M The sa algorithm 6899 E08 Terminology: T= Design Vector (ie. Design Architecture E= System Energy(ie Objective Function Valu T= System Temperature A=Difference in System Energy Between Two Design Vectors The Simulated Annealing Algorithm 1)Choose a random Ti, select the initial system temperature, and outline the cooling (ie. annealing) schedule 2)Evaluate E( i using your simulation model 3)Perturb to obtain a neighboring Design Vector( + 1) 4) Evaluate E(+1 using your simulation model 5)If E(T+<E(i, T +1 is the new current solution 6)If E(/+1> E( i), then accept +1 as the new current solution with a probability ef-At where△=E(I+)-E( 7)Reduce the system temperature according to the cooling schedule 8) Terminate the algorithm TPF Example: We will walk through each of the 8 steps 8 O Massachusetts Institute of Technology-Dr. Cyrus D Jilla& Prof. Olivier de Weck Engineering Systems Division and Dept of Aeronautics& AstronauticsThe SA Algorithm The SA Algorithm • Terminology: – Γ = Design Vector (ie. Design Architecture) – E = System Energy (ie. Objective Function Value) – T = System Temperature – ∆ = Difference in System Energy Between Two Design Vectors • The Simulated Annealing Algorithm 1) Choose a random Γ , select the initial system temperature, and outline the cooling i (ie. annealing) schedule 2) Evaluate E(Γ ) using your simulation model i 3) Perturb Γ to obtain a neighboring Design Vector (Γi+1) i 4) Evaluate E(Γi+1) using your simulation model 5) If E(Γi+1)< E(Γ ), Γi+1 is the new current solution i 6) If E(Γi+1)> E(Γ ), then accept Γi+1 as the new current solution with a probability e(- ∆/T) i where ∆ = E(Γi+1) - E(Γ ). i 7) Reduce the system temperature according to the cooling schedule. 8) Terminate the algorithm. • TPF Example: We will walk through each of the 8 steps. © Massachusetts Institute of Technology – Dr. Cyrus D. Jilla & Prof. Olivier de Weck Engineering Systems Division and Dept. of Aeronautics & Astronautics 8