Parallel compact artificial protozoa optimizer algorithm and its application in 3D coverage

At present, wireless sensor networks are undergoing continuous development, and their application scenarios have extended into multiple fields. It is therefore of great importance to improve the quality of network services, and the optimization of node coverage constitutes an important approach to this end. However, when existing metaheuristic solution methods address this high-dimensional optimization problem, they often require a considerable amount of memory owing to population maintenance and tend to get trapped in local optima; thus, meeting the dual requirements of efficiency and accuracy in practical deployment becomes difficult. To accurately resolve the aforementioned bottlenecks, this study presents an improved artificial protozoa optimizer algorithm that integrates a parallel communication mechanism and a compact model. This algorithm adopts a compact strategy, using a probabilistic model to replace the traditional population, thereby significantly reducing memory consumption. Furthermore, it introduces a parallel communication strategy to enhance global search capability and effectively avoid falling into local optima. Extensive experiments are conducted using the CEC2022 and CEC2014 benchmark test functions, covering 10-, 20-, and 100-dimensional spaces. The proposed parallel compact artificial protozoa optimizer (PCAPO) algorithm is compared with state-of-the-art algorithms: compact particle swarm optimization (CPSO), compact bat algorithm (CBA), compact sine cosine algorithm (CSCA), parallel CSCA, parallel compact gannet optimization algorithm, compact cuckoo search, and compact pigeon-inspired optimization. Statistical results show that the PCAPO achieves the optimal average fitness in 22 out of 30 functions in the 100-dimensional tests and outperforms the CPSO and CBA in all 12 functions in the 10-dimensional tests. This demonstrates that the improved algorithm exhibits superior exploration capability and convergence performance over other algorithms of the same type. Finally, applying the improved algorithm to the 3D coverage problem and the compression spring design problem indicates that compared with other methods, the improved optimizer achieves significantly higher coverage efficiency and optimal design parameters. • Using a compact model instead of a traditional population saves the use of computer memory. • Adopting parallel communication and proposing a new ring communication method. • Compared with other algorithms in the same series, PCAPO has better performance. • Applying the PCAPO algorithm to 3D coverage can greatly improve sensor coverage.