An optimal sequence of tasks for autonomous learning systems

In this paper, we consider an optimal sequence of tasks for systems that improve their performances due to autonomous learning (learning-by-doing). In particular, we focus on a problem of determining sequence of performed tasks for the autonomous learning systems to minimize the total weighted completion times of tasks. Fundamental for the presented approach is that schedule (a sequence of tasks) allows to efficiently utilize learning abilities of the system to optimize its objective, but it does not affect the system itself. To solve the problem, we prove an eliminating property that is used to construct a branch and bound algorithm and present some fast heuristic and metaheuristic methods. An extensive analysis of the efficiency of the proposed algorithms is also provided.