A note on the learning effect in multi-agent optimization

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.