## 1 Introduction  
Design optimization, which involves the selection of design variables to achieve desired objectives, is important within many areas of engineering. Manufacturing processes must be optimized to reduce waste and power consumption while simultaneously maximizing desirable outcomes, such as quality control and manufacturing speed. The discovery of new materials with superior mechanical, electrical, or thermal properties can also be framed as an optimization problem, where the goal is to find the processing and compositional parameters that maximize the desired properties. Other examples include the optimization of lithium-ion batteries to reduce the risk of thermal runaway, minimizing the drag on an airfoil or wind turbine blades, and optimizing the combustion processes in an engine to reduce greenhouse gas emissions, just to name a few. In some of these examples, the process or performance of the system may be affected by a large number of variables interacting in complicated ways [1]. In some cases, the problem of optimization is further complicated by the presence of several local optima, an objective function that is expensive or time-consuming to evaluate, or the existence of constraints. One way to classify the existing algorithms for design optimization is by their utilization of derivatives for finding optimal designs. On the one hand, gradient-based optimizers use the local information of the function's derivatives to search for the optimal values of the design variables [2]. Although they possess fast convergence rates and can perform well for smooth problems with many design variables, one of the major disadvantages of gradient-based approaches is that global optimization is difficult to ensure when dealing with non-smooth problems with several local optima [2]. In addition to this limitation, gradient-based optimizers are difficult to apply in situations where the functional form is not readily available, often referred to as black-box optimization (BBO). In such cases, we can observe the outputs of the function based on some given input parameters, but the form of the function is unavailable. On the other hand, derivative-free optimization methods have been developed, which, as the name implies, do not utilize gradients for optimization. Among these are some evolutionary algorithms as well as swarm-based techniques, which are inspired by the social behavior in biological swarms. Derivative-free optimizers possess advantages such as robustness to the occurrence of local optima, suitability for black-box optimization (BBO) problems, and ease of implementation (since analytically and numerically computed derivatives are not required) [3]. In particular, swarm-based optimizers operate based on the principle of swarm intelligence (SI), which occurs in the collective intelligent behavior of decentralized and self-organized systems [4]. Some examples of swarm-based optimizers are Ant Colony Optimization (ACO) [5], Artificial Bee Colony (ABC) [6], Cuckoo Search Algorithm (CSA) [7], Glowworm Swarm Optimization (GSO) ([PERSON] and [PERSON] 2009) [8], and Particle Swarm Optimization (PSO) [9; 10; 11]. These algorithms typically operate by successively updating each particle's position within the design space based on a rule that governs how it interacts with the other swarm members. As opposed to each swarm member updating its position based on only its knowledge of the design space, the swarm members work together to find the global optimum, thus achieving better performance than attainable with a single member working alone. Despite their success in optimizing non-convex multimodal functions, swarm-based optimizers sometimes suffer from slow convergence and require several function evaluations to find the global optima [12]. Also, in many engineering applications, evaluating the objective function can be expensive or time-consuming.