Handbook on Scheduling - From Theory to Applications by Scott M. Strayer, Peter L. Reynolds, Mark H. Ebell

By Scott M. Strayer, Peter L. Reynolds, Mark H. Ebell

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By Scott M. Strayer, Peter L. Reynolds, Mark H. Ebell

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If the cooling is too slow, then the running time becomes prohibitive. ^ and parameters CQ and a a generic simulated annealing algorithm can be presented as follows. 1 Simulated annealing [LA87, AK89]. begin Initialize (x^^snv ^O' ^)^* k:=0} •^ - ^ -^start^' repeat DefineL(/:)or5; f o r t:=lto L(k) do begin Generate a neighbor y e 9{ix) ; A:=Y(x)-Y(j); i f random[0,l] < ap^(A) t h e n end; x\=y k'=k+l} u n t i l some stopping criterion is met end; Under some reasonable assumptions on the cooling schedule, theoretical results can be established concerning convergence to a global optimum or the complexity of the procedure (see [LA87, AK89]).

Let S = {V,<)ht di precedence graph, and let for each v E V, P^= {V^, <^)ht di precedence graph, where all the sets ^^ (y e. 1/) and 1^ are pair-wise disjoint. Let U= KJ V^ , Define (IZ, ^<^) as the following precedence graph: for p, q e U, p <

Older moves are disregarded. The tabu status derived from the / most recent moves forces the algorithm to go / moves away from any explored solution before the first step backwards is allowed. Obviously, this approach may disallow more moves than necessary to avoid returning to a yet visited solution. This encourages the intention to keep / as small as possible without disregarding the principle aim of never exploring a solution twice. Consequently, if / is too small the algorithm probably will return to a local optimum just left.

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