Fig 1.
(a) Random initialized population distribution (b) Good point set initialized population distribution.
Fig 2.
Flowchart of OP-ZOA algorithm.
Table 1.
CEC2017 basic functions.
Table 2.
Ablation comparison experimental data.
Table 3.
The p-values obtained by Wilcoxon signed-rank test of ablation experiments.
Fig 3.
Iterative curve of ablation experiment.
Fig 4.
Box plot of ablation experiment data.
Fig 5.
Convergence analysis plot for OP-ZOA (Search history, Average fitness, Trajectory of 1st dimension, Population diversity, Changes in the percentage of exploration and exploitation).
Fig 6.
CEC2017 test function images and iteration curves of different algorithms.
Fig 7.
Box plots of different algorithms on CEC2017 test function.
Table 4.
CEC2017 test function test results.
Table 5.
The p-values obtained by Wilcoxon signed-rank test.
Table 6.
Sensitivity analysis of escape coefficient (R) and escape strategy probability threshold (Ps) (based on Mean value).
Fig 8.
Escape coefficient (R) and escape strategy probability threshold (Ps) unimodal functions analysis.
Fig 9.
Escape coefficient (R) and escape strategy probability threshold (Ps) hybrid functions analysis.
Fig 10.
Escape coefficient (R) and escape strategy probability threshold (Ps) composition functions analysis.
Fig 11.
CEC2017 Summary Analysis of Optimal Function Parameters.
Table 7.
Path data for different algorithms in four different environments.
Fig 12.
Path planning chart for Environment 1 (10 × 10, destination containing obstacles).
Fig 12 demonstrates the path planning performance in a 10 × 10 environment from start point (1,1) to target (7,9). The traditional APF method becomes trapped in a local optimum at (6.97,9.05), exhibiting endpoint oscillations. In contrast, OP-ZOA and the seven comparison algorithms successfully escape this local optimum, achieving collision-free path completion. This comparative result highlights OP-ZOA’s effectiveness in overcoming the characteristic limitations of APF methods.
Fig 13.
Path planning chart for Environment 2 (10 × 10, destination containing obstacles).
Fig 13 illustrates path planning performance in a 10 × 10 environment from start point (5,0) to target (5,9). The traditional APF method becomes trapped in a local optimum at (4.93,9.0), resulting in endpoint oscillations. However, OP-ZOA and all seven comparison algorithms successfully overcome this local optimum, completing collision-free path planning. These results further demonstrate the superior capability of OP-ZOA in handling local optima compared to traditional APF approaches.
Fig 14.
Path planning chart for Environment 3 (15 × 15, U-shaped obstacles).
Fig 14 presents path planning results in a 15 × 15 environment from start point (14,13) to target (1,0). The APF method encounters a U-shaped obstacle at (8.79,6.98) and becomes trapped in a local optimum. While OP-ZOA and six other comparison algorithms successfully escape this local optimum and complete collision-free path planning, the SWO algorithm fails due to obstacle collisions. This comparative analysis demonstrates OP-ZOA’s robust performance in complex obstacle environments where traditional methods like APF and certain optimization algorithms (SWO) exhibit limitations.
Fig 15.
Path planning chart for Environment 4 (15 × 15, U-shaped obstacles).
Fig 15 demonstrates path planning performance in a 15 × 15 environment from start point (15,2) to target (3,4). The traditional APF method encounters a U-shaped obstacle at (8.82,6.9) and becomes trapped in a local optimum. While OP-ZOA and five other algorithms successfully escape this local optimum and achieve collision-free path completion, the SWO, BSLO, and PLO algorithms fail due to obstacle collisions. These findings further substantiate OP-ZOA’s enhanced robustness in complex navigation environments where multiple comparative algorithms demonstrate performance constraints.
Fig 16.
Iteration curves of different algorithms.
Fig 17.
Planning path distances for four different algorithms in four different environments.