Recently, a new iterative optimization framework utilizing an evolutionary algorithm called"Prototype Optimization with Evolved iMprovement Steps"(POEMS) was introduced, which showed good performance on hard optimization problems - large instances of TSP and real-valued optimization problems. Especially, on discrete optimization problems such as the TSP the algorithm exhibited much better search capabilities than the standard evolutionary approaches. In many real-world optimization problems a solution is sought for multiple (conflicting) optimization criteria. This paper proposes a multiobjective version of the POEMS algorithm (mPOEMS), which was experimentally evaluated on the multiobjective 0/1 knapsack problem with alternative multiobjective evolutionary algorithms. Major result of the experiments was that the proposed algorithm performed comparable to or better than the alternative algorithms.