This paper proposes the hybrid adaptive genetic algorithm (HAGA) as an improved method for solving the NP-hard two-dimensional rectangular packing problem to maximize the filling rate of a rectangular sheet. The packing sequence and rotation state are encoded in a two-stage approach, and the initial population is constructed from random generation by a combination of sorting rules. After using the sort-based method as an improved selection operator for the hybrid adaptive genetic algorithm, the crossover probability and mutation probability are adjusted adaptively according to the joint action of individual fitness from the local perspective and the global perspective of population evolution. The approach not only can obtain differential performance for individuals but also deals with the impact of dynamic changes on population evolution to quickly find a further improved solution. The heuristic placement algorithm decodes the rectangular packing sequence and addresses the two-dimensional rectangular packing problem through continuous iterative optimization. The computational results of a wide range of benchmark instances from zero-waste to non-zero-waste problems show that the HAGA outperforms those of two adaptive genetic algorithms from the related literature. Compared with some recent algorithms, this algorithm, which can be increased by up to 1.6604% for the average filling rate, has great significance for improving the quality of work in fields such as packing and cutting.

In order to achieve dynamic production of smart plants, it is necessary to dynamically adjust schedule for disturbances in the manufacturing process. An executable optimized rescheduling plan needs developing, so the study of rescheduling cost is necessary. Based on the essential analysis of the rescheduling problem, a new flexible job shop rescheduling execution cost is proposed. The correctness of the execution cost is illustrated by the application in a modified genetic algorithm. The result shows that the rescheduling method with the execution cost as the fitness can generate a new plan with less deviation from the original schedule, which has a great significance for actual manufacturing.