This paper researches the problem of Beyond Visual Range (BVR) air combat maneuver intention recognition. To achieve efficient and accurate intention recognition, an Attention enhanced Tuna Swarm Optimization-Parallel Bidirectional Gated Recurrent Unit network (A-TSO-PBiGRU) is proposed, which constructs a novel Parallel BiGRU (PBiGRU). Firstly, PBiGRU has a parallel network structure, whose proportion of forward and backward network can be adjusted by forward coefficient and backward coefficient. Secondly, to achieve object-oriented adjustment of forward and backward coefficients, the tuna swarm optimization algorithm is introduced and the negative log-likelihood estimation loss function is used as the objective function, it realizes the dynamic combination of sequence guidance and reverse correction. Finally, the attention mechanism is used to obtain more useful information to improve the recognition accuracy. Through offline recognition experiment, it is proved that A-TSO-PBiGRU can effectively improve the convergence speed and recognition accuracy compared with GRU-related networks. Compared with the other six comparison algorithms, maneuver intention recognition accuracy also has significant advantages. In the online recognition experiment, maneuver intention recognition accuracy of A-TSO-PBiGRU is 93.7%, it shows excellent maneuver intention recognition ability.

To further improve the performance of adaptive gaining-sharing knowledge-based algorithm (AGSK), a novel adaptive gaining sharing knowledge-based algorithm with historical probability expansion (HPE-AGSK) is proposed by modifying the search strategies. Based on AGSK, three improvement strategies are proposed. First, expansion sharing strategy is proposed and added in junior gaining-sharing phase to boost local search ability. Second, historical probability expansion strategy is proposed and added in senior gaining-sharing phase to strengthen global search ability. Last, reverse gaining strategy is proposed and utilized to expand population distribution at the beginning of iterations. The performance of HPE-AGSK is initially evaluated using IEEE CEC 2021 test suite, compared with fifteen state-of-the-art algorithms (AGSK, APGSK, APGSK-IMODE, GLAGSK, EDA2, AAVS-EDA, EBOwithCMAR, LSHADE-SPACMA, HSES, IMODE, MadDE, CJADE, and iLSHADE-RSP). The results demonstrate that HPE-AGSK outperforms both state-of-the-art GSK-based variants and past winners of IEEE CEC competitions. Subsequently, GSK-based variants and other exceptional algorithms in CEC 2021 are selected to further evaluate the performance of HPE-AGSK using IEEE CEC 2018 test suite. The statistical results show that HPE-AGSK has superior exploration ability than the comparison algorithms, and has strong competition with APGSK (state-of-the-art AGSK variant) and IMODE (CEC 2020 Winner) in exploitation ability. Finally, HPE-AGSK is utilized to solve the beyond visual range escape maneuver decision making problem. Its success rate is 100%, and mean maneuver time is 9.10 s, these results show that HPE-AGSK has good BVR escape maneuver decision-making performance. In conclusion, HPE-AGSK is a highly promising AGSK variant that significantly enhances the performance, and is an outstanding development of AGSK. The code of HPE-AGSK can be downloaded from https://github.com/xieleilei0305/HPE-AGSK-CODE.git. (The link will be available for readers after the paper is published).

As optimization problems become more complex, the need of new algorithms becomes greater. In this paper, a new powerful algorithm based on nuclear reaction process, namely, nuclear reaction optimization, is proposed for numerical optimization. The NRO algorithm which includes nuclear fission and fusion phases mimics the fission and fusion processes. In the first phase, the Gaussian walk and differential evolution operators are used for modeling fission process. In the second phase, the variants of differential evolution operators are employed for modeling the ionization stage and fusion stage. Additionally, six benchmark functions and unconstrained engineering design problem are evaluated by NRO and other compared algorithms. The optimization results indicate that the NRO has presented feasibility and superiority performance.