diff --git a/kernel_tuner/strategies/dual_annealing.py b/kernel_tuner/strategies/dual_annealing.py
index 598151ea..93c7a746 100644
--- a/kernel_tuner/strategies/dual_annealing.py
+++ b/kernel_tuner/strategies/dual_annealing.py
@@ -1,5 +1,6 @@
 """The strategy that uses the dual annealing optimization method."""
 import scipy.optimize
+import numpy as np
 
 from kernel_tuner.util import StopCriterionReached
 from kernel_tuner.searchspace import Searchspace
@@ -16,7 +17,7 @@ def tune(searchspace: Searchspace, runner, tuning_options):
     method, max_fevals = common.get_options(tuning_options.strategy_options, _options)
 
     #scale variables in x to make 'eps' relevant for multiple variables
-    cost_func = CostFunc(searchspace, tuning_options, runner, scaling=True)
+    cost_func = CostFunc(searchspace, tuning_options, runner, scaling=True, invalid_value=np.inf)
 
     bounds, x0, _ = cost_func.get_bounds_x0_eps()
 
diff --git a/kernel_tuner/strategies/simulated_annealing.py b/kernel_tuner/strategies/simulated_annealing.py
index 962a1e34..ffd8f3bd 100644
--- a/kernel_tuner/strategies/simulated_annealing.py
+++ b/kernel_tuner/strategies/simulated_annealing.py
@@ -96,7 +96,7 @@ def acceptance_prob(old_cost, new_cost, T):
     # if start pos is not valid, always move
     if isinstance(old_cost, ErrorConfig):
         res = 1.0
-    # if we have found a valid ps before, never move to nonvalid pos
+    # if we have found a valid pos before, never move to nonvalid pos
     elif isinstance(new_cost, ErrorConfig):
         res = 0.0
     # always move if new cost is better
@@ -108,7 +108,7 @@ def acceptance_prob(old_cost, new_cost, T):
         abs_diff = old_cost - new_cost
 
         # relative to abs(old_cost), as the cost might be negative
-        rel_diff = abs_diff / np.abs(old_cost)
+        rel_diff = abs_diff / (np.abs(old_cost) if old_cost != 0.0 else 1e-20)
 
         # exponential decay
         res = np.exp(rel_diff / T)