A probability model based evolutionary algorithm with priori and posteriori knowledge for multiobjective knapsack problems

Most evolutionary algorithms utilize the posteriori knowledge learned from the running process to guide the search. It is arguable that the priori knowledge about the problems to tackle can also play an important role in problem solving. To demonstrate the importance of both priori and posteriori knowledge, in this paper, we proposes a decomposition based estimation of distribution algorithm with priori and posteriori knowledge (MEDA/D-PP) to tackle multiobjective knapsack problems (MOKPs). In MEDA/D-PP, an MOKP is decomposed into a number of single objective subproblems and those subproblems are optimized simultaneously. A probability model, which incorporates both priori and posteriori knowledge, is built for each subproblem to sample new trail solutions. The proposed method is applied to a variety of test instances and the experimental results show that the proposed algorithm is promising. It is demonstrated that priori knowledge can improve the search ability of the algorithm and posteriori knowledge is helpful to guide the search.