A meta-exact approach to improve intensification in combinatorial optimization problems

Technical impossibility to solve exactly NP-hard combinatorial optimization problems for large instances requires the use of heuristics. Nevertheless, the exact methods can be useful, when sub-problems can be extracted from the whole problem. Indeed, their resolution contributes in the global solution search, by combining exact resolution of sub-problems and heuristic resolution of the global problem. This approach is generally efficient, because it combines the advantages of two different methods. In this paper we propose to hybridize the metaheuristic MA|PM (memetic algorithm with population management) and B&B to solve combinatorial optimization problems. Our idea is to add in the metaheuristic, an exact method, which has an absolute research power, in order to improve the intensification around the best current solution found by the metaheuristic. We have realized experiments on well-known benchmarks in the literature of the knapsack problem. The results obtained show the effectiveness of Meta/Exact hybridization.