A Recommender System Approach for Very Large-scale Multiobjective Optimization

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.