Imitation Learning for Multiobjective Optimization-AlphaMOEA

In the last decade, a variety of multiobjective evolutionary algorithms (MOEAs) with specific enhancements have been developed for solving multiobjective optimization problems (MOPs). In this article, unlike MOEAs, we provide a new artificial intelligence approach to solve MOPs, which adopts an imitation learning-based end-to-end method, namely AlphaMOEA. AlphaMOEA is entirely a model composed of neural networks that mainly follow the architecture of multitask learning (MTL). It has two training stages: the supervised learning (SL) stage and the reinforcement learning (RL) stage. In the SL stage, AlphaMOEA fits the solutions in the decision space provided by a number of selected MOEAs. Since neural networks in AlphaMOEA are composed of parameters with high dimensions, the fitting process can be viewed as a transformation of the solutions from a low-dimensional space into a high-dimensional space. This allows AlphaMOEA to obtain different valuable knowledge from a perspective of high dimensionality. Then, AlphaMOEA is trained in the RL stage to obtain good performance for MOPs with various problem characteristics in a self-driven manner. The RL stage relies on several designed components, including a similarity-based state design to measure the distance between solutions, an evolution operator-based action set to provide exploration behavior, and an indicator-guided reward to produce an incremental evaluation. Experimental results demonstrate that AlphaMOEA can learn valuable information about the decision space in high-dimensional representations, thereby achieving a desirable balance between exploration and exploitation. AlphaMOEA can further improve the performance for solving MOPs with various problem characteristics in a reasonable time.