A Robust Optimization Approach for Optimal Chain Pillar Sizing Under Uncertainty

The design of pillars in underground spaces presents a critical challenge due to significant heterogeneity in soil and rock mechanical characteristics. Accurately predicting these properties under conditions of uncertainty is crucial for ensuring structural stability and safety. This study addresses these challenges by employing robust optimization theory, which provides a risk-averse framework for managing uncertain information. By integrating robust optimization techniques and considering uncertainties in mechanical specifications, we successfully achieve dimension design for longwall chain pillars. The primary objective is to develop a solution that remains robust in the face of data uncertainty, thereby mitigating potential risks. To achieve this, we use the GAMS software platform to formulate fundamental equations as robust optimization code, define the objective function, and establish problem constraints. Our findings highlight that adopting a box uncertainty set leads to a more conservative approach compared to an ellipsoidal uncertainty set. As a result, pillar dimensions within the box uncertainty set tend to be larger than those within the ellipsoidal set. The application of this method demonstrates its effectiveness in addressing uncertainties during chain pillar design, establishing a reliable foundation for pillar design in underground mines. This research contributes to advancing pillar design methodologies, offering insights into managing uncertainties and enhancing the stability and safety of underground mining operations. By leveraging robust optimization techniques, this comprehensive approach strengthens the resilience of pillar designs and provides valuable guidance for engineers and practitioners involved in underground mine planning and design.