R2 Indicator and Deep Reinforcement Learning Enhanced Adaptive Multi-Objective Evolutionary Algorithm

Abstract

Choosing an appropriate optimization algorithm is essential to achieving success in optimization challenges. Here we present a new evolutionary algorithm structure that utilizes a reinforcement learning-based agent aimed at addressing these issues. The agent employs a double deep q-network to choose a specific evolutionary operator based on feedback it receives from the environment during optimization. The algorithm's structure contains five single-objective evolutionary algorithm operators. This single-objective structure is transformed into a multi-objective one using the R2 indicator. This indicator serves two purposes within our structure: first, it renders the algorithm multi-objective, and second, provides a means to evaluate each algorithm's performance in each generation to facilitate constructing the reinforcement learning-based reward function. The proposed R2-reinforcement learning multi-objective evolutionary algorithm (R2-RLMOEA) is compared with six other multi-objective algorithms that are based on R2 indicators. These six algorithms include the operators used in R2-RLMOEA as well as an R2 indicator-based algorithm that randomly selects operators during optimization. We benchmark performance using the CEC09 functions, with performance measured by inverted generational distance and spacing. The R2-RLMOEA algorithm outperforms all other algorithms with strong statistical significance (p<0.001) when compared with the average spacing metric across all ten benchmarks.