Combining metaheuristics is a common technique that may produce high quality solutions to complex problems. In this paper, we propose a combination of Genetic Programming (GP) and Genetic Algorithm (GA) to obtain ensembles of priority rules to solve a scheduling problem, denoted \((1,Cap(t)||\sum T_i)\), on-line. In this problem, a set of jobs must be scheduled on a single machine whose capacity varies over time. The proposed approach interleaves GP and GA so that a GP is in charge of evolving single priority rules and a GA is executed after each iteration of the GP to evolve ensembles from the rules produced by the GP in this iteration, at the same time as the GP evolves the next generation of rules. Therefore, the ensembles are obtained in an anytime fashion. In the experimental study, we compare the proposed approach to a previous one in which the GP was firstly run to evolve a large pool of candidate priority rules, and then the GA was run to obtain ensembles from that pool of rules. The results of this study revealed that the ensembles produced by the interleaved combination of GP and GA are better than those obtained by the sequential combination of GP and GA. So, these results, together with the ensembles being available earlier, make this approach more appropriate to the on-line requirements of the scheduling problem.

结合元启发法是一种常见的技术，可以为复杂的问题提供高质量的解决方案。在本文中，我们提出了遗传规划（GP）和遗传算法（GA）的组合，以获得优先级规则集合来解决调度问题，表示为\（（1，Cap（t）|| \ sum T_i）\），在线。在此问题中，必须在容量随时间变化的单台计算机上计划一组作业。所提出的方法将GP和GA交织在一起，以便GP负责演化单个优先级规则，并且在GP的每次迭代之后执行一次GA，以根据该迭代中GP生成的规则来演化集合，与此同时GP进化了下一代规则。因此，可以以任何方式获得合奏。在实验研究中，我们将所提出的方法与先前的方法进行了比较，在该方法中，首先运行GP来演化大的候选优先级规则池，然后运行GA从该规则池中获得集合。这项研究的结果表明，由GP和GA交错组合产生的合奏要比由GP和GA顺序组合获得的合奏更好。因此，这些结果以及较早提供的集成使此方法更适合于调度问题的在线要求。