Broad reinforcement learning based adaptive state transition algorithm for global optimization

The state transition algorithm (STA) is an efficient intelligent optimization method with superior search capabilities in diverse applications, while its key operator selection strategies depend on manual design. The integration of deep reinforcement learning (DRL) with STA offers a promising paradigm for adaptive selection strategy during optimization. However, conventional DRL methods require extensive training data and iterative model refinement, creating fundamental barriers with limited evaluation budgets. Therefore, this paper proposes a novel STA framework incorporating broad reinforcement learning to develop an adaptive operator selection mechanism. First, the selection strategy is formulated as a Markov decision process, where an agent learns to identify optimal operators based on real-time state. Specifically, environmental states are characterized through systematic landscape analysis derived from population information. Second, a broad learning system replaces neural networks in DRL frameworks. The associated incremental learning mechanism is carefully designed to enhance training efficiency. Third, a Gaussian mixture model-based data augmentation mechanism is proposed to generate sufficient training samples under limited interactions. The proposed method is evaluated using benchmark functions and practical applications, with comparisons against STA variants and other prominent optimization algorithms. Experimental results demonstrate that BRL-STA achieves competitive performance compared with competitors.