diff --git a/smt/applications/tests/test_ego.py b/smt/applications/tests/test_ego.py
index 24c07da4d..71766801e 100644
--- a/smt/applications/tests/test_ego.py
+++ b/smt/applications/tests/test_ego.py
@@ -11,7 +11,7 @@
 import os
 import unittest
 import numpy as np
-from sys import argv
+from sys import argv, platform
 
 try:
     import matplotlib
@@ -1005,11 +1005,15 @@ def f_obj(X):
         )
         x_opt, y_opt, dnk, x_data, y_data = ego.optimize(fun=f_obj)
         if ds.HAS_CONFIG_SPACE:  # results differs wrt config_space impl
-            self.assertAlmostEqual(np.sum(y_data), 2.7639515433083854, delta=1e-4)
-            self.assertAlmostEqual(np.sum(x_data), 32.11001423996299, delta=1e-4)
+            if platform.startswith("linux"):  # results differs wrt platform
+                self.assertAlmostEqual(np.sum(y_data), 1.0355815090110578, delta=1e-12)
+                self.assertAlmostEqual(np.sum(x_data), 38.56885202767958, delta=1e-12)
+            else:
+                self.assertAlmostEqual(np.sum(y_data), 0.9606415626557894, delta=1e-12)
+                self.assertAlmostEqual(np.sum(x_data), 38.23494224077761, delta=1e-12)
         else:
-            self.assertAlmostEqual(np.sum(y_data), 2.03831406306514, delta=1e-4)
-            self.assertAlmostEqual(np.sum(x_data), 33.56885202767958, delta=1e-4)
+            self.assertAlmostEqual(np.sum(y_data), 1.8911720770059735, delta=1e-12)
+            self.assertAlmostEqual(np.sum(x_data), 47.56885202767958, delta=1e-12)
 
     def test_ego_gek(self):
         ego, fun = self.initialize_ego_gek()
diff --git a/smt/surrogate_models/krg_based.py b/smt/surrogate_models/krg_based.py
index 98fcc2e3e..9a912d0d2 100644
--- a/smt/surrogate_models/krg_based.py
+++ b/smt/surrogate_models/krg_based.py
@@ -191,6 +191,8 @@ def _initialize(self):
         self.best_iteration_fail = None
         self.nb_ill_matrix = 5
         self.is_acting_points = {}
+        # Make internal optim multistart reproducible
+        self.random_state = np.random.RandomState(41)
         supports["derivatives"] = True
         supports["variances"] = True
         supports["variance_derivatives"] = True
@@ -1741,7 +1743,7 @@ def grad_minus_reduced_likelihood_function(log10t):
                 # to theta in (0,2e1]
                 theta_bounds = self.options["theta_bounds"]
                 if self.theta0[i] < theta_bounds[0] or self.theta0[i] > theta_bounds[1]:
-                    self.theta0[i] = np.random.rand()
+                    self.theta0[i] = self.random_state.rand()
                     self.theta0[i] = (
                         self.theta0[i] * (theta_bounds[1] - theta_bounds[0])
                         + theta_bounds[0]
@@ -1770,7 +1772,7 @@ def grad_minus_reduced_likelihood_function(log10t):
             else:
                 theta_bounds = self.options["theta_bounds"]
                 log10t_bounds = np.log10(theta_bounds)
-                theta0_rand = np.random.rand(len(self.theta0))
+                theta0_rand = self.random_state.rand(len(self.theta0))
                 theta0_rand = (
                     theta0_rand * (log10t_bounds[1] - log10t_bounds[0])
                     + log10t_bounds[0]
@@ -1829,7 +1831,9 @@ def grad_minus_reduced_likelihood_function(log10t):
 
                 if self.options["n_start"] > 1:
                     sampling = LHS(
-                        xlimits=theta_limits, criterion="maximin", random_state=41
+                        xlimits=theta_limits,
+                        criterion="maximin",
+                        random_state=self.random_state,
                     )
                     theta_lhs_loops = sampling(self.options["n_start"])
                     theta_all_loops = np.vstack((theta_all_loops, theta_lhs_loops))
diff --git a/smt/tests/test_kpls_auto.py b/smt/tests/test_kpls_auto.py
index c4213ad64..d561d415a 100644
--- a/smt/tests/test_kpls_auto.py
+++ b/smt/tests/test_kpls_auto.py
@@ -7,6 +7,7 @@
 import numpy as np
 import unittest
 import inspect
+from sys import platform
 
 from collections import OrderedDict
 
@@ -35,8 +36,6 @@ def setUp(self):
         problems["exp"] = TensorProduct(ndim=ndim, func="exp")
         problems["tanh"] = TensorProduct(ndim=ndim, func="tanh")
         problems["cos"] = TensorProduct(ndim=ndim, func="cos")
-        sms = OrderedDict()
-        sms["KPLS"] = KPLS(eval_n_comp=True)
 
         t_errors = {}
         e_errors = {}
@@ -47,14 +46,16 @@ def setUp(self):
         n_comp_opt["Branin"] = 2
         n_comp_opt["Rosenbrock"] = 1
         n_comp_opt["sphere"] = 1
-        n_comp_opt["exp"] = 3
+        if platform.startswith("linux"):  # result depends on platform
+            n_comp_opt["exp"] = 2
+        else:
+            n_comp_opt["exp"] = 3
         n_comp_opt["tanh"] = 1
         n_comp_opt["cos"] = 1
 
         self.nt = nt
         self.ne = ne
         self.problems = problems
-        self.sms = sms
         self.t_errors = t_errors
         self.e_errors = e_errors
         self.n_comp_opt = n_comp_opt
@@ -68,15 +69,13 @@ def run_test(self):
 
         sampling = LHS(xlimits=prob.xlimits, random_state=42)
 
-        np.random.seed(0)
         xt = sampling(self.nt)
         yt = prob(xt)
 
-        np.random.seed(1)
         xe = sampling(self.ne)
         ye = prob(xe)
 
-        sm0 = self.sms[sname]
+        sm0 = KPLS(eval_n_comp=True)
 
         sm = sm0.__class__()
         sm.options = sm0.options.clone()