# A Fusion Multi-Strategy Marine Predator Algorithm for Mobile Robot Path Planning
## 3 Fusion Multi-Strategy Marine Predator Algorithm
### Nonlinear Convex Decreasing Weight  
In the equal-velocity ratio stage, both prey and predators are foraging, and the populations are divided into parallel architectures that perform exploitation and exploration simultaneously. However, the communication of populations is limited by the parallel architectures, and the imbalance of exploitation and exploration leads to the algorithm obtaining premature convergence. Therefore, a nonlinear convex weighting strategy is proposed in this paper. Convex decreasing weights \(w\) are introduced in the position update of prey exploitation and predator exploration, and they nonlinearly decrease with the increase in iterations. The predator position receives a large weight that ensures the search domain broadly in the intermediate phase of optimization. The weights decrease drastically in the late phase, allowing the exploitation performance to be enhanced graduallyand as far as possible to accurately search around the optimal individual. To balance the global exploration and local exploitation capabilities. The model for the nonlinear convex decreasing weights \(w\) is shown in Equation (16):  
\[w=(w_{max}-w_{min})\cdot\left(1-\left(\frac{Iter}{Max\_Iter}\right)^{\eta} \right)^{\frac{1}{\eta}}+w_{min} \tag{16}\]  
where \(w_{max}\) and \(w_{min}\) are the preset maximum and minimum values, respectively, and \(\eta\) is a regulating factor. After several experiments, the experimental results are optimal when \(w_{max}=0.5\), \(w_{min}=0.05\), and \(\eta=3\). The comparison chart of different \(\eta\) values is shown in Figure 2.  
The fixed step size of MPA makes the search agents vary in the same proportion continuously, which results in a single search mode and reduced population diversity. In this paper, a dynamic step control factor \(p\) is proposed that changes adaptively with the iterations. The step-size factor is maintained at a large value to ensure the global optimal of FMMPA in the initial iteration [23], so that the search agents have a strong exploration ability and update the search space constantly. The algorithm is guided to approach the globally optimal individual with a small value of \(p\) in the late iteration. Reduce the convergence of populations. The mathematical model for the dynamic step control factor \(p\) is shown in (17):  
\[p=p_{max}-\left(\frac{Iter}{Max\_Iter}\right)\cdot(p_{max}-p_{min}) \tag{17}\]  
where \(p_{max}\) and \(p_{min}\) are the bounds of \(p\), which take the values of [0.05, 0.5]. The model of position updates that the nonlinear convex decreasing weight strategy as shown in Equations (18) and (19):  
\[P_{new}^{l+1}=w\cdot P_{i}^{t}+p\cdot R\otimes s_{i},\;\;i\leq n/2 \tag{18}\]  
Figure 1: Improved Archimedes’ spiral.  
Figure 2: Comparison of different \(\eta\).  
\[P_{new}^{t+1}=w\cdot E_{i}^{t}+p\cdot CF\otimes s_{i},\ \ i>n/2 \tag{19}\]  
where \(w\) is the nonlinear convex decreasing weight and \(p\) is the dynamic step control factor. Position updating with \(w\) can ensure population diversity, and the global search ability of the predator is enhanced in the initial iteration. \(p\) makes the prey have strong local exploitation and accelerates the convergence. This strategy can balance global exploration and local exploitation even in practical problems.