We define very large multi-objective optimization problems to be multiobjective optimization problems in which the number of decision variables is greater than 100,000 dimensions. This is an important class of problems as many real-world problems require optimizing hundreds of thousands of variables. Existing evolutionary optimization methods fall short of such requirements when dealing with problems at this very large scale. Inspired by the success of existing recommender systems to handle very large-scale items with limited historical interactions, in this paper we propose a method termed Very large-scale Multiobjective Optimization through Recommender Systems (VMORS). The idea of the proposed method is to transform the defined such very large-scale problems into a problem that can be tackled by a recommender system. In the framework, the solutions are regarded as users, and the different evolution directions are items waiting for the recommendation. We use Thompson sampling to recommend the most suitable items (evolutionary directions) for different users (solutions), in order to locate the optimal solution to a multiobjective optimization problem in a very large search space within acceptable time. We test our proposed method on different problems from 100,000 to 500,000 dimensions, and experimental results show that our method not only shows good performance but also significant improvement over existing methods.
翻译:我们将决策变量数量大于100,000个维度的多目标优化问题定义为极大规模多目标优化问题。这是一类重要问题,因为许多实际问题需要优化数十万个变量。当处理此规模的问题时,现有的进化优化方法存在不足。受现有推荐系统处理带有有限历史交互的极大规模项目的成功的启发,本文提出了一种称为通过推荐系统进行极大规模多目标优化的方法(VMORS)。该方法的想法是将定义的这种极大规模问题转化为一个可以通过推荐系统解决的问题。在该框架中,解决方案被视为用户,不同的进化方向是等待推荐的项目。我们使用汤普森抽样来推荐最适合不同用户(解决方案)的项目(进化方向),以便在合理时间内在非常大的搜索空间中定位多目标优化问题的最优解。我们在100,000到500,000维度的不同问题上测试了我们的方法,实验结果表明,我们的方法不仅显示出良好的性能,而且比现有方法有显着的改进。