Integrated Geometry and Adaptive PTO Optimisation of Hybrid Wind–Wave Energy Systems Using Reinforcement Learning-Assisted Co-Evolution

Abstract

Hybrid wind–wave energy systems (HWESs) require coordinated geometry and control design to balance long-term energy capture and floating-platform response under variable offshore conditions. This study develops a constrained multi-objective framework that jointly optimises fixed wave energy converter (WEC) geometry and sea-state-dependent power take-off (PTO) settings over probability-weighted wind–wave states. The objectives are to maximise annual mean WEC power and minimise root-mean-square (RMS) nacelle acceleration subject to a state-wise operational vertical-clearance constraint. An enhanced reinforcement-learning-assisted constrained multi-objective evolutionary algorithm, termed DRLOS2-EMCMO, is developed using an adaptive GA–DE variation portfolio, stage-aware reward learning, and diversity-aware dual-population search. On 28 constrained benchmark problems, DRLOS2-EMCMO reduces accumulated inverted generational distance (IGD) by 3.14%, increases accumulated hypervolume (HV) by 1.18%, and reduces runtime by 23.48% relative to DRLOS-EMCMO. Applied to four offshore HWES sites, the method identifies clear trade-offs between energy capture and structural response. The selected knee designs retain 45.8–66.0% of the power of the power-oriented designs while reducing RMS nacelle acceleration by 42.2–46.2%. WEC radius governs most of the attainable power range within the investigated design space, with a one-step reduction from the knee-design radius decreasing annual mean WEC power by 11.1–17.6%, whereas adaptive PTO scheduling primarily redistributes energy capture and platform response among sea states. The sea states controlling the clearance margin do not necessarily coincide with those contributing most to annual power, supporting site-specific joint geometry–control optimisation over the long-term environmental distribution.