This study is motivated by the need to support concept selection under conflicting objectives. A recent idea concerning concept-based relaxed-Pareto-optimality is employed to develop a "soft" evolutionary search approach.The proposed method allows set-based conceptual solutions,with performances close to those of the concept-based Paretooptimal set, to survive the evolutionary search process. This allows designers, which are engaged in concept selection to examine not only the Pareto-optimal solutions from the different concepts. The relaxed-optimality exposes, within a desired performance resolution, other particular solutions of interest in concept selection. The proposed numerical solution approach involves a modification of NSGA-II to meet the needs of solving the described problem. The suggested algorithm is demonstrated using both an academic test function and aconceptual path planning problem.