## 1 Introduction  
The food industry operates within an increasingly competitive and resource-constrained environment, where the demand for innovation and efficiency continues to grow. This sector faces multifaceted challenges, including the need to optimize critical resources such as time, financial investments, and energy consumption while ensuring high levels of process efficiency and sustainability. Addressing these challenges is vital for the industry to meet evolving consumer expectations, comply with regulatory requirements, and contribute to global sustainability goals. Within this context, optimization has emerged as a key tool, enabling the systematic improvement of production systems by identifying the most favorable operating conditions to achieve optimal outcomes [1]. Historically, optimization efforts in food processes relied on simplistic, single-variable experimental approaches. These methods focused on evaluating the effect of one parameter at a time on a given response while maintaining all other factors constant. While effective for certain scenarios, this approach introduced substantial limitations. It neglected the potential interactions between variables, which are often critical in understanding the complexity of food production systems. Furthermore, it required a large number of experiments to comprehensively explore the variable space, resulting in higher costs, extended timelines, and inefficiencies in process development [1; 2]. In recent decades, the food industry has shifted its priorities to align with key objectives such as cost reduction, productivity enhancement, and achieving optimal product quality. These goals have driven innovation in product development and process optimization, fostering the adoption of advanced tools and techniques that address the inherent limitations of traditional approaches. These advancements are critical for ensuring the industry's ability to deliver consistent, high-quality products while optimizing resource utilization and minimizing environmental impact [3]. To overcome the constraints of traditional methodologies, modern optimization techniques have been integrated into food production processes. Among these, the response surface methodology (RSM) has gained significant prominence. RSM combines mathematical and statistical methods to model and analyze systems influenced by multiple variables. This approach not only identifies significant relationships between factors but also determines optimal operating conditions, reducing the number of experiments needed and increasing the accuracy and reliability of results. The efficiency of RSM has made it a widely adopted tool in the food industry, contributing to significant advancements in process design and product innovation [2]. However, as food production systems have grown more complex, single-objective optimization methods like RSM alone have become insufficient for addressing multifaceted industrial challenges. Modern food production often requires balancing multiple, sometimes conflicting objectives, such as maximizing product quality, minimizing production costs, and improving energy efficiency. To address these challenges, multi-objective optimization techniques have emerged as indispensable tools. Multi-objective optimization tackles problems that involve multiple responses or variables simultaneously, offering solutions that optimize various objectives concurrently. This approach is particularly relevant to food science, where competing goals often require trade-offs. Among the most widely used methods in multi-objective optimization are linear, non-linear, and evolutionary algorithms. Each method offers unique strengths and limitations, allowing practitioners to select the most appropriate technique based on the specific requirements of a given application. Evolutionary algorithms, for instance, excel in solving non-linear and multi-modal problems, making them highly effective in the dynamic and variable-rich environments of food production systems [4].