Convergence of an annealing algorithm
Mathematical Programming: Series A and B
Computers and Operations Research
Minimizing mean flow time in two-machine open shops and flow shops
Journal of Algorithms
Insertion techniques for the heuristic solution of the job shop problem
Proceedings of the workshop on Discrete algorithms
A branch & bound algorithm for the open-shop problem
GO-II Meeting Proceedings of the second international colloquium on Graphs and optimization
Open Shop Scheduling to Minimize Finish Time
Journal of the ACM (JACM)
Open shop scheduling with makespan and total completion time criteria
Computers and Operations Research
New and improved algorithms for minsum shop scheduling
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
The total completion time open shop scheduling problem with a given sequence of jobs on one machine
Computers and Operations Research
Computers and Operations Research
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IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
Compiling finite linear CSP into SAT
CP'06 Proceedings of the 12th international conference on Principles and Practice of Constraint Programming
On the complexity of preemptive open-shop scheduling problems
Operations Research Letters
A contribution and new heuristics for open shop scheduling
Computers and Operations Research
Particle swarm optimisation for open shop problems with fuzzy durations
IWINAC'11 Proceedings of the 4th international conference on Interplay between natural and artificial computation - Volume Part I
A multi-level genetic algorithm for a multi-stage space allocation problem
Mathematical and Computer Modelling: An International Journal
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International Journal of Bio-Inspired Computation
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IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
Binary Accelerated Particle Swarm Algorithm (BAPSA) for discrete optimization problems
Journal of Global Optimization
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This paper considers the problem of scheduling n jobs on m machines in an open shop environment so that the sum of completion times or mean flow time becomes minimal. It continues recent work by Brasel et al. [H. Brasel, A. Herms, M. Morig, T. Tautenhahn, T. Tusch, F. Werner, Heuristic constructive algorithms for open shop scheduling to minmize mean flow time, European J. Oper. Res., in press (doi.10.1016/j.ejor.2007.02.057)] on constructive algorithms. For this strongly NP-hard problem, we present two iterative algorithms, namely a simulated annealing and a genetic algorithm. For the simulated annealing algorithm, several neighborhoods are suggested and tested together with the control parameters of the algorithm. For the genetic algorithm, new genetic operators are suggested based on the representation of a solution by the rank matrix describing the job and machine orders. Extensive computational results are presented for problems with up to 50 jobs and 50 machines, respectively. The algorithms are compared relative to each other, and the quality of the results is also estimated partially by a lower bound for the corresponding preemptive open shop problem. For most of the problems, the genetic algorithm is superior when fixing the same number of 30000 generated solutions for each algorithm. However, in contrast to makespan minimization problems, where the focus is on problems with an equal number of jobs and machines, it turns out that problems with a larger number of jobs than machines are the hardest problems.