Scheduling problems are widely used in recent production systems. In order to model a production scheduling problem more effectively, it is necessary to build a mathematical modeling technique that automatically generates an appropriate schedule instead of an actual human operator. This paper addresses two types of model estimation methods for weighting factors in the multi-objective scheduling problems from input-output data. The one is a machine learning-based method, and the other one is the parameter estimation method based on an inverse optimization. These methods are applied to three-objectives parallel machine scheduling problems, whose objective functions consist of makespan, the weighted sum of completion time, the weighted sum of tardiness, the weighted sum of earliness and tardiness, and setup costs. The accuracy of the proposed machine learning and inverse optimization methods is evaluated. A surrogate model that learns input-output data is proposed to reduce the computational efforts. Computational results show the effectiveness of the proposed method for weighting factors in the objective function from the optimal solutions.

Boolean networks are known as models of gene regulatory networks. For this system models, this paper addresses a structural monostability problem with the assumption where the node dynamics has a symmetric property. We present a necessary and sufficient condition for the so-called flower-shaped Boolean networks to be structurally-monostable. This allows us to capture the structural property by three simple characteristics of the network topology.