Costly optimization of range actions

docs/castor/linear-problem/discrete-pst-tap-filler.md

@@ -23,12 +23,15 @@ information [here](/input-data/crac/json.md#range-actions))
 
 ## Defined optimization variables
 
-| Name                                         | Symbol                | Details                                                                                                                 | Type    | Index                                                                                         | Unit                     | Lower bound | Upper bound |
-|----------------------------------------------|-----------------------|-------------------------------------------------------------------------------------------------------------------------|---------|-----------------------------------------------------------------------------------------------|--------------------------|-------------|-------------|
-| PstRangeAction tap upward variation          | $\Delta t^{+} (r, s)$ | upward tap variation of PstRangeAction $r$, at state $s$, between two iterations of the optimisation                    | Integer | One variable for every element of PstRangeActions and for evey state in which it is optimized | No unit (number of taps) | 0           | $+\infty$   |
-| PstRangeAction tap downward variation        | $\Delta t^{-} (r, s)$ | downward tap variation of PstRangeAction $r$, at state $s$, between two iterations of the optimisation                  | Integer | One variable for every element of PstRangeActions and for evey state in which it is optimized | No unit (number of taps) | 0           | $+\infty$   |
-| PstRangeAction tap upward variation binary   | $\delta ^{+} (r, s)$  | indicates whether the tap of PstRangeAction $r$ has increased, at state $s$, between two iterations of the optimisation | Binary  | One variable for every element of PstRangeActions and for evey state in which it is optimized | No unit                  | 0           | 1           |
-| PstRangeAction tap downward variation binary | $\delta ^{-} (r, s)$  | indicates whether the tap of PstRangeAction $r$ has decreased, at state $s$, between two iterations of the optimisation | Binary  | One variable for every element of PstRangeActions and for evey state in which it is optimized | No unit                  | 0           | 1           |
+| Name                                         | Symbol                        | Details                                                                                                                 | Type    | Index                                                                                          | Unit                     | Lower bound | Upper bound |
+|----------------------------------------------|-------------------------------|-------------------------------------------------------------------------------------------------------------------------|---------|------------------------------------------------------------------------------------------------|--------------------------|-------------|-------------|
+| PstRangeAction tap upward variation          | $\Delta t^{+} (r, s)$         | upward tap variation of PstRangeAction $r$, at state $s$, between two iterations of the optimisation                    | Integer | One variable for every element of PstRangeActions and for evey state in which it is optimized  | No unit (number of taps) | 0           | $+\infty$   |
+| PstRangeAction tap downward variation        | $\Delta t^{-} (r, s)$         | downward tap variation of PstRangeAction $r$, at state $s$, between two iterations of the optimisation                  | Integer | One variable for every element of PstRangeActions and for evey state in which it is optimized  | No unit (number of taps) | 0           | $+\infty$   |
+| PstRangeAction tap upward variation binary   | $\delta ^{+} (r, s)$          | indicates whether the tap of PstRangeAction $r$ has increased, at state $s$, between two iterations of the optimisation | Binary  | One variable for every element of PstRangeActions and for evey state in which it is optimized  | No unit                  | 0           | 1           |
+| PstRangeAction tap downward variation binary | $\delta ^{-} (r, s)$          | indicates whether the tap of PstRangeAction $r$ has decreased, at state $s$, between two iterations of the optimisation | Binary  | One variable for every element of PstRangeActions and for evey state in which it is optimized  | No unit                  | 0           | 1           |
+| PstRangeAction tap                           | $\tau (r, s)$                 | tap position of the PST of range action $r$ at state $s$                                                                | Integer | One variable for every element of PstRangeActions and for evey state in which it is optimized  | No unit                  | min PST tap | max PST tap |
+| Total PstRangeAction upward tap variation    | $\Delta_{total} t^{+} (r, s)$ | total upward tap variation of PstRangeAction $r$, at state $s$, from the pre-perimeter tap position                     | Integer | One variable for every element of PstRangeActions and for evey state in which it is optimized  | No unit                  | 0           | $+\infty$   |
+| Total PstRangeAction downward tap variation  | $\Delta_{total} t^{-} (r, s)$ | total downward tap variation of PstRangeAction $r$, at state $s$, from the pre-perimeter tap position                     | Integer | One variable for every element of PstRangeActions and for evey state in which it is optimized  | No unit                  | 0           | $+\infty$   |
 
 ## Used optimization variables
 
@@ -88,6 +91,18 @@ $c^{+}_{tap \rightarrow a}(r, s)$ (resp. $c^{-}_{tap \rightarrow a}(r, s)$) is s
 
 <br>
 
+### Tap variable
+
+$$\tau(r, s) = \Delta t^{+} - \Delta t^{-} + t_{n}(r, s)$$
+
+### Total tap variation
+
+$$\Delta_{total} t^{+} (r, s) - \Delta_{total} t^{-} (r, s) = \tau(r, s) -
+\begin{cases}
+    \tau(r, s') & \text{if $r$ was previously available at state $s'$}\\
+    t_{0}(r, s) & \text{otherwise}
+\end{cases}$$
+
 ### Tap variation can only be in one direction, upward or downward
 
 $$

ra-optimisation/search-tree-rao/src/main/java/com/powsybl/openrao/searchtreerao/castor/algorithm/CastorSecondPreventive.java

@@ -206,7 +206,7 @@ RaoResult runSecondPreventiveAndAutoRao(CastorContingencyScenarios castorConting
             if (entry.getValue() instanceof SkippedOptimizationResultImpl) {
                 newPostContingencyResults.put(state, new SkippedOptimizationResultImpl(state, new HashSet<>(), new HashSet<>(), postCraSensitivityAnalysisOutput.getSensitivityStatus(entry.getKey()), raoParameters.getLoadFlowAndSensitivityParameters().getSensitivityFailureOvercost()));
             } else {
-                newPostContingencyResults.put(state, new CurativeWithSecondPraoResult(state, entry.getValue(), secondPreventiveRaoResult.perimeterResult(), secondPreventiveRaoResult.remedialActionsExcluded(), postCraSensitivityAnalysisOutput));
+                newPostContingencyResults.put(state, new CurativeWithSecondPraoResult(state, entry.getValue(), secondPreventiveRaoResult.perimeterResult(), secondPreventiveRaoResult.remedialActionsExcluded(), postCraSensitivityAnalysisOutput, raoParameters.getObjectiveFunctionParameters().getType().costOptimization()));
             }
         }
         RaoLogger.logMostLimitingElementsResults(BUSINESS_LOGS, postCraSensitivityAnalysisOutput, raoParameters.getObjectiveFunctionParameters().getType(), NUMBER_LOGGED_ELEMENTS_END_RAO);

ra-optimisation/search-tree-rao/src/main/java/com/powsybl/openrao/searchtreerao/linearoptimisation/algorithms/BestTapFinder.java

@@ -40,7 +40,7 @@ private BestTapFinder() {
     /**
      * This function computes the best tap positions for PstRangeActions that were optimized in the linear problem.
      * It is a little smarter than just rounding the optimal angle to the closest tap position:
-     * if the optimal angle is close to the limit between two tap positions, it will chose the one that maximizes the
+     * if the optimal angle is close to the limit between two tap positions, it will choose the one that maximizes the
      * minimum margin on the 10 most limiting elements (pre-optim)
      * If virtual costs are an important part of the optimization, it is highly recommended to use APPROXIMATED_INTEGERS
      * taps in the linear optimization, rather than relying on the best tap finder to round the taps.
@@ -157,7 +157,7 @@ static Map<Integer, Double> computeMinMarginsForBestTaps(Network network,
         double approxLimitAngle = 0.5 * (closestAngle + otherAngle);
         if (Math.abs(angle - approxLimitAngle) / Math.abs(closestAngle - otherAngle) < 0.15) {
             // Angle is too close to the limit between two tap positions
-            // Chose the tap that maximizes the margin on the most limiting element
+            // Choose the tap that maximizes the margin on the most limiting element
             Pair<Double, Double> margins = computeMinMargins(network, pstRangeAction, closestAngle, otherAngle, linearOptimizationResult, unit);
             if (margins.getRight() > margins.getLeft()) {
                 return Map.of(closestTap, margins.getLeft(), otherTap, margins.getRight());