Summary: Because of the necessity for considering various creative and engineering design criteria, optimal design of an engineering system results in a highly-constrained multi-objective optimization problem. Major numerical approaches to such optimal design are to force the problem into a single objective function by introducing unjustifiable additional parameters and solve it using a single-objective optimization method. Due to its difference from human design in process, the resulting design often becomes completely different from that by a human designer.This paper presents a novel numerical design approach, which resembles the human design process. Similar to the human design process, the approach consists of two steps: (1) search for the solution space of the highly-constrained multi-objective optimization problem and (2) derivation of a final design solution from the solution space. Multi-objective gradient-based method with Lagrangian multipliers (MOGM-LM) and centre-of-gravity method (CoGM) are further proposed as numerical methods for each step.The proposed approach was first applied to problems with test functions where the exact solutions are known, and results demonstrate that the proposed approach can find robust solutions, which cannot be found by conventional numerical design approaches. The approach was then applied to two practical design problems. Successful design in both the examples concludes that the proposed approach can be used for various design problems that involve both the creative and engineering design criteria.