# Hybrid Arctic Puffin Algorithm for Solving Design Optimization Problems
###### Abstract  
This study presents an innovative hybrid evolutionary algorithm that combines the Arctic Puffin Optimization (APO) algorithm with the JADE dynamic differential evolution framework. The APO algorithm, inspired by the foraging patterns of Arctic puffins, demonstrates certain challenges, including a tendency to converge prematurely at local minima, a slow rate of convergence, and an insufficient equilibrium between the exploration and exploitation processes. To mitigate these drawbacks, the proposed hybrid approach incorporates the dynamic features of JADE, which enhances the exploration-exploitation trade-off through adaptive parameter control and the use of an external archive. By synergizing the effective search mechanisms modeled after the foraging behavior of Arctic puffins with JADE's advanced dynamic strategies, this integration significantly improves global search efficiency and accelerates the convergence process. The effectiveness of APOJADE is demonstrated through benchmark tests against well-known IEEE CEC 2022 unimodal and multimodal functions, showing superior performance over 32 compared optimization algorithms. Additionally, APO-JADE is applied to complex engineering design problems, including the optimization of engineering structures and mechanisms, revealing its practical utility in navigating challenging, multi-dimensional search spaces typically encountered in real-world engineering problems. The results confirm that APO-JADE outperformed all of the compared optimizers, effectively addressing the challenges of unknown and complex search areas in engineering design optimization. article [color=black]0.05,0.  
techniques and linear programming, often grapple with several limitations that undermine their effectiveness in such complex scenarios [3]. One of the most significant limitations of traditional methods is their tendency to converge to local optima rather than global ones. This issue is particularly problematic in complex design landscapes that feature numerous feasible solutions, separated by suboptimal regions [4]. Furthermore, traditional methods often entail high computational costs, especially as the dimensionality of the problem increases, which can make them impractical for large-scale applications or for use in real-time scenarios [5]. Additionally, these methods typically rely on the availability and accuracy of gradient information, which may not be obtainable for all types of problems, such as those involving discontinuous or non-differentiable spaces [6]. In recent years, there has been significant growth in the development of metaheuristic algorithms to address these challenges [7]. These algorithms provide a powerful, adaptable, and efficient approach to solving optimization problems in diverse fields [8]. Unlike traditional methods, metaheuristics operate independently of gradient information, employing strategies inspired by natural or social processes to locate optimal solutions [9]. Their flexibility enables their application across a broad spectrum of problems, ranging from abstract mathematical models to real-world engineering design challenges [10; 11]. Additionally, metaheuristics are highly regarded for their capability to overcome local optima, ensuring a more thorough exploration of the solution space and enhancing the probability of identifying global optima [12]. Due to their stochastic and dynamic nature, these algorithms are particularly well suited for addressing the complexities and uncertainties characteristic of engineering design, offering innovative and efficient solutions in a rapidly advancing technological landscape [13]. The Arctic Puffin Optimization (APO) algorithm, introduced by [14], is a recently developed metaheuristic inspired by the distinctive foraging strategies of Arctic puffins. This algorithm draws on the puffins' ability to navigate and adapt to the harsh and variable conditions of the Arctic, effectively balancing exploration and exploitation phases.