Real-world manufacturing scenarios usually lead to difficult assembly scheduling problems.Besides strict precedence constraints between jobs or operations, such problems incorporate constraints related to maintenance activities on working stations (machines) and specific setup times when different operations are executed on the same machine.This paper analyzes the performance of several approaches, based on mathematical programming and on (meta)heuristics, to solve flexible assembly scheduling problems characterized by an arbitrary tree-like structure of the operation network.In this context, a specific encoding of candidate solutions and some specific perturbation operators are proposed.The encoding and the operators allow the distribution of sub(batches) of operations on several machines which leads, for some assembly scheduling problems, to a significant decrease of the makespan.

The performance of Differential Evolution (DE) algorithms is highly dependent on the trial population diversity and on the way the control parameter space is sampled. Therefore, identifying critical regions containing control parameters (e.g. scale factor, crossover rate) which can induce undesired behaviour (e.g. premature convergence) is useful. In this context, the aim of the paper is twofold. On one hand, the paper revisits some existing theoretical results on the expected variance of the trial population aiming to provide a comparative image on critical regions in the control parameter space for several DE variants: DE/rand/1/*, DE/best/1/*, DE/rand-to-best/*, DE/either-or. On the other hand, a new theoretical result on DE/rand/1/* population variance evolution is obtained under the assumption that the bound constraints are handled by random reinitialization of infeasible components. The relationship between the probability of violating the bound constraints and the value of the scale factor, F, is theoretically derived for DE/rand/1/* and empirically analyzed for other DE mutation operators.