Path planning is a key technology currently being researched in the field of mobile robotics, but traditional path planning algorithms have complex search spaces and are easily trapped in local minima. To solve the above problems and obtain the global optimal path of the mobile robot, a fusion multi-strategy marine predator algorithm (FMMPA) is proposed in this paper. The algorithm uses a spiral complex path search strategy based on Archimedes’ spiral curve for perturbation to expand the global exploration range, enhance the global search ability of the population and strengthen the steadiness of the algorithm. In addition, nonlinear convex decreasing weights are introduced to balance the ability of the algorithm for global exploration and local exploitation to achieve dynamic updating of the predator and prey population positions. At the same time, the golden sine algorithm idea is combined to update the prey position, narrow the search range of the predator population, and improve the convergence accuracy and speed. Furthermore, the superiority of the proposed FMMPA is verified by comparison with the original MPA and several well-known intelligent algorithms on 16 classical benchmark functions, the Wilcoxon rank sum test and part of the CEC2014 complex test functions. Finally, the feasibility of FMMPA in practical application optimization problems is verified by testing and analyzing the mobile robot path planning application design experiments.

<p style='text-indent:20px;'>In this paper, we prove that every quasiconformal deformation of a subhyperbolic rational map on the boundary of a hyperbolic component <inline-formula><tex-math id="M1">\begin{document}$ \mathcal{H} $\end{document}</tex-math></inline-formula> still lies on <inline-formula><tex-math id="M2">\begin{document}$ \partial \mathcal{H} $\end{document}</tex-math></inline-formula>. As an application, we construct geometrically finite rational maps with buried critical points on the boundaries of some hyperbolic components.</p>

In this paper, we construct geometrically finite rational maps with buried critical points on the boundaries of some hyperbolic components by using the pinching and plumbing deformations.