# What's wrong with my NMinimize code with the definite constraints?

I have a problem with my NMinimize code, the answer based on the paper is Mu1 = 8 and Mu2 = 19,34 that's the optimal Mu1 and Mu2. But my answer is Mu1 = 5,17 and Mu2 = 17,17. The paper said "adopt the direct search method for solving it. The value of Q = 131 is the optimal value of the ETC with the value of Mu1 = 8 and Mu2 = 19,34. So I tried the optimal condition, but the answer of Mu is different with the paper. I don't know how to solve it, Thanks so much.

K11 = 30 ; K12 = 20 ; K22 = 10 ; m1 = 8 ; m2 = 20 ; δ1 = 1 ; δ2 = 0.5 ; θ1 = 1 ; θ2 = 0.4 ; ⁢ a = 0.5 ; b = 0.5 ; λ = 0.05 ; α = 10 ; β = 3 ; P = 500 ; d = 300 ; CR = 4 ; S = 100 ; r = 0.2 ; ⁢ CA = 30 ; Q = 131 ; σ1 = Sqrt [ a ] ; σ2 = Sqrt [ b ] ; ⁢

NMinimize [ { ( d / Q ⁢ ( K11 ⁢ ( a + ( μ1 - m1 ) ^ 2 ) + K22 ⁢ ( b ⁢ ( μ2 - m2 ) ^ 2 ) + K12 ⁢ ( ( μ1 - m1 ) * ( μ2 - m2 ) ) ) ⁢ Q / P + ( K11 ⁢ a + K22 ⁢ b ) ⁢ ( ( ( Q / P ) ^ 2 ) / 2 - ( Q / P ) / λ + ( 1 - Exp [ - λ ⁢ Q / P ] ) / λ ^ 2 ) + ( ( K11 ⁢ ( 2 ⁢ ( μ1 - m1 ) ⁢ δ1 ) + K22 ⁢ ( 2 ⁢ ( μ2 - m2 ) ⁢ δ2 ) + K12 ⁢ ( ( μ1 - m1 ) ⁢ δ2 + ( μ2 - m2 ) ⁢ δ1 ) ) + ( K11 ⁢ δ1 ^ 2 + K22 ⁢ δ2 ^ 2 + K12 ⁢ δ1 ⁢ δ2 ) ) ⁢ ( Q / P - ( 1 - Exp [ - λ ⁢ Q / P ] ) / λ ) + ( ( K11 ⁢ ( 2 ⁢ ( μ1 - m1 ) ⁢ θ1 ) + K22 ⁢ ( 2 ⁢ ( μ2 - m2 ) ⁢ θ2 ) + K12 ⁢ ( ( μ1 - m1 ) ⁢ θ2 + ( μ2 - m2 ) ⁢ θ1 ) ) + ( K11 ⁢ ( 2 ⁢ δ1 ⁢ θ1 ) + K22 ⁢ ( 2 ⁢ δ2 ⁢ θ2 ) + K22 ⁢ ( δ1 ⁢ θ2 + δ2 ⁢ θ1 ) ) ) ⁢ ( 0.5 ( Q / P ) ^ 2 - ( Q / P ) / λ + ( 1 - Exp [ - λ ⁢ Q / P ] ) / λ ^ 2 ) + ( K11 ⁢ θ1 ^ 2 + K22 ⁢ θ2 ^ 2 + K12 ⁢ θ1 ⁢ θ2 ) * ( ( ( Q / P ) ^ 3 ) / 3 - ( Q / P ) ^ 2 / λ + 2 ⁢ ( Q / P ) / λ ^ 2 + 2 ⁢ ( 1 - Exp [ - λ ⁢ Q / P ] ) / λ ^ 3 ) ) + ( d / Q * ( CR ⁢ ( ( μ1 + δ1 ) ⁢ Q / P - δ1 ⁢ ( 1 - Exp [ - λ ⁢ Q / P ] ) / λ + θ1 ⁢ ( 0.5 ( Q / P ) ^ 2 - ( Q / P ) / λ + ( 1 - Exp [ - λ ⁢ Q / P ] ) / λ ^ 2 ) ) + CR ⁢ ( ( μ2 + δ2 ) ⁢ Q / P - δ2 ⁢ ( 1 - Exp [ - λ ⁢ Q / P ] ) / λ + θ2 * ( 0.5 ( Q / P ) ^ 2 - ( Q / P ) / λ + ( 1 - Exp [ - λ ⁢ Q / P ] ) / λ ^ 2 ) ) ) ) + ( S ⁢ d / Q ) + ( r * ( CR * ( ( μ1 + δ1 ) ⁢ Q / P - δ1 ⁢ ( 1 - Exp [ - λ ⁢ Q / P ] ) / λ + δ1 ⁢ ( 0.5 ( Q / P ) ^ 2 - ( Q / P ) / λ + ( 1 - Exp [ - λ ⁢ Q / P ] ) / λ ^ 2 ) ) + CR ⁢ ( ( μ2 + δ2 ) ⁢ Q / P - δ2 ⁢ ( 1 - Exp [ - λ ⁢ Q / P ] ) / λ + θ2 * ( 0.5 ( Q / P ) ^ 2 - ( Q / P ) / λ + ( 1 - Exp [ - λ ⁢ Q / P ] ) / λ ^ 2 ) ) ) ⁢ Q ⁢ ( P - d ) / 2 ⁢ P ) + ( d / Q ⁢ CA ) + ( d / Q ⁢ ( α ⁢ Q / P + 0.5 β ⁢ ( Q / P ) ^ 2 ) ) , m1 - 4 ⁢ σ1 < μ1 < m1 + 4 ⁢ σ1 && m2 - 4 ⁢ σ2 < μ2 < m2 + 4 ⁢ σ2 } , { μ1 , μ2 } ]


Here is my output {3.07061*10^7, {[Mu]1 -> 5.17157, [Mu]2 -> 17.1716}}

• You can format inline code and code blocks by selecting the code and clicking the {} button above the edit window. The edit window help button ? is useful for learning how to format your questions and answers. You may also find this meta Q&A helpful – Michael E2 Apr 30 at 2:50
• @MichaelE2 I've tried that Michael, but I don't know to make a better formating on my question. I'm so sorry if it makes difficult to understand my question – Habib Asnan Apr 30 at 3:00
• Habib, so your only problem is that your solution differs from the paper's? Well, that happens; I could be that the authors made a mistake, or you --- or both you and the authors. With the complexity of these expressions, this is very likely. We other users cannot check that. By the way: After rationalizing your data (replacing all floating point numbers (those with a .) by rational numbers), one can apply Minimize to obtain the exact solution {\[Mu]1 -> 8 - 2 Sqrt[2], \[Mu]2 -> 20 - 2 Sqrt[2]}. – Henrik Schumacher Apr 30 at 3:51
• my problem is not only that @HenrikSchumacher but if I change the value of Q with other number, the value of Mu1 and Mu2 is constant 5,17 and 17,17. I think it should be different if I changed the value of Q and I think the numbers of my Mu1 and Mu2 are the lower number of "the constraints scope" not the optimal solution (Minimizing). I don't know what should I used to get the optimal Mu1 and Mu2 like the paper. Should I used "Minimize" or "NMinimize" or "FindMinimum" or other code to make sure that the value is same with the paper – Habib Asnan Apr 30 at 13:07
• drive.google.com/open?id=1qDCM3Q67uR9_tZL68xFnlSqp6e4PXNJV Maybe you can see my work there, thanks so much before @HenrikSchumacher – Habib Asnan Apr 30 at 13:14