M he analog 6899 E508 Statistical Mechanics: The behavior of systems with many degrees of freedom in thermal equilibrium at a finite temperature Combinatorial Optimization: Finding the minimum of a given function depending on many parameters Analogy: If a liquid material (ie. metal)cools and anneals too quickly, then the material will solidify into a sub-optimal configuration. If the liquid material cools slowly, the crystals within the material will solidify optimally into a state of minimum energy (ie. ground state This ground state corresponds to the minimum of the cost function in an optimization problem O Massachusetts Institute of Technology-Dr. Cyrus D Jilla& Prof. Olivier de Weck Engineering Systems Division and Dept of Aeronautics& AstronauticsThe Analogy The Analogy • Statistical Mechanics: The behavior of systems with many degrees of freedom in thermal equilibrium at a finite temperature. • Combinatorial Optimization: Finding the minimum of a given function depending on many parameters. • Analogy: If a liquid material (ie. metal) cools and anneals too quickly, then the material will solidify into a sub-optimal configuration. If the liquid material cools slowly, the crystals within the material will solidify optimally into a state of minimum energy (ie. ground state). – This ground state corresponds to the minimum of the cost function in an optimization problem. © Massachusetts Institute of Technology – Dr. Cyrus D. Jilla & Prof. Olivier de Weck Engineering Systems Division and Dept. of Aeronautics & Astronautics 6