Simulated_Ann_P2_stud_2Pp

Simulated_Ann_P2_stud_2Pp - Simulated annealing 2/8/05 M....

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2/8/05 M. A. Breuer 1 Simulated annealing 2/8/05 M. A. Breuer 2 Introduction: Bi-partitioning a graph ! A simple initial assignment Nodes can have weights, e.g. associated with area or power; edges can have weights, e.g. associated with criticality or bus width. Cut=6
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2/8/05 M. A. Breuer 3 A single move This move increased the cut by 2 (see a and b) and decreased it by 1 (see c), for a net gain of -1. Should we allow such a move when trying to get to an optimal (minimal) cut value via some iterative means? b a c 2/8/05 M. A. Breuer 4 A pairwise move What if x and y are connected, i.e., how is the cut value effected by their interchange? x y
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2/8/05 M. A. Breuer 5 Nets cut after each iteration Iteration Nets cut A Markov chain describes at successive times the states of a system. At these times the system may have changed from the state it was in the moment before to another or stayed in the same state. The changes of state are called transitions. The Markov property means the system is memoryless, i.e., it does not "remember" the states it was in before, just "knows" its present state, and hence bases its "decision" to which future state it will transit purely on the present, not considering the past. 2/8/05 M. A. Breuer 6 Simulated Annealing (SA) SA is a technique for combinational optimization for problems that are usually NP-complete and have a large number of variables. It is a “general technique”. It is a major extension of pairwise interchange and the Kernighan-Lin graph partitioning procedure discussed in EE 680. It was developed by __________ and motivated by an analogy to stochastic mechanics used in the annealing of solids. fill-in
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2/8/05 M. A. Breuer 7 Annealing of solids ! Low energy states of materials are usually a solid – usually a _____ crystalline structure – lattice structure of molecules. ! Annealing : Heat to a _______ temperature to permit atomic rearrangements; cool carefully and slowly. Material “freezes” into a crystal. These crystals usually exhibit “good” properties, such as regularity. ! SA is an analogy to this process. Take an unordered arrangement and organize it into an optimized one. ! SA is a heuristic strategy for solving combinatorial optimization problems. fill-in 2/8/05 M. A. Breuer 8 f ( X ) X = x 1 X 1 0 X 1 * uphill downhill X 1 0 , X 1 1 , X 1 2 , ˇ Sequence of values for x 1 Combinatorial optimization ! Find values for the n -variable vector X = { x 1 , x 2 , …, x n } such that f ( X ) is minimized. ! Objective: Perturb current solution X 1 0 to get to optimal X 1 * , we need to decrease and then increase f ( X ). When we change from one configuration to another, X = X + ! X , X can be better than or worse than X .
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2/8/05 M. A. Breuer 9 Metropolis Algorithm ! To simulate the cooling procedure we need a schedule to instruct us as to how and when to change the temperature. We can use the Metropolis algorithm for this.
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Simulated_Ann_P2_stud_2Pp - Simulated annealing 2/8/05 M....

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