now working

backend/src/optimization/optimizer.py

@@ -493,10 +493,21 @@ class Optimizer:
 
 
     def warm_start(self, x: list[pl.LpVariable], L: int) :
+        """
+        This function sets the initial values of the decision variables to a feasible solution.
+        This can help the solver start with a feasible or heuristic solution,
+        potentially speeding up convergence.
 
+        Args:
+        x (list[pl.LpVariable]): A list of PuLP decision variables (binary variables).
+        L (int): The size parameter, representing a dimension (likely related to a grid or matrix).
+
+        Returns:
+        list[pl.LpVariable]: The modified list of PuLP decision variables with initial values set.
+        """
         for i in range(L*L) :
             x[i].setInitialValue(0)
-            
+
         x[1].setInitialValue(1)
         x[2*L-1].setInitialValue(1)
 
@@ -579,7 +590,7 @@ class Optimizer:
         try :
             prob.solve(pl.PULP_CBC_CMD(msg=False, timeLimit=self.time_limit+1, gapRel=self.gap_rel))
         except Exception as exc :
-            raise Exception(f"No solution found: {exc}") from exc 
+            raise Exception(f"No solution found: {exc}") from exc
         status = pl.LpStatus[prob.status]
         solution = [pl.value(var) for var in x]  # The values of the decision variables (will be 0 or 1)
 
@@ -607,8 +618,8 @@ class Optimizer:
             try :
                 prob.solve(pl.PULP_CBC_CMD(msg=False, timeLimit=self.time_limit, gapRel=self.gap_rel))
             except Exception as exc :
-                raise Exception(f"No solution found: {exc}") from exc 
-        
+                raise Exception(f"No solution found: {exc}") from exc
+
             solution = [pl.value(var) for var in x]
 
             if pl.LpStatus[prob.status] != 'Optimal' :