Fix tests

test/integration/examples/continuous/continuous_2.jl

@@ -1,50 +1,100 @@
 """
- (x11 + x12 + x21 + x22 + x31 + x32 - 4 - s1 - s2)^2
- x11*x11 + x11*x12 + x11*x21 + x11*x22 + x11*x31 + x11*x32 - 4*x11 - s1*x11 - s2*x11 +
-  x12*x11 + x12*x12 + x12*x21 + x12*x22 + x12*x31 + x12*x32 - 4*x12 - s1*x12 - s2*x12 +
-  x21*x11 + x21*x12 + x21*x21 + x21*x22 + x21*x31 + x21*x32 - 4*x21 - s1*x21 - s2*x21 +
-  x22*x11 + x22*x12 + x22*x21 + x22*x22 + x22*x31 + x22*x32 - 4*x22 - s1*x22 - s2*x22 +
-  x31*x11 + x31*x12 + x31*x21 + x31*x22 + x31*x31 + x31*x32 - 4*x31 - s1*x31 - s2*x31 +
-  x32*x11 + x32*x12 + x32*x21 + x32*x22 + x32*x31 + x32*x32 - 4*x32 - s1*x32 - s2*x32 +
- -4*x11 - 4*x12 - 4*x21 - 4*x22 - 4*x31 - 4*x32 + 16 + 4*s1 + 4*s2 +
- -s1*x11 - s1*x12 - s1*x21 - s1*x22 - s1*x31 - s1*x32 + 4*s1 + s1*s1 + s1*s2 +
- -s2*x11 - s2*x12 - s2*x21 - s2*x22 - s2*x31 - s2*x32 + 4*s2 + s1*s2 + s2*s2
+
+min f(x) = x₁ + 2x₂ + 3x₃
+    s.t. x₁ + x₂ + x₃ ≥ 4
+         x₁, x₂, x₃ ∈ [0, 2] ⊂ ℤ
+
+
+QUBO formulation:
+
+x₁ ↤ x₁,₁ + x₁,₂
+x₂ ↤ x₂,₁ + x₂,₂
+x₃ ↤ x₃,₁ + x₃,₂
+
+min f(x) = x₁,₁ + x₁,₂ + 2 (x₂,₁ + x₂,₂) + 3 (x₃,₁ + x₃,₂)
+      s.t. x₁,₁ + x₁,₂ + x₂,₁ + x₂,₂ + x₃,₁ + x₃,₂ ≥ 4
+           x₁,₁, x₁,₂, x₂,₁, x₂,₂, x₃,₁, x₃,₂ ∈ 𝔹
+
+Adding a slack variable s ∈ [0, 2]:
+
+min f(x) = x₁,₁ + x₁,₂ + 2 (x₂,₁ + x₂,₂) + 3 (x₃,₁ + x₃,₂)
+      s.t. x₁,₁ + x₁,₂ + x₂,₁ + x₂,₂ + x₃,₁ + x₃,₂ - s - 4 = 0
+           x₁,₁, x₁,₂, x₂,₁, x₂,₂, x₃,₁, x₃,₂ ∈ 𝔹
+           s ∈ [0, 2] ⊂ ℤ
+
+Encoding s using binary variables:
+
+min f(x) = x₁,₁ + x₁,₂ + 2 (x₂,₁ + x₂,₂) + 3 (x₃,₁ + x₃,₂)
+      s.t. x₁,₁ + x₁,₂ + x₂,₁ + x₂,₂ + x₃,₁ + x₃,₂ - 4 - s₁ - 2 s₂ = 0
+           x₁,₁, x₁,₂, x₂,₁, x₂,₂, x₃,₁, x₃,₂, s₁, s₂ ∈ 𝔹
+
+Moving the constraint to the objective as a penalty:
+
+min f(x) = x₁,₁ + x₁,₂ + 2 (x₂,₁ + x₂,₂) + 3 (x₃,₁ + x₃,₂) + ρ (x₁,₁ + x₁,₂ + x₂,₁ + x₂,₂ + x₃,₁ + x₃,₂ - 4 - s₁ - 2 s₂)²
+      s.t. x₁,₁, x₁,₂, x₂,₁, x₂,₂, x₃,₁, x₃,₂, s₁, s₂ ∈ 𝔹
+
+ (x₁,₁ + x₁,₂ + x₂,₁ + x₂,₂ + x₃,₁ + x₃,₂ - 4 - s₁ - s₂)^2 = 
+  - 7 x₁,₁ - 7 x₁,₂ - 7 x₂,₁ - 7 x₂,₂ - 7 x₃,₁ - 7 x₃,₂ + 9 s₁ + 9 s₂
+  x₁,₁ x₁,₂ + x₁,₁ x₂,₁ + x₁,₁ x₂,₂ + x₁,₁ x₃,₁ + x₁,₁ x₃,₂ - 2 s₁ x₁,₁ - 2 s₂ x₁,₁ +
+  x₁,₂ x₁,₁ + x₁,₂ x₂,₁ + x₁,₂ x₂,₂ + x₁,₂ x₃,₁ + x₁,₂ x₃,₂ - 2 s₁ x₁,₂ - 2 s₂ x₁,₂ +
+  x₂,₁ x₁,₁ + x₂,₁ x₁,₂ + x₂,₁ x₂,₂ + x₂,₁ x₃,₁ + x₂,₁ x₃,₂ - 2 s₁ x₂,₁ - 2 s₂ x₂,₁ +
+  x₂,₂ x₁,₁ + x₂,₂ x₁,₂ + x₂,₂ x₂,₁ + x₂,₂ x₃,₁ + x₂,₂ x₃,₂ - 2 s₁ x₂,₂ - 2 s₂ x₂,₂ +
+  x₃,₁ x₁,₁ + x₃,₁ x₁,₂ + x₃,₁ x₂,₁ + x₃,₁ x₂,₂ + x₃,₁ x₃,₂ - 2 s₁ x₃,₁ - 2 s₂ x₃,₁ +
+  x₃,₂ x₁,₁ + x₃,₂ x₁,₂ + x₃,₂ x₂,₁ + x₃,₂ x₂,₂ + x₃,₂ x₃,₁ - 2 s₁ x₃,₂ - 2 s₂ x₃,₂ +
+  + 2 s₁ s₂ + 16
 
 """
 function test_continuous_2()
-    @testset "Greater than constraint penalty hint" begin
-
-        ρ = 3.0 
-
-        Q = [
-              1-7ρ 2ρ 2ρ 2ρ 2ρ 2ρ -2ρ -2ρ
-            0   1-7ρ  2ρ 2ρ 2ρ 2ρ -2ρ -2ρ
-            0 0   1-7ρ   2ρ 2ρ 2ρ -2ρ -2ρ
-            0 0 0   1-7ρ    2ρ 2ρ -2ρ -2ρ
-            0 0 0 0   1-7ρ     2ρ -2ρ -2ρ
-            0 0 0 0 0   1-7ρ      -2ρ -2ρ
-            0 0 0     0     0  0   9ρ   0
-            0 0 0 0 0 0             0  9ρ    
+    @testset "Greater than constraint penalty hint" begin   
+        ρ̄ = 3.0
+        ᾱ = 1.0
+        β̄ = 16ρ̄
+
+        F̄ = [
+            1 0 0 0 0 0 0 0
+            0 1 0 0 0 0 0 0
+            0 0 2 0 0 0 0 0
+            0 0 0 2 0 0 0 0
+            0 0 0 0 3 0 0 0
+            0 0 0 0 0 3 0 0
+            0 0 0 0 0 0 0 0
+            0 0 0 0 0 0 0 0
         ]
 
+        Ḡ = [
+            -7  2 2 2 2 2 -2 -2
+             0 -7 2 2 2 2 -2 -2
+             0 0 -7 2 2 2 -2 -2
+             0 0 0 -7 2 2 -2 -2
+             0 0 0 0 -7 2 -2 -2
+             0 0 0 0 0 -7 -2 -2
+             0 0 0 0 0  0  9  2
+             0 0 0 0 0  0  0  9
+        ]
+
+        Q̄ = F̄ + ρ̄ * Ḡ
+
+        x̄ = [2.0, 2.0, 0.0]
+        ȳ = 6
+
         model = Model(() -> ToQUBO.Optimizer(ExactSampler.Optimizer))
 
         @variable(model, 0 <= x[1:3] <= 2, Int)
         @constraint(model, c, sum(x) >= 4)
-        @objective(model, Min, sum(x))
+        @objective(model, Min, sum(i * x[i] for i = 1:3))
 
+        set_attribute(c, ToQUBO.Attributes.ConstraintEncodingPenaltyHint(), ρ̄)
 
-        JuMP.set_attribute(c, ToQUBO.Attributes.ConstraintEncodingPenaltyHint(), 3.0)
-
-
         optimize!(model)
 
-
         n, L, Q, α, β = QUBOTools.qubo(model, :dense)
 
+        ρ = get_attribute(c, ToQUBO.Attributes.ConstraintEncodingPenalty())
+
         Q̂ = Q + diagm(L)
 
         @test n == 8
+        @test ρ ≈ ρ̄
         @test α ≈ ᾱ
         @test β ≈ β̄
         @test Q̂ ≈ Q̄
@@ -55,7 +105,7 @@ function test_continuous_2()
 
         @test x̂ ≈ x̄
         @test ŷ ≈ ȳ
-
     end
-    return
-end
+
+    return nothing
+end