Fig. 1

Schematic diagram of game calculation in two dimensional space

Fig. 2

Pursuit direction of failed individual in target space

Fig. 3

Schematic diagram of elite individual screening strategy based on dominance

Fig. 4

Schematic diagram of the effectiveness of paired elite sets of four individuals in two games

Fig. 5

Elite individual screening strategy based on Pareto dominance relationship and multi-index

Fig. 6

Example of box counting dimension in two-dimensional space

Fig. 7

IGD curves of MOMEIG algorithm with different k values

Table 1

Test function properties

Table 2

Algorithm parameters

Table 3

IGD mean of MOMEIG algorithm with three ablation variants on standard test functions

Fig. 8

Results of particle distribution in outer space of ZDT4 function

Fig. 9

Algorithm function test results

Table 4

Comparison of IGD index between MOMEIG algorithm and other classical algorithms

Fig. 10

MOMEIG and four classical algorithms run independently for 30 times IGD index box diagram

Table 5

Comparison of IGD mean values of MOMEIG and GMOPSO(N=100, Gen=100)

Table 6

Comparison of IGD mean values of MOMEIG and AMOPSO-DA(N=100, Rep=100, Gen=200)

Table 7

Comparison of IGD mean values of MOMEIG and pccsAMOPSO(N=100, Rep=100, Gen=300)

Table 8

Comparison of IGD mean values of MOMEIG and MOFA-MCS(N=100, Rep=100, Gen=200)

Fig. 11

A simple water supply network

Table 9

Coded representation of pump scheduling problem

Fig. 12

Optimal solution set of pump scheduling

Table 10

Cost of pump scheduling scheme