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Although the single machine scheduling problem to minimize the total weighted completion times with the sum-of-processing time based learning or aging effects have been known for a decade, it is still an open question whether these problems are strongly NP-hard. We resolve this issue and prove them to be strongly NP-hard with the learning effect as well as with the aging effect. Furthermore, we construct an exact parallel branch and bound algorithm for the problem with general sum-of-processing time based models, which can solve optimally moderate problem instances in reasonable time. [ABSTRACT FROM AUTHOR]

Abstract: The importance of the role that learning plays in manufacturing, industry and computer systems is undeniable as well as the profit that can be increased if this phenomenon is taken into consideration for short- and long-term optimization. In this paper, we focus on scheduling jobs on a single processor, where its effectiveness can increase with the number of processed jobs, to minimize one of the following objectives: the maximum completion time with the release dates, the maximum lateness and the number of late jobs. It is proved that these well known polynomially solvable problems become at least NP-hard with the considered learning models. To solve them we provide some elimination procedures that are used to construct a branch and bound algorithm. Furthermore, we propose some fast heuristics for the problem of minimizing the number of late jobs with the general model of the learning effect. [Copyright &y& Elsevier]

Abstract: In this paper, we point out that the learning effect, in the form known from industrial systems or services sectors, takes place in multi-agent optimization. In particular, we show that the minimization of a total transmission cost of packets in a computer network that uses a reinforcement learning routing algorithm can be expressed as the single machine makespan minimization scheduling problem with the learning effect. On this basis, we prove this problem is at least NP-hard (even off-line version). However, we derive properties, which allow us to construct on-line scheduling algorithms that can be applied in the computer network to increase its efficiency by the utilization of its learning ability. [ABSTRACT FROM AUTHOR]

There is a limited number of results concerning fast and efficient solution algorithms for scheduling problems with general learning models. Therefore, we develop a fast insert neighborhood search (FINS) for a group of identical parallel machine scheduling problems with general learning curves under the following minimization objectives: the maximum completion time (makespan) and the maximum lateness. Our fast search scheme allows to calculate criterion values in a constant time per solution in a neighborhood. The application is presented on the basis of Nawaz–Enscore–Ham's method (NEH), iterative local search, tabu search, particle swarm optimization and hybrid simulated annealing — tabu search algorithms, where the efficiency of their standard implementations are compared to their versions enhanced by our fast insert neighborhood search. The computational experiments confirm the theoretical analysis that our method essentially overwhelms the well known approaches. The metaheuristics augmented by our FINS are about 120 times faster than their standard versions and improve the criterion values by up to 25% for analyzed instances with 100–800 jobs and 5–80 machines. • Parallel machine scheduling problems with general learning curves are analyzed. • A fast insert neighborhood search for a group of scheduling problems is developed. • Iterative local search, NEH, tabu search, particle swarm optimization algorithms are enhanced. • The experiments confirm that our method overwhelms the standard approaches. [ABSTRACT FROM AUTHOR]