diff --git a/doc-sources/reference/lincs.rst b/doc-sources/reference/lincs.rst
index f9af061e..2902fd49 100644
--- a/doc-sources/reference/lincs.rst
+++ b/doc-sources/reference/lincs.rst
@@ -865,10 +865,15 @@
 
                     Indexed by ``[model_index][boundary_index][criterion_index]``. The current rank of each low profile, for each model and criterion.
 
+                .. property:: high_profile_rank_indexes
+                    :type: list[unsigned]
+
+                    Indexed by ``[criterion_index]``. The index in ``high_profile_ranks``, for each single-peaked criterion.
+
                 .. property:: high_profile_ranks
                     :type: list[list[list[int]]]
 
-                    Indexed by ``[model_index][boundary_index][criterion_index]``. The current rank of each high profile, for each model and criterion.
+                    Indexed by ``[model_index][boundary_index][high_profile_rank_indexes[criterion_index]]``. The current rank of each high profile, for each model and single-peaked criterion.
 
                 .. property:: accuracies
                     :type: list[int]
diff --git a/doc-sources/reference/lincs.yml b/doc-sources/reference/lincs.yml
index 6dad2b5a..81834de1 100644
--- a/doc-sources/reference/lincs.yml
+++ b/doc-sources/reference/lincs.yml
@@ -360,6 +360,8 @@ children:
               type: list[list[int]]
             - name: low_profile_ranks
               type: list[list[list[int]]]
+            - name: high_profile_rank_indexes
+              type: list[unsigned]
             - name: high_profile_ranks
               type: list[list[list[int]]]
             - name: accuracies
diff --git a/integration-tests/dir-all/liblincs.txt b/integration-tests/dir-all/liblincs.txt
index 4a2ab858..daf3329d 100644
--- a/integration-tests/dir-all/liblincs.txt
+++ b/integration-tests/dir-all/liblincs.txt
@@ -204,6 +204,7 @@ liblincs: module
             criteria_count: property
             get_best_accuracy: instancemethod
             get_best_model: instancemethod
+            high_profile_rank_indexes: property
             high_profile_ranks: property
             iteration_index: property
             low_profile_ranks: property
diff --git a/integration-tests/dir-all/lincs.txt b/integration-tests/dir-all/lincs.txt
index ea066370..05960945 100644
--- a/integration-tests/dir-all/lincs.txt
+++ b/integration-tests/dir-all/lincs.txt
@@ -184,6 +184,7 @@ lincs: module
                 criteria_count: property
                 get_best_accuracy: instancemethod
                 get_best_model: instancemethod
+                high_profile_rank_indexes: property
                 high_profile_ranks: property
                 iteration_index: property
                 low_profile_ranks: property
diff --git a/lincs/liblincs/learning/mrsort-by-weights-profiles-breed.cpp b/lincs/liblincs/learning/mrsort-by-weights-profiles-breed.cpp
index 00ce25dd..37283720 100644
--- a/lincs/liblincs/learning/mrsort-by-weights-profiles-breed.cpp
+++ b/lincs/liblincs/learning/mrsort-by-weights-profiles-breed.cpp
@@ -26,7 +26,8 @@ LearnMrsortByWeightsProfilesBreed::LearningData::LearningData(
   model_indexes(models_count),
   accuracies(models_count, zeroed),
   low_profile_ranks(models_count, boundaries_count, criteria_count, uninitialized),
-  high_profile_ranks(models_count, boundaries_count, criteria_count, uninitialized),
+  high_profile_rank_indexes(criteria_count, uninitialized),
+  high_profile_ranks(models_count, boundaries_count, count_single_peaked_criteria(), uninitialized),
   weights(models_count, criteria_count, uninitialized)
 {
   CHRONE();
@@ -36,6 +37,25 @@ LearnMrsortByWeightsProfilesBreed::LearningData::LearningData(
   for (unsigned model_index = 0; model_index != models_count; ++model_index) {
     random_generators[model_index].seed(random_seed * (model_index + 1));
   }
+
+  unsigned count = 0;
+  for (unsigned criterion_index = 0; criterion_index != criteria_count; ++criterion_index) {
+    if (single_peaked[criterion_index]) {
+      high_profile_rank_indexes[criterion_index] = count;
+      ++count;
+    }
+  }
+  assert(high_profile_ranks.s0() == count);
+}
+
+unsigned LearnMrsortByWeightsProfilesBreed::LearningData::count_single_peaked_criteria() const {
+  unsigned count = 0;
+  for (unsigned criterion_index = 0; criterion_index != criteria_count; ++criterion_index) {
+    if (single_peaked[criterion_index]) {
+      ++count;
+    }
+  }
+  return count;
 }
 
 Model LearnMrsortByWeightsProfilesBreed::LearningData::get_model(const unsigned model_index) const {
@@ -57,8 +77,8 @@ Model LearnMrsortByWeightsProfilesBreed::LearningData::get_model(const unsigned
     boundary_profile.reserve(criteria_count);
     for (unsigned criterion_index = 0; criterion_index != criteria_count; ++criterion_index) {
       const unsigned low_profile_rank = low_profile_ranks[model_index][boundary_index][criterion_index];
-      const unsigned high_profile_rank = high_profile_ranks[model_index][boundary_index][criterion_index];
       if (single_peaked[criterion_index]) {
+        const unsigned high_profile_rank = high_profile_ranks[model_index][boundary_index][high_profile_rank_indexes[criterion_index]];
         boundary_profile.push_back(std::make_pair(low_profile_rank, high_profile_rank));
       } else {
         boundary_profile.push_back(low_profile_rank);
@@ -176,7 +196,7 @@ bool LearnMrsortByWeightsProfilesBreed::is_accepted(
   const unsigned alternative_rank = learning_data.performance_ranks[criterion_index][alternative_index];
   const unsigned low_profile_rank = learning_data.low_profile_ranks[model_index][boundary_index][criterion_index];
   if (learning_data.single_peaked[criterion_index]) {
-    const unsigned high_profile_rank = learning_data.high_profile_ranks[model_index][boundary_index][criterion_index];
+    const unsigned high_profile_rank = learning_data.high_profile_ranks[model_index][boundary_index][learning_data.high_profile_rank_indexes[criterion_index]];
     return low_profile_rank <= alternative_rank && alternative_rank <= high_profile_rank;
   } else {
     return low_profile_rank <= alternative_rank;
diff --git a/lincs/liblincs/learning/mrsort-by-weights-profiles-breed.hpp b/lincs/liblincs/learning/mrsort-by-weights-profiles-breed.hpp
index 9efed930..179f7155 100644
--- a/lincs/liblincs/learning/mrsort-by-weights-profiles-breed.hpp
+++ b/lincs/liblincs/learning/mrsort-by-weights-profiles-breed.hpp
@@ -71,7 +71,8 @@ struct LearnMrsortByWeightsProfilesBreed::LearningData : public PreProcessedLear
   std::vector<unsigned> model_indexes;  // [model_index_index]: this is a reordering of the models' indexes
   Array1D<Host, unsigned> accuracies;  // [model_index]
   Array3D<Host, unsigned> low_profile_ranks;  // [model_index][boundary_index][criterion_index]
-  Array3D<Host, unsigned> high_profile_ranks;  // [model_index][boundary_index][criterion_index]
+  Array1D<Host, unsigned> high_profile_rank_indexes;  // [criterion_index], meaningful only for single-peaked criteria (i.e. when single_peaked[criterion_index] is true)
+  Array3D<Host, unsigned> high_profile_ranks;  // [model_index][boundary_index][high_profile_rank_indexes[criterion_index]]
   Array2D<Host, float> weights;  // [model_index][criterion_index]
   // @todo(Performance, later) Add models' ages
 
@@ -86,6 +87,9 @@ struct LearnMrsortByWeightsProfilesBreed::LearningData : public PreProcessedLear
   bool model_is_correct(unsigned model_index) const;
   bool models_are_correct() const;
   #endif
+
+ private:
+  unsigned count_single_peaked_criteria() const;
 };
 
 struct LearnMrsortByWeightsProfilesBreed::ProfilesInitializationStrategy {
diff --git a/lincs/liblincs/learning/mrsort-by-weights-profiles-breed/improve-profiles/accuracy-heuristic-on-cpu.cpp b/lincs/liblincs/learning/mrsort-by-weights-profiles-breed/improve-profiles/accuracy-heuristic-on-cpu.cpp
index bee215c5..90ec7237 100644
--- a/lincs/liblincs/learning/mrsort-by-weights-profiles-breed/improve-profiles/accuracy-heuristic-on-cpu.cpp
+++ b/lincs/liblincs/learning/mrsort-by-weights-profiles-breed/improve-profiles/accuracy-heuristic-on-cpu.cpp
@@ -57,6 +57,8 @@ void ImproveProfilesWithAccuracyHeuristicOnCpu::improve_low_profile_then_high_pr
   const unsigned boundary_index,
   const unsigned criterion_index
 ) {
+  assert(learning_data.single_peaked[criterion_index]);
+
   improve_low_profile(
     model_index,
     boundary_index,
@@ -65,7 +67,7 @@ void ImproveProfilesWithAccuracyHeuristicOnCpu::improve_low_profile_then_high_pr
       0 :
       learning_data.low_profile_ranks[model_index][boundary_index - 1][criterion_index],
     boundary_index == learning_data.boundaries_count - 1 ?
-      learning_data.high_profile_ranks[model_index][boundary_index][criterion_index]:
+      learning_data.high_profile_ranks[model_index][boundary_index][learning_data.high_profile_rank_indexes[criterion_index]]:
       learning_data.low_profile_ranks[model_index][boundary_index + 1][criterion_index]
   );
 
@@ -75,10 +77,10 @@ void ImproveProfilesWithAccuracyHeuristicOnCpu::improve_low_profile_then_high_pr
     criterion_index,
     boundary_index == learning_data.boundaries_count - 1 ?
       learning_data.low_profile_ranks[model_index][boundary_index][criterion_index] :
-      learning_data.high_profile_ranks[model_index][boundary_index + 1][criterion_index],
+      learning_data.high_profile_ranks[model_index][boundary_index + 1][learning_data.high_profile_rank_indexes[criterion_index]],
     boundary_index == 0 ?
       learning_data.values_counts[criterion_index] - 1 :
-      learning_data.high_profile_ranks[model_index][boundary_index - 1][criterion_index]
+      learning_data.high_profile_ranks[model_index][boundary_index - 1][learning_data.high_profile_rank_indexes[criterion_index]]
   );
 }
 
@@ -307,11 +309,12 @@ void ImproveProfilesWithAccuracyHeuristicOnCpu::improve_high_profile(
   const unsigned lowest_destination_rank,
   const unsigned highest_destination_rank
 ) {
+  assert(learning_data.single_peaked[criterion_index]);
   assert(lowest_destination_rank <= highest_destination_rank);
   if (lowest_destination_rank == highest_destination_rank) {
-    assert(learning_data.high_profile_ranks[model_index][boundary_index][criterion_index] == lowest_destination_rank);
+    assert(learning_data.high_profile_ranks[model_index][boundary_index][learning_data.high_profile_rank_indexes[criterion_index]] == lowest_destination_rank);
   } else {
-    unsigned best_destination_rank = learning_data.high_profile_ranks[model_index][boundary_index][criterion_index];
+    unsigned best_destination_rank = learning_data.high_profile_ranks[model_index][boundary_index][learning_data.high_profile_rank_indexes[criterion_index]];
     float best_desirability = Desirability().value();
 
     if (highest_destination_rank - lowest_destination_rank >= max_destinations_count) {
@@ -342,7 +345,7 @@ void ImproveProfilesWithAccuracyHeuristicOnCpu::improve_high_profile(
     }
 
     if (std::uniform_real_distribution<float>(0, 1)(learning_data.random_generators[model_index]) <= best_desirability) {
-      learning_data.high_profile_ranks[model_index][boundary_index][criterion_index] = best_destination_rank;
+      learning_data.high_profile_ranks[model_index][boundary_index][learning_data.high_profile_rank_indexes[criterion_index]] = best_destination_rank;
     }
   }
 }
@@ -376,7 +379,8 @@ void ImproveProfilesWithAccuracyHeuristicOnCpu::update_move_desirability_for_hig
   const unsigned alternative_index,
   Desirability* desirability
 ) {
-  const unsigned current_rank = learning_data.high_profile_ranks[model_index][boundary_index][criterion_index];
+  assert(learning_data.single_peaked[criterion_index]);
+  const unsigned current_rank = learning_data.high_profile_ranks[model_index][boundary_index][learning_data.high_profile_rank_indexes[criterion_index]];
   const float weight = learning_data.weights[model_index][criterion_index];
 
   const unsigned alternative_rank = learning_data.performance_ranks[criterion_index][alternative_index];
diff --git a/lincs/liblincs/learning/mrsort-by-weights-profiles-breed/improve-profiles/accuracy-heuristic-on-gpu.cu b/lincs/liblincs/learning/mrsort-by-weights-profiles-breed/improve-profiles/accuracy-heuristic-on-gpu.cu
index d57353f1..8d7b4eac 100644
--- a/lincs/liblincs/learning/mrsort-by-weights-profiles-breed/improve-profiles/accuracy-heuristic-on-gpu.cu
+++ b/lincs/liblincs/learning/mrsort-by-weights-profiles-breed/improve-profiles/accuracy-heuristic-on-gpu.cu
@@ -16,6 +16,7 @@ bool is_accepted(
   const ArrayView2D<Device, const unsigned> performance_ranks,
   const ArrayView1D<Device, const bool> single_peaked,
   const ArrayView3D<Device, const unsigned> low_profile_ranks,
+  const ArrayView1D<Device, const unsigned> high_profile_rank_indexes,
   const ArrayView3D<Device, const unsigned> high_profile_ranks,
   const unsigned model_index,
   const unsigned boundary_index,
@@ -25,7 +26,7 @@ bool is_accepted(
   const unsigned alternative_rank = performance_ranks[criterion_index][alternative_index];
   const unsigned low_profile_rank = low_profile_ranks[model_index][boundary_index][criterion_index];
   if (single_peaked[criterion_index]) {
-    const unsigned high_profile_rank = high_profile_ranks[model_index][boundary_index][criterion_index];
+    const unsigned high_profile_rank = high_profile_ranks[model_index][boundary_index][high_profile_rank_indexes[criterion_index]];
     return low_profile_rank <= alternative_rank && alternative_rank <= high_profile_rank;
   } else {
     return low_profile_rank <= alternative_rank;
@@ -38,6 +39,7 @@ unsigned get_assignment(
   const ArrayView2D<Device, const float> weights,
   const ArrayView1D<Device, const bool> single_peaked,
   const ArrayView3D<Device, const unsigned> low_profile_ranks,
+  const ArrayView1D<Device, const unsigned> high_profile_rank_indexes,
   const ArrayView3D<Device, const unsigned> high_profile_ranks,
   const unsigned model_index,
   const unsigned alternative_index
@@ -52,7 +54,7 @@ unsigned get_assignment(
     const unsigned boundary_index = category_index - 1;
     float accepted_weight = 0;
     for (unsigned criterion_index = 0; criterion_index != criteria_count; ++criterion_index) {
-      if (is_accepted(performance_ranks, single_peaked, low_profile_ranks, high_profile_ranks, model_index, boundary_index, criterion_index, alternative_index)) {
+      if (is_accepted(performance_ranks, single_peaked, low_profile_ranks, high_profile_rank_indexes, high_profile_ranks, model_index, boundary_index, criterion_index, alternative_index)) {
         accepted_weight += weights[model_index][criterion_index];
       }
     }
@@ -70,6 +72,7 @@ void update_move_desirability_for_low_profile(
   const ArrayView2D<Device, const float> weights,
   const ArrayView1D<Device, const bool> single_peaked,
   const ArrayView3D<Device, const unsigned> low_profile_ranks,
+  const ArrayView1D<Device, const unsigned> high_profile_rank_indexes,
   const ArrayView3D<Device, const unsigned> high_profile_ranks,
   const unsigned model_index,
   const unsigned boundary_index,
@@ -91,6 +94,7 @@ void update_move_desirability_for_low_profile(
     weights,
     single_peaked,
     low_profile_ranks,
+    high_profile_rank_indexes,
     high_profile_ranks,
     model_index,
     alternative_index);
@@ -98,7 +102,7 @@ void update_move_desirability_for_low_profile(
   float accepted_weight = 0;
   // There is a 'criterion_index' parameter above, *and* a local 'crit_index' just here
   for (unsigned crit_index = 0; crit_index != criteria_count; ++crit_index) {
-    if (is_accepted(performance_ranks, single_peaked, low_profile_ranks, high_profile_ranks, model_index, boundary_index, crit_index, alternative_index)) {
+    if (is_accepted(performance_ranks, single_peaked, low_profile_ranks, high_profile_rank_indexes, high_profile_ranks, model_index, boundary_index, crit_index, alternative_index)) {
       accepted_weight += weights[model_index][crit_index];
     }
   }
@@ -202,6 +206,7 @@ void compute_move_desirabilities_for_low_profile__kernel(
   const ArrayView2D<Device, const float> weights,
   const ArrayView1D<Device, const bool> single_peaked,
   const ArrayView3D<Device, const unsigned> low_profile_ranks,
+  const ArrayView1D<Device, const unsigned> high_profile_rank_indexes,
   const ArrayView3D<Device, const unsigned> high_profile_ranks,
   const unsigned model_index,
   const unsigned boundary_index,
@@ -223,6 +228,7 @@ void compute_move_desirabilities_for_low_profile__kernel(
       weights,
       single_peaked,
       low_profile_ranks,
+      high_profile_rank_indexes,
       high_profile_ranks,
       model_index,
       boundary_index,
@@ -270,6 +276,7 @@ void update_move_desirability_for_high_profile(
   const ArrayView2D<Device, const float> weights,
   const ArrayView1D<Device, const bool> single_peaked,
   const ArrayView3D<Device, const unsigned> low_profile_ranks,
+  const ArrayView1D<Device, const unsigned> high_profile_rank_indexes,
   const ArrayView3D<Device, const unsigned> high_profile_ranks,
   const unsigned model_index,
   const unsigned boundary_index,
@@ -281,7 +288,7 @@ void update_move_desirability_for_high_profile(
   const unsigned alternatives_count = performance_ranks.s0();
   const unsigned criteria_count = performance_ranks.s1();
 
-  const unsigned current_rank = high_profile_ranks[model_index][boundary_index][criterion_index];
+  const unsigned current_rank = high_profile_ranks[model_index][boundary_index][high_profile_rank_indexes[criterion_index]];
   const float weight = weights[model_index][criterion_index];
 
   const unsigned alternative_rank = performance_ranks[criterion_index][alternative_index];
@@ -291,6 +298,7 @@ void update_move_desirability_for_high_profile(
     weights,
     single_peaked,
     low_profile_ranks,
+    high_profile_rank_indexes,
     high_profile_ranks,
     model_index,
     alternative_index);
@@ -298,7 +306,7 @@ void update_move_desirability_for_high_profile(
   float accepted_weight = 0;
   // There is a 'criterion_index' parameter above, *and* a local 'crit_index' just here
   for (unsigned crit_index = 0; crit_index != criteria_count; ++crit_index) {
-    if (is_accepted(performance_ranks, single_peaked, low_profile_ranks, high_profile_ranks, model_index, boundary_index, crit_index, alternative_index)) {
+    if (is_accepted(performance_ranks, single_peaked, low_profile_ranks, high_profile_rank_indexes, high_profile_ranks, model_index, boundary_index, crit_index, alternative_index)) {
       accepted_weight += weights[model_index][crit_index];
     }
   }
@@ -402,6 +410,7 @@ void compute_move_desirabilities_for_high_profile__kernel(
   const ArrayView2D<Device, const float> weights,
   const ArrayView1D<Device, const bool> single_peaked,
   const ArrayView3D<Device, const unsigned> low_profile_ranks,
+  const ArrayView1D<Device, const unsigned> high_profile_rank_indexes,
   const ArrayView3D<Device, const unsigned> high_profile_ranks,
   const unsigned model_index,
   const unsigned boundary_index,
@@ -423,6 +432,7 @@ void compute_move_desirabilities_for_high_profile__kernel(
       weights,
       single_peaked,
       low_profile_ranks,
+      high_profile_rank_indexes,
       high_profile_ranks,
       model_index,
       boundary_index,
@@ -435,6 +445,7 @@ void compute_move_desirabilities_for_high_profile__kernel(
 
 __global__
 void apply_best_move_for_high_profile__kernel(
+  const ArrayView1D<Device, const unsigned> high_profile_rank_indexes,
   const ArrayView3D<Device, unsigned> high_profile_ranks,
   const unsigned model_index,
   const unsigned boundary_index,
@@ -459,7 +470,7 @@ void apply_best_move_for_high_profile__kernel(
   }
 
   if (best_desirability >= desirability_threshold) {
-    high_profile_ranks[model_index][boundary_index][criterion_index] = best_destination_rank;
+    high_profile_ranks[model_index][boundary_index][high_profile_rank_indexes[criterion_index]] = best_destination_rank;
   }
 }
 
@@ -473,7 +484,8 @@ ImproveProfilesWithAccuracyHeuristicOnGpu::GpuLearningData::GpuLearningData(cons
   single_peaked(host_learning_data.single_peaked.template clone_to<Device>()),
   weights(host_learning_data.models_count, host_learning_data.criteria_count, uninitialized),
   low_profile_ranks(host_learning_data.models_count, host_learning_data.boundaries_count, host_learning_data.criteria_count, uninitialized),
-  high_profile_ranks(host_learning_data.models_count, host_learning_data.boundaries_count, host_learning_data.criteria_count, uninitialized),
+  high_profile_rank_indexes(host_learning_data.high_profile_rank_indexes.template clone_to<Device>()),
+  high_profile_ranks(host_learning_data.models_count, host_learning_data.boundaries_count, host_learning_data.high_profile_ranks.s0(), uninitialized),
   desirabilities(host_learning_data.models_count, ImproveProfilesWithAccuracyHeuristicOnGpu::max_destinations_count, uninitialized),
   destination_ranks(host_learning_data.models_count, ImproveProfilesWithAccuracyHeuristicOnGpu::max_destinations_count, uninitialized)
 {}
@@ -537,6 +549,8 @@ void ImproveProfilesWithAccuracyHeuristicOnGpu::improve_low_profile_then_high_pr
   const unsigned boundary_index,
   const unsigned criterion_index
 ) {
+  assert(host_learning_data.single_peaked[criterion_index]);
+
   improve_low_profile(
     model_index,
     boundary_index,
@@ -545,7 +559,7 @@ void ImproveProfilesWithAccuracyHeuristicOnGpu::improve_low_profile_then_high_pr
       0 :
       host_learning_data.low_profile_ranks[model_index][boundary_index - 1][criterion_index],
     boundary_index == host_learning_data.boundaries_count - 1 ?
-      host_learning_data.high_profile_ranks[model_index][boundary_index][criterion_index]:
+      host_learning_data.high_profile_ranks[model_index][boundary_index][host_learning_data.high_profile_rank_indexes[criterion_index]]:
       host_learning_data.low_profile_ranks[model_index][boundary_index + 1][criterion_index]
   );
 
@@ -555,10 +569,10 @@ void ImproveProfilesWithAccuracyHeuristicOnGpu::improve_low_profile_then_high_pr
     criterion_index,
     boundary_index == host_learning_data.boundaries_count - 1 ?
       host_learning_data.low_profile_ranks[model_index][boundary_index][criterion_index] :
-      host_learning_data.high_profile_ranks[model_index][boundary_index + 1][criterion_index],
+      host_learning_data.high_profile_ranks[model_index][boundary_index + 1][host_learning_data.high_profile_rank_indexes[criterion_index]],
     boundary_index == 0 ?
       host_learning_data.values_counts[criterion_index] - 1 :
-      host_learning_data.high_profile_ranks[model_index][boundary_index - 1][criterion_index]
+      host_learning_data.high_profile_ranks[model_index][boundary_index - 1][host_learning_data.high_profile_rank_indexes[criterion_index]]
   );
 }
 
@@ -616,6 +630,7 @@ void ImproveProfilesWithAccuracyHeuristicOnGpu::improve_low_profile(
       gpu_learning_data.weights,
       gpu_learning_data.single_peaked,
       gpu_learning_data.low_profile_ranks,
+      gpu_learning_data.high_profile_rank_indexes,
       gpu_learning_data.high_profile_ranks,
       model_index,
       boundary_index,
@@ -657,9 +672,10 @@ void ImproveProfilesWithAccuracyHeuristicOnGpu::improve_high_profile(
   const unsigned lowest_destination_rank,
   const unsigned highest_destination_rank
 ) {
+  assert(host_learning_data.single_peaked[criterion_index]);
   assert(lowest_destination_rank <= highest_destination_rank);
   if (lowest_destination_rank == highest_destination_rank) {
-    assert(host_learning_data.high_profile_ranks[model_index][boundary_index][criterion_index] == lowest_destination_rank);
+    assert(host_learning_data.high_profile_ranks[model_index][boundary_index][host_learning_data.high_profile_rank_indexes[criterion_index]] == lowest_destination_rank);
   } else {
     Array1D<Host, unsigned> host_destination_ranks(max_destinations_count, uninitialized);
     unsigned actual_destinations_count = 0;
@@ -686,6 +702,7 @@ void ImproveProfilesWithAccuracyHeuristicOnGpu::improve_high_profile(
       gpu_learning_data.weights,
       gpu_learning_data.single_peaked,
       gpu_learning_data.low_profile_ranks,
+      gpu_learning_data.high_profile_rank_indexes,
       gpu_learning_data.high_profile_ranks,
       model_index,
       boundary_index,
@@ -696,6 +713,7 @@ void ImproveProfilesWithAccuracyHeuristicOnGpu::improve_high_profile(
     check_last_cuda_error_sync_stream(cudaStreamDefault);
 
     apply_best_move_for_high_profile__kernel<<<1, 1>>>(
+      gpu_learning_data.high_profile_rank_indexes,
       ref(gpu_learning_data.high_profile_ranks),
       model_index,
       boundary_index,
@@ -706,9 +724,11 @@ void ImproveProfilesWithAccuracyHeuristicOnGpu::improve_high_profile(
       std::uniform_real_distribution<float>(0, 1)(host_learning_data.random_generators[model_index]));
     check_last_cuda_error_sync_stream(cudaStreamDefault);
 
+    assert(0 <= host_learning_data.high_profile_rank_indexes[criterion_index]);
+    assert(host_learning_data.high_profile_rank_indexes[criterion_index] < host_learning_data.high_profile_ranks.s0());
     check_cuda_error(cudaMemcpy(
-      host_learning_data.high_profile_ranks[model_index][boundary_index].data() + criterion_index,
-      gpu_learning_data.high_profile_ranks[model_index][boundary_index].data() + criterion_index,
+      host_learning_data.high_profile_ranks[model_index][boundary_index].data() + host_learning_data.high_profile_rank_indexes[criterion_index],
+      gpu_learning_data.high_profile_ranks[model_index][boundary_index].data() + host_learning_data.high_profile_rank_indexes[criterion_index],
       1 * sizeof(unsigned),
       cudaMemcpyDeviceToHost));
   }
diff --git a/lincs/liblincs/learning/mrsort-by-weights-profiles-breed/improve-profiles/accuracy-heuristic-on-gpu.hpp b/lincs/liblincs/learning/mrsort-by-weights-profiles-breed/improve-profiles/accuracy-heuristic-on-gpu.hpp
index 46ac2a1a..8186a7be 100644
--- a/lincs/liblincs/learning/mrsort-by-weights-profiles-breed/improve-profiles/accuracy-heuristic-on-gpu.hpp
+++ b/lincs/liblincs/learning/mrsort-by-weights-profiles-breed/improve-profiles/accuracy-heuristic-on-gpu.hpp
@@ -21,7 +21,8 @@ class ImproveProfilesWithAccuracyHeuristicOnGpu : public LearnMrsortByWeightsPro
     Array1D<Device, bool> single_peaked;  // [criterion_index]
     Array2D<Device, float> weights;  // [criterion_index][model_index]
     Array3D<Device, unsigned> low_profile_ranks;  // [criterion_index][boundary_index][model_index]
-    Array3D<Device, unsigned> high_profile_ranks;  // [criterion_index][boundary_index][model_index]
+    Array1D<Device, unsigned> high_profile_rank_indexes;  // [criterion_index]
+    Array3D<Device, unsigned> high_profile_ranks;  // [criterion_index][boundary_index][high_profile_rank_indexes[criterion_index]]
 
     Array2D<Device, Desirability> desirabilities;  // [model_index][desination_index]
     Array2D<Device, unsigned> destination_ranks;  // [model_index][desination_index]
diff --git a/lincs/liblincs/learning/mrsort-by-weights-profiles-breed/initialize-profiles/probabilistic-maximal-discrimination-power-per-criterion.cpp b/lincs/liblincs/learning/mrsort-by-weights-profiles-breed/initialize-profiles/probabilistic-maximal-discrimination-power-per-criterion.cpp
index 121bf272..185452a8 100644
--- a/lincs/liblincs/learning/mrsort-by-weights-profiles-breed/initialize-profiles/probabilistic-maximal-discrimination-power-per-criterion.cpp
+++ b/lincs/liblincs/learning/mrsort-by-weights-profiles-breed/initialize-profiles/probabilistic-maximal-discrimination-power-per-criterion.cpp
@@ -184,10 +184,10 @@ void InitializeProfilesForProbabilisticMaximalDiscriminationPowerPerCriterion::i
           if (boundary_index == learning_data.boundaries_count - 1) {
             high_rank = std::max(high_rank, low_rank);
           } else {
-            high_rank = std::max(high_rank, learning_data.high_profile_ranks[model_index][boundary_index + 1][criterion_index]);
+            high_rank = std::max(high_rank, learning_data.high_profile_ranks[model_index][boundary_index + 1][learning_data.high_profile_rank_indexes[criterion_index]]);
           }
 
-          learning_data.high_profile_ranks[model_index][boundary_index][criterion_index] = high_rank;
+          learning_data.high_profile_ranks[model_index][boundary_index][learning_data.high_profile_rank_indexes[criterion_index]] = high_rank;
         }
       }
     }
diff --git a/lincs/liblincs/liblincs-module/learning-classes.cpp b/lincs/liblincs/liblincs-module/learning-classes.cpp
index 3d21f570..c1ee6b14 100644
--- a/lincs/liblincs/liblincs-module/learning-classes.cpp
+++ b/lincs/liblincs/liblincs-module/learning-classes.cpp
@@ -50,7 +50,8 @@ void define_learning_classes(py::module& m) {
       .def_readonly("model_indexes", &lincs::LearnMrsortByWeightsProfilesBreed::LearningData::model_indexes, "Indexed by ``0`` to ``models_count - 1``. Indexes of in-progress models ordered by increasing accuracy.")
       .def_readonly("accuracies", &lincs::LearnMrsortByWeightsProfilesBreed::LearningData::accuracies, "Indexed by ``[model_index]``. Accuracy of each in-progress model.")
       .def_readonly("low_profile_ranks", &lincs::LearnMrsortByWeightsProfilesBreed::LearningData::low_profile_ranks, "Indexed by ``[model_index][boundary_index][criterion_index]``. The current rank of each low profile, for each model and criterion.")
-      .def_readonly("high_profile_ranks", &lincs::LearnMrsortByWeightsProfilesBreed::LearningData::high_profile_ranks, "Indexed by ``[model_index][boundary_index][criterion_index]``. The current rank of each high profile, for each model and criterion.")
+      .def_readonly("high_profile_rank_indexes", &lincs::LearnMrsortByWeightsProfilesBreed::LearningData::high_profile_rank_indexes, "Indexed by ``[criterion_index]``. The index in ``high_profile_ranks``, for each single-peaked criterion.")
+      .def_readonly("high_profile_ranks", &lincs::LearnMrsortByWeightsProfilesBreed::LearningData::high_profile_ranks, "Indexed by ``[model_index][boundary_index][high_profile_rank_indexes[criterion_index]]``. The current rank of each high profile, for each model and single-peaked criterion.")
       .def_readonly("weights", &lincs::LearnMrsortByWeightsProfilesBreed::LearningData::weights, "Indexed by ``[model_index][criterion_index]``. The current MR-Sort weight of each criterion for each model.")
       .def("get_best_accuracy", &lincs::LearnMrsortByWeightsProfilesBreed::LearningData::get_best_accuracy, "Return the accuracy of the best model so far.")
       .def("get_best_model", &lincs::LearnMrsortByWeightsProfilesBreed::LearningData::get_best_model, "Return the best model so far.")
diff --git a/lincs/liblincs_module_tests.py b/lincs/liblincs_module_tests.py
index 0e833533..9c96dbbd 100644
--- a/lincs/liblincs_module_tests.py
+++ b/lincs/liblincs_module_tests.py
@@ -1063,9 +1063,13 @@ def test_access_wpb_learning_data(self):
 
         self.assertEqual(list(learning_data.single_peaked), [False, True, False, False, True])
 
+        self.assertEqual(len(learning_data.high_profile_rank_indexes), 5)
+        self.assertEqual(learning_data.high_profile_rank_indexes[1], 0)
+        self.assertEqual(learning_data.high_profile_rank_indexes[4], 1)
+
         self.assertEqual(len(learning_data.high_profile_ranks), 9)
         self.assertEqual(len(learning_data.high_profile_ranks[0]), 2)
-        self.assertEqual(len(learning_data.high_profile_ranks[0][0]), 5)
+        self.assertEqual(len(learning_data.high_profile_ranks[0][0]), 2)
         self.assertIsInstance(learning_data.high_profile_ranks[0][0][0], int)
 
         self.assertEqual(len(learning_data.weights), 9)