This research develops rigorous mathematical foundations for consensus-based optimization algorithms, where large groups of interacting particles collaboratively search for optimal solutions. Using mean-field theory and propagation of chaos, the work proves long-term stability and improves optimization methods for applications including robotics, aircraft design, and drug discovery under real-world constraints.

This research improves large-scale optimisation by combining problem decomposition with machine learning. By identifying similarities between subproblems, it predicts solutions instead of solving each independently, reducing computational cost. The approach enhances efficiency in logistics and extends to applications such as healthcare scheduling and transport network design.