A reinforcement learning-based multi-objective optimization in an interval and dynamic environment

There are many fields involving multi-objective optimization problems in presence of dynamic and interval environments (DI-MOPs), in which the number of objective functions is greater than one, the objectives are conflicting with each other, the problem is varying with time, and the parameters are interval-valued. Conflicts between multiple objectives make interval problems more difficult to be optimized in the dynamic environment. Recent works suffer from the lack of accuracy in change severity detection, the lack of adaptability in change response, and insufficient consideration of reducing imprecision. To tackle these issues, a novel reinforcement learning-based algorithm is proposed in this study, which has three original contributions: (1) Internal interval similarity is specially designed for the interval detection of change severity. To be specific, this operator is proposed for higher accuracy, including the hybridization between the interval similarity and point similarity, and the decision of the detection object and strategy. (2) Q learning is embedded into the optimization algorithm to select the optimal change response after the change occurs. The benefit of this operator is that the response mechanism is dynamically changed in accordance to the environments. (3) To reduce the uncertainty of problems, a new crowding distance operator is presented to guide the search to simultaneously increase diversity, speed up convergence, and decrease imprecision. The computational results from the benchmark sets demonstrate that the proposed algorithm is more efficient than other state-of-the-art algorithms, generating Pareto sets with stronger convergence, wider distribution, and less uncertainty.