Multi-objective optimization of total solid waste filling ratio based on NSGA-III and entropy-weighted TOPSIS method

To alleviate the growing disposal pressure of coal-based solid wastes and high-salinity wastewater from coal-chemical industries, and to reduce the cost and carbon footprint related to conventional Portland-cement binders for backfilling, the study develops a cemented backfill material derived entirely from industrial by-products. Modified magnesium slag (MMS), coarse coal gasification slag (CGS), desulfurized gypsum (DG), and high-salinity wastewater (HSW) were combined to formulate the total solid waste-based cemented backfill (TSW-CPB) system, and a multi-objective mix-design strategy integrating response surface methodology (RSM)-NSGA-III-entropy-weighted TOPSIS was established. Using an RSM-based Box-Behnken design (BBD), mass concentration (72-80%), aggregate-to-cement ratio (1-2), and aggregate grading index (0.3-0.7) were selected as input factors, while the unconfined compressive strength (UCS) at the 3rd, 14th, and 28th day and the slump were used as responses. The developed regression models were highly significant, without lack-of-fit (P < 0.0001; P > 0.05). Under workability constraints (slump of 15-20 cm for pumping and 23-27 cm for self-flowing) and with economic performance incorporated, a Pareto-optimum solution set was generated and further screened for each workability interval. For the optimal mix proportion under pumping condition, the mass concentration, aggregate-to-cement ratio, and grading index were separately 78.758%, 1.3911, and 0.30504, whereas for the self-flowing condition, they were 77.527%, 1.0003, and 0.5864, respectively. Hydration calorimetry and microstructural analyses indicate that CGS retards the reaction kinetics of the binary system, whereas DG and HSW markedly enhance heat evolution; additionally, HSW facilitates Friedel's salt formation and pore filling, thereby improving matrix densification and strength development. Overall, this work provides a low-cost backfill solution and a transferable multi-objective optimization methodology for synergetic valorization of industrial solid wastes from multiple sources and HSW.