Solving NP-hard combinatorial problems in the practical sense Invited presentation
It was a remarkable theoretical achievement that complexity theory (in particular the NP-hardness) was able to prove that some combinatorial problems were inherently difficult. However, there is a slight hesitation in saying that NP-hard problems are “intractable”, because there are efficient exact algorithms known for some problems (e.g., knapsack problem, traveling salesman problem and so forth), which can solve very large problem instances. Also recent advances of metaheuristic type algorithms have greatly widen the range of “practically tractable” problems, provided that the proof of exact optimality of the obtained solutions is not required (though in many cases the solutions are actually optimal).
genetic algorithm Then, based on our computational experiments, I try to explain why these approaches are successful in the practical sense, followed by computational results with our codes for some NP-hard problems, including graph coloring, set-covering, generalized assignment, MAX-SAT and those encountered in real applications. The talk will be concluded by pointing out some research directions.