Combinatorial Optimization

Combinatorial optimization is a category of problems that involve optimizing functions over combinations of discrete objects, with solutions being constrained by specific conditions. The goal in this field is to find the optimal or near-optimal solution while satisfying certain constraints. Many combinatorial optimization problems are NP-hard, meaning that exact solutions cannot be found within polynomial time; instead, algorithms are used to obtain approximate solutions with a certain degree of error within polynomial time. Combinatorial optimization holds significant application value in areas such as path planning, resource allocation, and scheduling.