## 4 Collision Avoidance Decision Support Based on CIPSO Algorithm
### CIPSO Algorithm  
In the PSO, the inertia weight controls the speed and direction of the particles moving in the search space. If the inertia weight is excessively large, the particles may skip the global optimal solution and fall into the local optimal solution. Conversely, if the inertia weight is excessively small, particles may persistently meander around the local optimal solution and find it difficult to jump out. By dynamically adjusting the inertia weights, the curve-increasing strategy can gradually increase the inertia weights when the individual optimal value of the particle continuously decreases, thus prompting the particle to jump out of the local optimal solution and move toward the global optimal solution. When the particle approaches the global optimal solution, the inertia weight will gradually decrease, thus enabling the particle to search repeatedly near the local optimal solution and improving the search accuracy of the algorithm. Therefore, the curve-increasing strategy can help the PSO to avoid falling into the local optimal solution too early, while maintaining a balance between global search and local search, thus improving the algorithm's search efficiency and convergence accuracy.  
Curve increasing is a control strategy based on the exponential function image proposed in this work, as shown in Figure 3, which tends to become smoother as the independent variable increases. Given the value of inertia weight \(w_{max}\), the curve-increasing formula is:  
\[w_{1}=w_{max}-(w_{max}/T_{max})t_{(time)} \tag{39}\]\[w=e^{-w_{1}} \tag{40}\]  
where \(w_{max}\) is the set of larger inertia weights (\(w_{max}\geq 1\)), \(t_{(time)}\) is the number of current iterations, and the maximum number of iterations is \(T_{max}\); as the number of iterations increases, \(w_{1}\) gradually decreases and \(w\) gradually increases. Using the above adaptive weight-change formula, the particle has a fine search ability in the early stage due to the small weight value and, combined with the image, it can be seen that the algorithm iterates the early \(w_{1}\) value in a large reduction trend range. This is extremely slow, ensuring the adequacy of the particle local search, and the later change trend gradually increases, causing a certain perturbation effect on several local solutions and ensuring that a global search is possible. \(w_{max}\) value late trend changes occur; the purpose of these is no longer to ensure faster convergence in the conventional sense, as the trend of change is actually relatively steep and absolutely smooth after the two transformations of Equations (39) and (40).  
Refarding the acceleration factor, this work proposes an improved second-order oscillation method, which introduces a curve-increasing strategy that combines two populations to improve the diversity of the population and further improve the global search ability of the algorithm. The improved formula is as follows:  
\[\begin{array}{c}v_{ij}\Big{(}t)\;=\;e^{-w_{1}}v_{ij}\Big{(}t)\;+\;r_{1}\Big{[} P_{ij}(t)-(1+\mu_{1})x_{ij}\Big{(}t)\;+\;\mu_{1}x_{ij}^{*}(t)\Big{]}+r_{2} \Big{[}P_{gi}(t)-(1+\mu_{2})x_{ij}\Big{(}t)\;+\;\mu_{2}x_{ij}^{*}(t)\,\Big{]}\\ \qquad\qquad\qquad\qquad\qquad\qquad\qquad x_{ij}^{*}(t)=x_{ij}(t)\\ x_{ij}(t+1)=x_{ij}(t)\;+\;v_{ij}(t+1)\end{array} \tag{41}\]  
where \(x_{ij}^{*}\) is a new species group; \(T\) is the current iteration number; second-order oscillation factor \(\mu_{1,2}\) is denoted as  
\[\mu_{1}=(2\,\sqrt{c_{1}rand()-1})\;\cdot\;rand()\;\cdot\;rand()/c_{1}\;w\;<2/3w _{max} \tag{42}\]  
\[\mu_{1}=(2\,\sqrt{c_{1}rand()-1})\;\cdot\;rand()\;\cdot\;(1+rand())/c_{1}\;w\; \geq 2/3w_{max} \tag{43}\]  
where \(c_{1}\) and \(c_{2}\) are an artificially set acceleration factor; _rand_ () is a random number from 0 to 1. The optimization process of the CIPSO algorithm is shown in Figure 4.  
Figure 3: Curve incremental strategy function.  
Finally, to further understand the solution process of the CIPSO algorithm, the pseudo-code of Algorithm 1 is presented.