342 Figure 10 - Flowchart for life cycle performance requirements design of coal mine cemented backfill 2.2 Multi-objective Ratio Optimization Method To design the optimal formulation based on the life cycle performance requirements of the backfill material, a multi-objective optimization approach employing the NSGA-III algorithm is adopted. This is combined with the Sobol sensitivity algorithm to select the Pareto optimal solutions (Liu et al., 2025), as illustrated in Fig. 2. Figure 11 - NSGA-III algorithm procedure flowchart The multi-objective optimization process for cemented backfill materials mix proportion design based on the Sobol-NSGA-III algorithm is as follows: (1) Prepare cemented backfill materials for performance testing; (2) Determine the reasonable range of influencing factors and establish a non-linear multivariate analysis model using statistical theory; (3) Employ the Sobol algorithm to analyze the sensitivity of material performance Tests data Step 3:Sobol and NSGA-III Analysis start Initial set of Parameters Pt F1 F2 F3 …… Qt Rt Pt+1 F1 F2 F3 …… Convergence ？ Pareto Solution set N Y Nondominant sort Individual normalization Gene manipulation Sort normalization Pruning ratio set Multivariate Nonlinear Regression Model Step 2:Establish Analysis Model Reasonable range of materials Performance indexes Second-order polynomial Third-order polynomial UCS BR Slump ST Step 1:Material Performance Test Optimal Ratio of Backfilling Material Step 4:Material Ratio Optimization The principle of Sobol-NSGA-III multi-objective optimization method Sobol sequence sampling sensitivity indices wi Xi Factors normalization =∑ i i i f Xw ~ 1 ( ) = − i Ti V S V y
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