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The experiment results show that the proposed method can effectively improve the estimation accuracy and avoid local optima problem.
Moreover, comparison with original algorithms concluded that it improved the accuracy of the final solution and had the capability to avoid the local optima problem.
As the numerical results indicate, embedding Lévy flights made a tremendous improvement towards solving the local optima problem of the traditional PSO.
When doing phylogeny inference the local optima problem really becomes an issue.
We have further shown that, for the hill-climbing algorithm, the all-important local optima problem can be addressed.
All codon-based analyses were conducted using the accepted species tree topology (fig. 2), the F3×4 codon frequency model (Goldman and Yang 1994), complete deletion, and three different starting ω values (0.01, 0.1, and 1) to overcome the multiple local optima problem.
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Stagnation and local optima problems would be avoided by adding diversity to the population, without losing the fast convergence characteristic of PSO.
By this way, the stagnation and local optima problems would be avoided without losing the fast convergence characteristic of PSO since the D2PSO would follow the PSO's behavior for the rest of situations.
Nonetheless, these methods may produce unreliable results due to convergence and local optima problems, as illustrated by the simulation analyses.
Care has been taken while designing the algorithm such that it automatically degenerates to efficient algorithms for solving other simpler optimization problems, such as single-objective uni-optimal problems, single-objective multi-optima problems and multi-objective uni-optimal problems.
We perform simulations to show that with our method fast simultaneous inference of substitution rates and branching times for a given tree topology is not only feasible on large trees but also largely unaffected by local-optima problems.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com