Two processor scheduling is in NC
SIAM Journal on Computing
Efficient parallel algorithms
Cooling schedules for optimal annealing
Mathematics of Operations Research
Simulated annealing and Boltzmann machines: a stochastic approach to combinatorial optimization and neural computing
The two-processor scheduling problem is in random NC
SIAM Journal on Computing
On the parallel complexity of discrete relaxation in constraint satisfaction networks
Artificial Intelligence
A parallel algorithm for two processors precedence constraint scheduling
Proceedings of the 18th international colloquium on Automata, languages and programming
Job shop scheduling by simulated annealing
Operations Research
On Unapproximable Versions of NP-Complete Problems
SIAM Journal on Computing
Local Search in Combinatorial Optimization
Local Search in Combinatorial Optimization
Fast Parallel Constraint Satisfaction
ICALP '93 Proceedings of the 20th International Colloquium on Automata, Languages and Programming
Landscape analysis for multicast routing
Computer Communications
Genetic local search for multicast routing with pre-processing by logarithmic simulated annealing
Computers and Operations Research
Solving the flow shop problem by parallel programming
Journal of Parallel and Distributed Computing
Journal of Intelligent Manufacturing
On single-walk parallelization of the job shop problem solving algorithms
Computers and Operations Research
Parallel cost function determination on GPU for the job shop scheduling problem
PPAM'11 Proceedings of the 9th international conference on Parallel Processing and Applied Mathematics - Volume Part II
Parallel tabu search algorithm for the hybrid flow shop problem
Computers and Industrial Engineering
Hi-index | 0.01 |
The paper is dealing with parallelized versions of simulated annealing-based heuristics for the classical job shop scheduling problem. The scheduling problem is represented by the disjunctive graph model and the objective is to minimize the length of longest paths. The problem is formulated for l jobs where each job has to process exactly one task on each of the m machines. The calculation of longest paths is the critical computation step of our heuristics and we utilize a parallel algorithm for this particular problem where we take into account the specific properties of job shop scheduling. In our heuristics, we employ a neighborhood relation which was introduced by Van Laarhoven et al. (Operations Research 40(1) (1992) 113-25). To obtain a neighbor, a single arc from a longest path is reversed and these transition steps always guarantee the feasibility of schedules. We designed two cooling schedules for homogeneous Markov chains and additionally we investigated a logarithmic cooling schedule for inhomogeneous Markov chains. Given O(n3) processors and a known npper bound Λ = Λ(l, m) for the length of longest paths, the expected run-times of parallelized versions are O(n log n log Λ) for the first cooling schedule and O(n2(log3/2 n)m1/2 log Λ) for the second cooling schedule, where n = lm is the number of tasks. For the logarithmic cooling schedule, a speed-up of O(n/(log n log Λ)) can be achieved. When Markov chains of constant length are assumed, we obtain a polylogarithmic run-time of O(log n log Λ) for the first cooling schedule. The analysis of famous benchmark problems led us to the conjecture that Λ ≤ O(l + m) could be a uniform upper bound for the completion time of job shop scheduling problems with l jobs on m machines. Although the number of processors is very large, the particular processors are extremely simple and the parallel processing system is suitable for hardware implementations.