An Integrated Online-Offline Hybrid Particle Swarm Optimization Framework for Medium Scale Expensive Problems*

Real-world optimization problems often involve computationally expensive evaluations, making efficient optimization crucial. To address medium-scale expensive optimization problems, this paper proposes and investigates an Integrated Online-Offline Hybrid Particle Swarm Optimization Framework (IOOPSOF). The framework integrates concepts from active learning and ensemble learning, iteratively querying the most uncertain and highest-precision solutions to achieve efficient utilization of evaluation resources. IOOPSOF employs two distinct sample selection criteria, with offline optimization for exploration and online optimization for exploitation. The effectiveness of the proposed method is validated through experiments on a series of low to medium-dimensional benchmark functions and the operational parameter optimization of Enhanced Geothermal Systems (EGS). Results demonstrate that IOOPSOF significantly outperforms existing methods, achieving global optimum (0) on most benchmark functions and showing superior performance over single surrogate-assisted evolutionary algorithms (SAEAs) on real-world problems, thereby showcasing its exceptional potential for solving expensive optimization problems.