1578 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 95 - 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 indicators to different factors, then apply the NSGA III algorithm to perform multiobjective optimization on the analytical models of multiple performance indicators, yielding a Pareto optimal mix proportion design within the reasonable range; (4) Rank factors based on sensitivity discrimination indices, then optimize the backfill material composition for different target properties to derive the optimal formulation. 3. MICROBIALLY CEMENTED BACKFILL MATERIALS FOR COAL MINES AND THEIR CONSOLIDATION MECHANISM 3.1 Microbially Cemented Backfill Materials for Coal Mines 3.1.1 Raw Material Composition (1) Microorganisms. Various microorganisms can be employed for microbially cemented backfill materials, among which urease-producing bacteria, such as Sporosarcina pasteurii, are most commonly used. (2) Nutrient solution. A commonly used nutrient solution is a mixed solution of calcium chloride and urea. The concentrations of urea and calcium chloride typically range from 0.25 to 3 mol/L, with the molar ratio of urea to calcium chloride generally maintained at 1:1. (3) Aggregates. The aggregates used in microbially cemented backfill materials are mainly solid wastes, such as coal gangue, and aeolian sand. 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 =å iii fXw Decrease？ Cost? Y N Solution set sort Optimal Solution Verification ~ 1 () =- i Ti V S Vy
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