feat: build objective from factors dict in product or sum mode

solve.py

@@ -1596,26 +1596,23 @@ def solve(
     # ======================================================================
     # OBJECTIVE IS SET HERE
     # ======================================================================
-    def Eprod(v):
-        return v * v
-
-    def Bprod(v):
-        return v
-
-    def Sprod(v):
-        return v * v
-
-    prodEE = m.NewIntVar(0, Eprod(capE), "prodEE")
-    m.AddMultiplicationEquality(prodEE, [finalE, finalE])
-    prodSS = m.NewIntVar(0, Sprod(capS), "prodSS")
-    m.AddMultiplicationEquality(prodSS, [finalS, finalS])
-    prodBB = m.NewIntVar(0, Bprod(capB), "prodBB")
-    m.AddMultiplicationEquality(prodBB, [finalB])
-    prodEB = m.NewIntVar(0, Eprod(capE) * Bprod(capB), "prodEB")
-    m.AddMultiplicationEquality(prodEB, [prodEE, prodBB])
-    obj = m.NewIntVar(0, Eprod(capE) * Bprod(capB) * Sprod(capS), "obj")
-    m.AddMultiplicationEquality(obj, [prodEB, prodSS])
-    m.Maximize(obj)
+    if objective_mode == "sum":
+        # Linear: CP-SAT takes weighted sums (negative weights included)
+        # directly, no auxiliary variables needed.
+        m.Maximize(sum(f * finals[k] for k, f in obj_factors.items() if f))
+    else:
+        # Product: maximize prod(finals[k] ** obj_factors[k]). Expand the
+        # exponents into a flat factor list and fold pairwise, carrying a
+        # running upper bound from the Phase-1 caps.
+        factor_keys = [k for k, f in obj_factors.items() for _ in range(f)]
+        obj = finals[factor_keys[0]]
+        bound = caps[factor_keys[0]]
+        for k in factor_keys[1:]:
+            bound *= caps[k]
+            nxt = m.NewIntVar(0, bound, "")
+            m.AddMultiplicationEquality(nxt, [obj, finals[k]])
+            obj = nxt
+        m.Maximize(obj)
 
     # ---- Phase 2: solve the product to optimality ----
     solver = cp_model.CpSolver()