Concept-based MOEAs are tailored MOEAs that aim at solving problems with a-priori defined subsets of solutions that represent conceptual solutions. In general, the concepts' subsets may be associated with different search spaces and the related mapping into a mutual objective space could have different characteristics from one concept to the other. Of a particular interest are characteristics that may cause premature convergence due to local Pareto-optimal sets within at least one of the concept subsets. First, the known ε-MOEA is tailored to cope with the aforementioned problem. Next, the performance of the new algorithm is compared with C 1-NSGA-II. Concept-based test cases are devised and studied. In addition to demonstrating the significance of premature convergence in concept-based problems, the presented comparison suggests that the proposed tailored MOEA should be preferred over C 1-NSGA-II. Suggestions for future work are also included.