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Wave energy technologies have the potential to play a significant role in the supply of renewable energy worldwide. One of the most promising designs for wave energy converters (WECs) are fully submerged buoys. In this paper, we explore the optimisation of WEC arrays consisting of three-tether buoys. Such arrays can be optimised for total energy output by adjusting the relative positions of buoys in a wave farm. As there are complex hydrodynamic interactions among WECs, the evaluation of each parameter setting is computationally expensive and thus limits the feasible number of full model evaluations that can be made. Furthermore, these WEC interactions make up a non-convex, multi-modal (with multiple local-optima), continuous and constrained optimisation problem. This problem is challenging to solve using optimisation methods. To tackle the challenge of optimising the positions of WECs in a wave farm, we propose a novel multi-swarm cooperative co-evolution algorithm which consists of three meta-heuristics: the multi verse optimiser (MVO) algorithm, the equilibrium optimisation (EO) method, and the moth flame optimisation (MFO) approach with a backtracking strategy, we introduce a fast, effective new surrogate model to speed up the process of optimisation. To assess the effectiveness of our proposed approach, 11 state-of-the-art bio-inspired algorithms and three recent hybrid heuristic techniques were compared in six real wave situations located on the coasts of Australia, with two wave farm sizes (four and nine WECs). The experimental study presented in this paper shows that our hybrid cooperative framework exhibited the best performance in terms of the quality of obtained solutions, computational efficiency, and convergence speed compared with other 14 state-of-the-art meta-heuristics. Furthermore, we found that the power output of the best-found 9-buoy arrangements were higher than that of perpendicular layouts at at 4.15%, 3.29%, 3.62%, 9.2%, 5.74%, and 2.43% for the Perth, Adelaide, Sydney, Tasmania, Brisbane, and Darwin wave sites, respectively. Our investigations reveal that the best-found arrangement at the Tasmania wave site was able to absorb the highest level of wave power relative to the other locations.

Wave energy technologies have the potential to play a significant role in the supply of renewable energy on a world scale. One of the most promising designs for wave energy converters (WECs) are fully submerged buoys. In this work, we explore the optimisation of WEC arrays consisting of a three-tether buoy model called CETO. Such arrays can be optimised for total energy output by adjusting both the relative positions of buoys in farms and also the power-take-off (PTO) parameters for each buoy. The search space for these parameters is complex and multi-modal. Moreover, the evaluation of each parameter setting is computationally expensive -- limiting the number of full model evaluations that can be made. To handle this problem, we propose a new hybrid cooperative co-evolution algorithm (HCCA). HCCA consists of a symmetric local search plus Nelder-Mead and a cooperative co-evolution algorithm (CC) with a backtracking strategy for optimising the positions and PTO settings of WECs, respectively. Moreover, a new adaptive scenario is proposed for tuning grey wolf optimiser (AGWO) hyper-parameter. AGWO participates notably with other applied optimisers in HCCA. For assessing the effectiveness of the proposed approach five popular Evolutionary Algorithms (EAs), four alternating optimisation methods and two modern hybrid ideas (LS-NM and SLS-NM-B) are carefully compared in four real wave situations (Adelaide, Tasmania, Sydney and Perth) with two wave farm sizes (4 and 16). According to the experimental outcomes, the hybrid cooperative framework exhibits better performance in terms of both runtime and quality of obtained solutions., Information Sciences (2020)