# An enhanced parrot optimizer with multiple strategies for wireless sensor network node deployment

## TL;DR

This paper introduces an improved parrot optimizer algorithm that solves optimization problems more efficiently and effectively, especially in wireless sensor network node deployment.

## Contribution

The paper introduces an Enhanced Parrot Optimizer (EPO) with five novel strategies to overcome limitations in previous optimization algorithms.

## Key findings

- EPO outperforms eleven state-of-the-art algorithms on the CEC2017 benchmark suite across multiple dimensions.
- EPO improves wireless sensor network node deployment coverage by up to 6.7% compared to the original parrot optimizer.
- Statistical tests confirm EPO's performance is significantly better in 81.2% to 91.6% of cases across different problem sizes.

## Abstract

This paper presents an Enhanced parrot Optimizer (EPO), a novel metaheuristic algorithm that synergistically integrates multiple advanced strategies to address the critical limitations of the original parrot Optimizer (PO)—namely, poor initial population diversity, susceptibility to premature convergence, slow convergence speed, and the absence of an effective restart mechanism. EPO introduces five key innovations across its behavioral phases: (1) Cubic chaotic mapping is employed to generate a high-quality, well-distributed initial population, enhancing global exploration from the outset; (2) a risk-aware alert-contraction mechanism—inspired by predator-avoidance strategies in swarm intelligence—is embedded in the staying behavior to proactively detect and escape local optima; (3) a nonlinear decay factor dynamically balances exploration and exploitation during the communicating behavior phase; (4) a dual-layer intelligent judgment system governs the “fear of strangers” behavior, combining elite-guided convergence (outer layer) with diversity preservation (inner layer); and (5) a hybrid local restart mechanism is activated upon three consecutive generations of stagnation, applying t-distribution perturbation to low-fitness individuals for large-scale jumps and Differential Evolution (DE) to high-fitness individuals for refined local search.The performance of EPO is rigorously evaluated on the CEC2017 benchmark suite at 30, 50, and 100 dimensions, with comprehensive comparisons against eleven state-of-the-art metaheuristic algorithms—including PO, MPO, SMO, BTO, HOA, HHO, DBO, BKA, PSO, DE, and the Ivy algorithm. EPO achieves the best mean ranking across all dimensionalities (2.31 at 30D, 2.03 at 50D, and 1.83 at 100D), consistently outperforming all competitors in terms of solution accuracy, convergence speed, and stability. Wilcoxon signed-rank tests at a significance level of α = 0.05 confirm that the EPO algorithm achieves statistically significantly better performance than its competitors in 212 cases (81.2%) at 30D, 225 cases (86.2%) at 50D, 225 cases (86.2%) at 50D, 239 cases (91.6%) at 100D. Furthermore, EPO is successfully applied to the real-world Wireless Sensor Network (WSN) node deployment problem, consistently outperforming the original PO across different network scales: with 20 nodes, coverage improves from 0.7765 to 0.8284 (+ 6.7%); with 30 nodes, from 0.9285 to 0.9871 (+ 6.3%); and with 40 nodes, from 0.9826 to 0.9992 (+ 1.7%).Collectively, these findings validate that EPO not only advances the theoretical foundation of parrot-inspired optimization but also provides a powerful and reliable tool for solving complex real-world optimization problems.