## 1 Introduction  
Advanced optimization methods are used in engineering design to obtain the best functional performance and/or minimum production cost of a complex product or system in the increasingly competitive international market. Nature-inspired global optimization algorithms with superior search efficiency and robustness have been continuously introduced and improved to solve various complex, nonlinear optimization problems, which most traditional gradient-based optimization methods are incapable to deal with. Moreover, these nature-inspired global optimization (GO) algorithms become more useful when the objective function of the problem of interest is in implicit, black-box form and/or its derivative information of is unavailable, unreliable, or expensive to obtain. Development of the nature-inspired global optimization algorithm dated back to the introductions of the GeneticAlgorithm (GA) based on [PERSON]'s principle of biological systems by [PERSON] et al. [1] Since then, Ant Colony Optimization (ACO) [2], Simulated Annealing (SA) [3], and Particle Swarm Optimization (PSO) [4], as the most recognized nature-inspired global optimization algorithms have been introduced. Due to their general applicability, ease of implantation, and relatively fast convergence, GA, PSO, ABC and SA have attracted much attention in the past, and have been applied successfully for a wide range of global optimization applications. For instance, [PERSON] et al. [5] employed GA optimizer to carry out multi-objective optimization for train schedules with minimum energy consumption and travel time; [PERSON] et al. [6] proposed an improved ant colony optimization (ACO) method for the route planning of the omnidirectional mobile vehicle; and [PERSON] et al. [4; 7] applied PSO in multi-objective optimization for reliability-redundancy assignments in design. Over the years, significant efforts have been devoted to the further developments of various global optimization methods of both deterministic and stochastic types. The deterministic approach solves an optimization problem through a predetermined sequence of searches and search points, converging to the same or very close global optimum. Direct search [8], branch and bound [9], clustering [10], and tunneling methods [11] are typical examples of this approach. Stochastic methods, including nature-inspired techniques, are based on randomly sampled search points. Therefore, their different runs may result in different optimization results due to the random nature of the search steps. These stochastic search algorithms have the capability to identify the global optimum efficiently for many optimization problems, simply using the evaluated values of the objective function without the need of its gradient information. With the advance of computation hardware and software, computational intensive, numerical analysis and simulation tools, such as Finite Element Analysis (FEA) and Computational Fluid Dynamics (CFD), became commonly used means for evaluating the performance of a new design with many design parameters. Global optimization can be used to search through the design space of these implicit and multimodal objective functions to identify the optimal design solution in principle. However, these types of computationally expensive, black-box function optimization problems require extensive computation during each evaluation of its objective function. Conventional nature-inspired optimization algorithms, such as GA and SA, which require very large number of objective function evaluations with lengthy computation time, particularly for high-dimensional problems with many design variables, become impractical and infeasible to use.