The open-shop scheduling problem is a typical NP-hard problem. Most of the existing research assumes that the processing time of a procedure is fixed. However, in real-world production scenarios, the processing time can be controlled by adjusting the processing power. At the same time, optimizing the two conflicting objectives of completion time and energy consumption is significant for the high-efficiency and energy-saving open-shop production. Therefore, the Multi-objective Open-shop Scheduling Problem with Controllable Processing Time (MOOSPCPT) was studied, a mixed-integer programming model was constructed with the objectives of minimizing makespan and total extra energy consumption, and a Multi-objective Hybrid Evolutionary Algorithm (MOHEA) was proposed to solve MOOSPCPT. Several strategies were developed in the MOHEA: 1) the migration strategy and mutation strategy in the biogeographic-based optimization algorithm were improved for global search, which facilitated the diversity of the population effectively; 2) a self-adjusting variable neighborhood search strategy was designed based on the critical path, which enhanced the local search performance of the algorithm; 3) a processing time resetting operator was designed, which improved the search efficiency of the algorithm significantly. Simulation results show that the proposed strategies are effective in improving algorithm performance; MOHEA solves MOOSPCPT more effectively compared with Non-dominated Sorting Genetic Algorithm Ⅱ (NSGA-Ⅱ), Non-dominated Sorting Genetic Algorithm Ⅲ (NSGA-Ⅲ) and Strength Pareto Evolutionary Algorithm 2 (SPEA2).
A spatial co-location pattern represents a subset of spatial features whose instances are frequently located together in spatial neighborhoods. The existing interesting metrics for spatial co-location pattern mining do not take account of the difference between features and the diversity between instances belonging to the same feature. In addition, using the traditional data-driven spatial co-location pattern mining method, the mining results often contain a lot of useless or uninteresting patterns. In view of the above problems, firstly, a more general study object-spatial instance with utility value was proposed, and the Utility Participation Index (UPI) was defined as the new interesting metric of the spatial high utility co-location patterns. Secondly, the domain knowledge was formalized into three kinds of semantic rules and applied to the mining process, and a new domain-driven iterative mining framework was put forward. Finally, by the extensive experiments, the differences between mined results with different interesting metrics were compared in two aspects of utility ratio and frequency, as well as the changes of the mining results after taking the domain knowledge into account. Experimental results show that the proposed UPI metric is a more reasonable measure in consideration of both frequency and utility, and the domain-driven mining method can effectively find the co-location patterns that users are really interested in.