Combinatorial Optimisation

Combinatorial optimization focuses on finding the best solution from a finite set of possibilities, often facing computationally hard problems. Current research emphasizes developing efficient approximation algorithms, including those leveraging neural networks and reinforcement learning, to tackle challenges like the knapsack and travelling salesman problems. These advancements are driven by the need for improved solution quality and scalability across diverse applications, from robotics and logistics to graph partitioning and Bayesian network structure learning. The field is also exploring methods to improve constraint satisfaction within neural network approaches and to certify the correctness of solutions obtained through symmetry and dominance breaking techniques.