*3.4. Accelerating Evolution*

The acceleration coefficients *c*1 and *c*2 (Equation (8)) are the cognitive attraction coefficients in the optimization process, and the optimization of the group is controlled by the learning situation. In the early stage of the optimization process, the particles need strong self-cognition and weak social cognition. The global search function is more important. At this time, the particle can traverse as many local extremes as possible in the search space.

In the later stage of optimization, the particles must have strong social cognition and weak self-awareness to avoid falling into local extremes in optimization. The values of the cognitive attraction coefficients reflect the degree of influence of the information exchange on particles, and the information exchange includes the experiential information of the particle itself and the global optimal information. Setting the learning factor to a value that is too large or too small is not conducive to the optimization of the particles, so it is necessary to balance the evolution speed of the particles in the early and late stages of the optimization process.

The enhancing effect of sine-cosine mapping on population diversity and convergence in the optimization process can be used to improve this linear asynchronous strategy. We use sine-cosine acceleration coefficients (SCACs) to adjust the balance between individual cognition and social cognition [42]. The cognitive attraction coefficient can be expressed as:

$$\begin{array}{l} c1 = a \times \sin\left(\left(1 - \frac{t}{T}\right) \times \frac{\pi}{2}\right) + \delta\\ c2 = a \times \cos\left(\left(1 - \frac{t}{T}\right) \times \frac{\pi}{2}\right) + \delta, \end{array} \tag{12}$$

where the constants *α* and *δ* are 2 and 0.5, respectively.
