This thesis is a result of a motivation to advance the computational tools, which are used to support designers during the conceptual design stage of a multi-objective engineering design problem. The thesis involves contributions concerning four major topics including: a. simultaneous concept-based evolution of concepts towards and along a Pareto front, b. interactive concept-based evolution towards optimal solutions of preferred concepts, c. assessment of concepts in the multi-objective space, and d. supporting decision making with uncertainties due to delayed decisions. It should be noted that, with respect to the first contribution, the problem of simultaneous mechanics and control design, at the conceptual design level, is of a particular motivation to this study. Together the contributions of this thesis advance the state-of-the-art of methods to search, compare and select solution concepts in multi-objective problems. In this thesis the concept-based multi-objective optimization problem is studied and its distinction from the traditional multi-objective problem is discussed. The concept-based problem involves concepts that are represented by particular designs (solution sets) which are associated with the concepts. The main assumption is that these concepts have reached a stage in which models are available for their evaluation. As a part of the presented study, novel evolutionary algorithms are developed, using a simultaneous search approach, to solve the concept-based multi-objective optimization problem. In particular, the suggested algorithms address the issue of resource sharing among concepts, and within each concept, while simultaneously evolving concepts towards a Pareto front by way of their representing sets. The introduced algorithms are compared with a sequential one from two major aspects: the computational time and the quality of the front's representation. Next, the concept-based multi-objective optimization problem is extended to include interactivity, which is the main motivation to the development of the simultaneous algorithms. The interactive concept-based problem involves both model-based optimality and the subjectivity of the designers. A novel interactive concept-based multi-objective algorithm is presented. The articulation of designers' preferences towards concepts and sub-concepts, as suggested in this thesis, establishes a new approach to the integration of preferences within evolutionary based algorithms. The results of both of the above suggested approaches are associated with the representation of the concepts solutions' performances within a multi-objective space. Selection between concepts based on these representations is the next step. In this thesis a new approach to support such a selection is introduced. Both aspects of optimality and variability, which are associated with concept selection, are taken into account. Furthermore, the uncertainty towards the preferences of objectives, which is inherent to multi-objectives problems, is also considered by the new approach. In addition, this thesis deals with an uncertainty involving delayed decisions. Such a situation could result from a temporary lack of information during a conceptual design. Here, for the first time, the delayed decision problem is introduced in the context of a MOP. Moreover, a computational tool to support concept selection with the presence of such uncertainty is suggested. To attend this problem, the proposed new selection approach is adapted to allow the assessment of the relative performance of concepts, which involves robustness to delayed decisions. The described concept-based techniques set the stage for a general approach to conceptual engineering design, for cases, with available models. Academic examples as well as engineering examples are used to study and demonstrate the suggested techniques including examples from structural mechanics and from mechatronics. The latter also serves to demonstrate the aptitude of the suggested techniques to deal with simultaneous mechanics and control design at the conceptual design stage.