Beam pattern optimization using Pareto-enhanced particle swarm with cross-variance optimization (PPS-CVO) algorithm

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In this paper, a novel metaheuristic optimization algorithm, the Pareto-Enhanced Particle Swarm with Cross-Variance Optimization (PPS-CVO) Algorithm, is proposed for the task of underwater acoustic beam pattern optimization. The proposed method introduces several ideas: (1) the incorporation of a Crossover Variational Operator, which enhances population diversity and improves the algorithm’s ability to escape local optima; (2) using the vector difference between two randomly selected high-performing feasible solutions as the step size for particle perturbation. In the early iterations, the step size corresponding to the vector difference is relatively large, allowing feasible solutions to search across the entire solution space, while in the later iterations, the step size becomes smaller, enabling more refined local searches; (3) applying the Pareto distribution to adjust the step size during perturbation, leveraging its long-tail characteristics to enhance the algorithm’s ability to escape local optima during local search in the stages of iteration; and (4) a twophase approach that balances exploration and exploitation throughout the optimization process. During each iteration, the exploration phase allows the feasible solutions to perform large step-size searches, and in the second phase, small step-size perturbations are introduced for local search to prevent the exploration from missing the optimal solution. The performance of the PPS-CVO algorithm was validated through numerical simulations using the CEC 2015 and CEC 2017 benchmark suites, which include a total of 20 test functions (10 from CEC 2015 and 10 from CEC 2017), as well as beamforming optimization tasks. Results from these benchmark suites demonstrate that the PPS-CVO algorithm outperforms 10 well-known algorithms in most unimodal and multimodal optimization problems. Specifically, in the underwater acoustic beamforming optimization problem, which is a high-dimensional, nonlinear challenge involving the shaping of the beam pattern. It can be seen from the experimental comparison between the PPS-CVO algorithm and other 10 famous algorithms, PPS-CVO shows significant improvements in sidelobe suppression and null-steering. This results in more precise interference rejection and faster convergence compared to other competing algorithms. These findings highlight the robustness and practical applicability of the PPS-CVO algorithm in complex engineering tasks.

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