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Cui et al. Complex Eng Syst 2023;3:3 I http://dx.doi.org/10.20517/ces.2022.57 Page 9 of 15

Figure 3. Optimization model of EHPS.

(2) Calculate the fitness degree of each individual by fitness function, sorting all individuals according to non-
dominated regulation;

(3) Generate the next population ( ) ≥ 1 by crossover and mutation, and the size of is . Forming a new
population consisted of and ;

(4) Calculate the fitness degree and crowd degree for each individual. Then, select individuals to constitute
a new population +1 according to the non-dominated regulation;

(5) = + 1;

(6) Run Step 3 to Step 5 repeatedly until equals to the maximum generation.

The flowchart of the NSGA-II algorithm is shown in Figure 4.

3.3. Optimization results
According to the established multi-objective collaborative optimization model of the EHPS system, the NSGA-
II is applied to the main system for the overall optimization of evaluation indexes, and the NLPQL algorithm
is applied to each subsystem for the consistency of design variables. Additionally, the multi-objective particle
swarm optimization algorithm (MOPSO) and NCGA multi-objective optimization algorithms are applied to
the main system, and the NSGA-II algorithm is used to optimize the whole EHPS system. The solution set
distribution of the optimization results is shown in Table 3, and the multi-objective optimization results are
shown in Table 4.

Table 4 shows the distribution of the Pareto solutions obtained by different multi-objective algorithms. It
should be noted that all algorithms are executed 2000 times.