## 1 Introduction
### Optimization Algorithm and Framework  
The Omni optimizer developed by [PERSON] et al. [39] was used by the optimization algorithm. The Omni optimizer is a powerful and universal optimization tool, being used to solve single-objective and multi-objective optimization problems with complex constraints. It integrates a series of efficient operators such as using SBX crossover and polynomial variation to generate new individuals and adopting \(\varepsilon\)-decision and adaptive niche techniques to maintain population diversity and avoid local convergence. However, it also integrates an efficient constraint handling mechanism that can handle any number of equality and inequality constraints. The Omni optimizer has been tested by a number of standard functions representing different features, including non-convex, nonlinear, and discontinuous, containing a large number of optimized variables and constraints, which have been proven to have excellent performances [39].  
The dominant selection constraint mechanism is adopted to deal with a large number of constraints in the power system optimization [39; 40]. This mechanism uses the binary tournament selection, where two solutions are picked from the population and the better solution is chosen. In the presence of constraints, each solution can be either feasible or infeasible. There may be at most three situations: (a) both solutions are feasible, (b) one is feasible and other is not, and (c) both are infeasible. Thereby, a simple domination rule is used for each case. A solution \(i\) is said to constrained-dominate a solution \(j\), if any of the following conditions is true. (1) Solution \(i\) is feasible and solution \(j\) is not, (2) solutions \(i\) and \(j\) are both infeasible but solution \(i\) has a smaller overall constraint violation, and (3) solutions \(i\) and \(j\) are feasible and solution \(i\) has a better objective value than solution \(j\). Since in no case constraints and objective function value are compared with each other, there is no need of having any penalty parameter. Moreover, the mechanism only needs to modify the selection operation of the optimization algorithm, and can be combined with various evolutionary algorithms.  
Coupled with the Omni optimizer, the connection topology and optimized framework for the wind farm power system are shown in Figure 3. The specific steps were as follows: First, the coordinates of the wind turbine group and basic parameters such as cables and algorithms were entered as the input the variables of the connection topology and cable cross section were coded; the initial population was randomly generated, and the power parameters of the generated topology were analyzed to obtain the values of the optimization target and the constraints; and the Omni optimizer's crossover, mutation, and elite preservation operations were performed to generate new population. Finally, the convergence was judged; if it converged, the result of the optimization was an output; if there was no convergence, the population was updated and the optimization operation of \(t+1\) generation was carried out.  
Figure 3: Optimization process of wind farm power system.