diff --git a/src/Algorithm/colgen/default.jl b/src/Algorithm/colgen/default.jl
index a03238d3c..ebe416f73 100644
--- a/src/Algorithm/colgen/default.jl
+++ b/src/Algorithm/colgen/default.jl
@@ -949,23 +949,19 @@ end
 
 ColGen.get_master_ip_primal_sol(output::ColGenPhaseOutput) = output.master_ip_primal_sol
 
-ColGen.update_stabilization_after_pricing_optim!(::NoColGenStab, ctx::ColGenContext, generated_columns, master, valid_db, pseudo_db, mast_dual_sol) = nothing
-function ColGen.update_stabilization_after_pricing_optim!(stab::ColGenStab, ctx::ColGenContext, generated_columns, master, valid_db, pseudo_db, mast_dual_sol)
+ColGen.update_stabilization_after_pricing_optim!(::NoColGenStab, ctx::ColGenContext, generated_columns, master, pseudo_db, smooth_dual_sol) = nothing
+function ColGen.update_stabilization_after_pricing_optim!(stab::ColGenStab, ctx::ColGenContext, generated_columns, master, pseudo_db, smooth_dual_sol)
     # At each iteration, we always update α after the first pricing optimization.
     # We don't update α if we are in a misprice sequence.
     if stab.automatic && stab.nb_misprices == 0
         is_min = ColGen.is_minimization(ctx)
         primal_sol = _primal_solution(master, generated_columns, is_min)
-        α = _dynamic_alpha_schedule(stab.base_α, mast_dual_sol, stab.cur_stab_center, subgradient_helper(ctx), primal_sol, is_min)
+        α = _dynamic_alpha_schedule(stab.base_α, smooth_dual_sol, stab.cur_stab_center, subgradient_helper(ctx), primal_sol, is_min)
         stab.base_α = α
     end
     
-    if isbetter(DualBound(master, valid_db), stab.valid_dual_bound)
-        stab.cur_stab_center = mast_dual_sol
-        stab.valid_dual_bound = DualBound(master, valid_db)
-    end
     if isbetter(DualBound(master, pseudo_db), stab.pseudo_dual_bound)
-        stab.stab_center_for_next_iteration = mast_dual_sol
+        stab.stab_center_for_next_iteration = smooth_dual_sol
         stab.pseudo_dual_bound = DualBound(master, pseudo_db)
     end
     return
diff --git a/src/Algorithm/colgen/printer.jl b/src/Algorithm/colgen/printer.jl
index cb4dc9a95..c2cbf5f4f 100644
--- a/src/Algorithm/colgen/printer.jl
+++ b/src/Algorithm/colgen/printer.jl
@@ -28,8 +28,8 @@ ColGen.is_minimization(ctx::ColGenPrinterContext) = ColGen.is_minimization(ctx.i
 ColGen.get_pricing_subprobs(ctx::ColGenPrinterContext) = ColGen.get_pricing_subprobs(ctx.inner)
 
 ColGen.setup_stabilization!(ctx::ColGenPrinterContext, master) = ColGen.setup_stabilization!(ctx.inner, master)
-function ColGen.update_stabilization_after_pricing_optim!(stab, ctx::ColGenPrinterContext, generated_columns, master, valid_db, pseudo_db, mast_dual_sol)
-    return ColGen.update_stabilization_after_pricing_optim!(stab, ctx.inner, generated_columns, master, valid_db, pseudo_db, mast_dual_sol)
+function ColGen.update_stabilization_after_pricing_optim!(stab, ctx::ColGenPrinterContext, generated_columns, master, pseudo_db, smooth_dual_sol)
+    return ColGen.update_stabilization_after_pricing_optim!(stab, ctx.inner, generated_columns, master, pseudo_db, smooth_dual_sol)
 end
 
 ColGen.new_phase_iterator(ctx::ColGenPrinterContext) = ColGen.new_phase_iterator(ctx.inner)
diff --git a/src/ColGen/ColGen.jl b/src/ColGen/ColGen.jl
index ff365affd..6c1f7fe6b 100644
--- a/src/ColGen/ColGen.jl
+++ b/src/ColGen/ColGen.jl
@@ -254,12 +254,13 @@ function run_colgen_iteration!(context, phase, stage, env, ip_primal_sol, stab)
         # pseudo dual bound is used for stabilization only.
         pseudo_db = compute_dual_bound(context, phase, sps_pb, generated_columns, sep_mast_dual_sol)
 
-        update_stabilization_after_pricing_optim!(stab, context, generated_columns, master, valid_db, pseudo_db, mast_dual_sol)
+        update_stabilization_after_pricing_optim!(stab, context, generated_columns, master, pseudo_db, sep_mast_dual_sol)
 
         # We have finished to solve all pricing subproblems.
-        # If we have stabilization, we need to check if we have misprice.
-        # If we have misprice, we need to update the stabilization center and solve again
-        # the pricing subproblems.
+        # If we have stabilization, we need to check if we have misprice, i.e. if smoothing is active 
+        # and no negative reduced cost columns are generated
+        # If we have misprice, we need to update the stabilization center and the smoothed dual solution 
+        # and solve again the pricing subproblems.
         # If we don't have misprice, we can stop the pricing loop.
         misprice = check_misprice(stab, generated_columns, mast_dual_sol)
         if misprice
diff --git a/src/ColGen/stabilization.jl b/src/ColGen/stabilization.jl
index abace6a55..91a182948 100644
--- a/src/ColGen/stabilization.jl
+++ b/src/ColGen/stabilization.jl
@@ -26,11 +26,10 @@ Returns the dual solution used for the pricing in the current column generation
 """
 Updates stabilization after pricing optimization where:
 - `mast_dual_sol` is the dual solution to the master problem
-- `valid_db` is the valid dual bound of the problem after optimization of the pricing problems
 - `pseudo_db` is the pseudo dual bound of the problem after optimization of the pricing problems
-- `mast_dual_sol` is the dual solution to the master problem
+- `smooth_dual_sol` is the current smoothed dual solution
 """
-@mustimplement "ColGenStab" update_stabilization_after_pricing_optim!(stab, ctx, generated_columns, master, valid_db, pseudo_db, mast_dual_sol) = nothing
+@mustimplement "ColGenStab" update_stabilization_after_pricing_optim!(stab, ctx, generated_columns, master, pseudo_db, smooth_dual_sol) = nothing
 
 """
 Updates stabilization after a misprice.
diff --git a/test/unit/ColGen/colgen_iteration.jl b/test/unit/ColGen/colgen_iteration.jl
index b06c4ce05..50bca9606 100644
--- a/test/unit/ColGen/colgen_iteration.jl
+++ b/test/unit/ColGen/colgen_iteration.jl
@@ -221,7 +221,7 @@ function ColGen.compute_dual_bound(::ColGenIterationTestContext, ::ColGenIterati
     return 22.5 - 23/4
 end
 
-ColGen.update_stabilization_after_pricing_optim!(::Coluna.Algorithm.NoColGenStab, ::ColGenIterationTestContext, _, _, _, _, _) = nothing
+ColGen.update_stabilization_after_pricing_optim!(::Coluna.Algorithm.NoColGenStab, ::ColGenIterationTestContext, _, _, _, _) = nothing
 
 struct TestColGenIterationOutput <: ColGen.AbstractColGenIterationOutput
     min_sense::Bool
@@ -274,7 +274,7 @@ function ColGen.new_iteration_output(::Type{<:TestColGenIterationOutput},
     )
 end
 
-ColGen.update_stabilization_after_pricing_optim!(::Coluna.Algorithm.NoColGenStab, ::TestColGenIterationContext, _, _, _, _, _) = nothing
+ColGen.update_stabilization_after_pricing_optim!(::Coluna.Algorithm.NoColGenStab, ::TestColGenIterationContext, _, _, _, _) = nothing
 
 function colgen_iteration_master_ok_pricing_ok()
     ctx = ColGenIterationTestContext()
diff --git a/test/unit/ColGen/colgen_stabilization.jl b/test/unit/ColGen/colgen_stabilization.jl
index 0fb007ea8..8d1106f70 100644
--- a/test/unit/ColGen/colgen_stabilization.jl
+++ b/test/unit/ColGen/colgen_stabilization.jl
@@ -379,8 +379,8 @@ ColGen.get_pricing_strategy(::ColGenStabFlowCtx, phase) = ColGenStabFlowPricingS
 ColGen.pricing_strategy_iterate(::ColGenStabFlowPricingStrategy) = nothing
 ColGen.compute_dual_bound(ctx::ColGenStabFlowCtx, phase, bounds, generated_columns, mast_dual_sol) = ctx.nb_compute_dual_bound += 1
 
-function ColGen.update_stabilization_after_pricing_optim!(stab::ColGenStabFlowStab, ctx, generated_columns, master, valid_db, pseudo_db, mast_dual_sol)
-    @test mast_dual_sol == [1.0, 1.0, 1.0] # we need the out point in this method.
+function ColGen.update_stabilization_after_pricing_optim!(stab::ColGenStabFlowStab, ctx, generated_columns, master, pseudo_db, smooth_dual_sol)
+    @test smooth_dual_sol == [0.5, 0.5, 0.5] # we need the out point in this method.
     stab.nb_update_stab_after_pricing_done += 1
     return true
 end