Cooling schedules for optimal annealing
Mathematics of Operations Research
Simulated annealing: theory and applications
Simulated annealing: theory and applications
Job shop scheduling by simulated annealing
Operations Research
On Unapproximable Versions of NP-Complete Problems
SIAM Journal on Computing
Journal of Complexity - Special issue for the Foundations of Computational Mathematics conference, Rio de Janeiro, Brazil, Jan. 1997
Stochastic simulations of two-dimensional composite packings
Journal of Computational Physics
Local Search in Combinatorial Optimization
Local Search in Combinatorial Optimization
Selected Papers from AISB Workshop on Evolutionary Computing
Scheduling: Theory, Algorithms, and Systems
Scheduling: Theory, Algorithms, and Systems
NP-complete scheduling problems
Journal of Computer and System Sciences
Convergence Analysis of Simulated Annealing-Based Algorithms Solving Flow Shop Scheduling Problems
CIAC '00 Proceedings of the 4th Italian Conference on Algorithms and Complexity
Logarithmic simulated annealing for X-ray diagnosis
Artificial Intelligence in Medicine
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In this paper, we focus on the complexity analysis of three simulated annealing-based cooling schedules applied to the classical, general job shop scheduling problem. The first two cooling schedules are used in heuristics which employ a non-uniform neighborhood relation. The expected run-time can be estimated by O(n3+Ɛ) for the first and O(n7/2+Ɛ/m1/2) for the second cooling schedule, where n is the number of tasks, m the number of machines and Ɛ represents O(ln ln n= ln n). The third cooling schedule utilizes a logarithmic decremental rule. The underlying neighborhood relation is non-reversible and therefore previous convergence results on logarithmic cooling schedules are not applicable. Let lmax denote the maximum number of consecutive transition steps which increase the value of the objective function.We prove a run-time bound of O(log1/ρ 1/δ) + 2O(lmax) to approach with probability 1 - δ the minimum value of the makespan. The theoretical analysis has been used to attack famous benchmark problems. We could improve five upper bounds for the large unsolved benchmark problems YN1, YN4, SWV12, SWV13 and SWV15. The maximum improvement has been achieved for SWV13 and shortens the gap between the lower and the former upper bound by about 57%.