string&)> log_callback);
+  void AddBestBoundCallback(std::function<void(double)> best_bound_callback);
 
   // Workaround for C#.
   void AddLogCallbackFromClass(LogCallback* log_callback);
+  void AddBestBoundCallbackFromClass(BestBoundCallback* best_bound_callback);
 
   operations_research::sat::CpSolverResponse Solve(
       const operations_research::sat::CpModelProto& model_proto);
diff --git a/ortools/sat/synchronization.cc b/ortools/sat/synchronization.cc
index 60f266aca7..213d60146c 100644
--- a/ortools/sat/synchronization.cc
+++ b/ortools/sat/synchronization.cc
@@ -304,6 +304,8 @@ void SharedResponseManager::UpdateInnerObjectiveBounds(
 
   const bool change =
       (lb > inner_objective_lower_bound_ || ub < inner_objective_upper_bound_);
+  if (!change) return;
+
   if (lb > inner_objective_lower_bound_) {
     // When the improving problem is infeasible, it is possible to report
     // arbitrary high inner_objective_lower_bound_. We make sure it never cross
@@ -328,21 +330,26 @@ void SharedResponseManager::UpdateInnerObjectiveBounds(
                SatProgressMessage("Done", wall_timer_.Get(), update_info));
     return;
   }
-  if (logger_->LoggingIsEnabled() && change) {
+  if (logger_->LoggingIsEnabled() || !best_bound_callbacks_.empty()) {
     const CpObjectiveProto& obj = *objective_or_null_;
     const double best =
         ScaleObjectiveValue(obj, best_solution_objective_value_);
     double new_lb = ScaleObjectiveValue(obj, inner_objective_lower_bound_);
-    double new_ub = ScaleObjectiveValue(obj, inner_objective_upper_bound_);
-    if (obj.scaling_factor() < 0) {
-      std::swap(new_lb, new_ub);
+    for (const auto& callback_entry : best_bound_callbacks_) {
+      callback_entry.second(new_lb);
+    }
+    if (logger_->LoggingIsEnabled()) {
+      double new_ub = ScaleObjectiveValue(obj, inner_objective_upper_bound_);
+      if (obj.scaling_factor() < 0) {
+        std::swap(new_lb, new_ub);
+      }
+      RegisterObjectiveBoundImprovement(update_info);
+      logger_->ThrottledLog(bounds_logging_id_,
+                            ProgressMessage("Bound", wall_timer_.Get(), best,
+                                            new_lb, new_ub, update_info));
     }
-    RegisterObjectiveBoundImprovement(update_info);
-    logger_->ThrottledLog(bounds_logging_id_,
-                          ProgressMessage("Bound", wall_timer_.Get(), best,
-                                          new_lb, new_ub, update_info));
   }
-  if (change) TestGapLimitsIfNeeded();
+  TestGapLimitsIfNeeded();
 }
 
 // Invariant: the status always start at UNKNOWN and can only evolve as follow:
@@ -473,6 +480,25 @@ void SharedResponseManager::UnregisterLogCallback(int callback_id) {
   LOG(DFATAL) << "Callback id " << callback_id << " not registered.";
 }
 
+int SharedResponseManager::AddBestBoundCallback(
+    std::function<void(double)> callback) {
+  absl::MutexLock mutex_lock(&mutex_);
+  const int id = next_best_bound_callback_id_++;
+  best_bound_callbacks_.emplace_back(id, std::move(callback));
+  return id;
+}
+
+void SharedResponseManager::UnregisterBestBoundCallback(int callback_id) {
+  absl::MutexLock mutex_lock(&mutex_);
+  for (int i = 0; i < best_bound_callbacks_.size(); ++i) {
+    if (best_bound_callbacks_[i].first == callback_id) {
+      best_bound_callbacks_.erase(best_bound_callbacks_.begin() + i);
+      return;
+    }
+  }
+  LOG(DFATAL) << "Callback id " << callback_id << " not registered.";
+}
+
 CpSolverResponse SharedResponseManager::GetResponseInternal(
     absl::Span<const int64_t> variable_values,
     const std::string& solution_info) {
diff --git a/ortools/sat/synchronization.h b/ortools/sat/synchronization.h
index bf310bcf78..b24a651eb4 100644
--- a/ortools/sat/synchronization.h
+++ b/ortools/sat/synchronization.h
@@ -269,6 +269,17 @@ class SharedResponseManager {
       std::function<std::string(const CpSolverResponse&)> callback);
   void UnregisterLogCallback(int callback_id);
 
+  // Adds a callback that will be called on each new best objective bound
+  // found. Returns its id so it can be unregistered if needed.
+  //
+  // Note that adding a callback is not free since some computation will be done
+  // before this is called.
+  //
+  // Note that currently the class is waiting for the callback to finish before
+  // accepting any new updates. That could be changed if needed.
+  int AddBestBoundCallback(std::function<void(double)> callback);
+  void UnregisterBestBoundCallback(int callback_id);
+
   // The "inner" objective is the CpModelProto objective without scaling/offset.
   // Note that these bound correspond to valid bound for the problem of finding
   // a strictly better objective than the current one. Thus the lower bound is
@@ -443,6 +454,10 @@ class SharedResponseManager {
       std::pair<int, std::function<std::string(const CpSolverResponse&)>>>
       search_log_callbacks_ ABSL_GUARDED_BY(mutex_);
 
+  int next_best_bound_callback_id_ ABSL_GUARDED_BY(mutex_) = 0;
+  std::vector<std::pair<int, std::function<void(double)>>> best_bound_callbacks_
+      ABSL_GUARDED_BY(mutex_);
+
   std::vector<std::function<void(std::vector<int64_t>*)>>
       solution_postprocessors_ ABSL_GUARDED_BY(mutex_);
   std::vector<std::function<void(CpSolverResponse*)>> postprocessors_