## 3 Multi-Objective Optimization
MOO offers a powerful tool for designing recipes and formulations that meet these criteria. For example, it can optimize the combination of ingredients to reduce sugar or sodium content, enhance protein levels, or fortify products with essential vitamins and minerals. These advancements contribute to public health while ensuring that food products remain appealing and accessible to a wide range of consumers. The environmental impact of the food industry has become a critical concern in the context of global sustainability. Agriculture, food production, and distribution are significant contributors to greenhouse gas emissions, deforestation, water usage, and waste generation. MOO addresses these challenges by optimizing resource use, reducing waste, and minimizing the carbon footprint of food systems. Whether through energy-efficient production processes, sustainable packaging design, or water-saving agricultural practices, MOO enables the industry to align its operations with environmental objectives. These efforts are instrumental in advancing a circular economy and mitigating the sector's contribution to climate change [35]. Beyond individual objectives, MOO aligns seamlessly with the Sustainable Development Goals (SDGs) outlined in the 2030 Agenda. Several SDGs directly relate to the food industry, including Zero Hunger (SDG 2), Responsible Consumption and Production (SDG 12), Climate Action (SDG 13), and Good Health and Well-being (SDG 3). MOO provides actionable strategies to achieve these goals. For instance, it facilitates efficient food production and equitable distribution, ensuring access to nutritious food (SDG 2). By optimizing resource use and minimizing waste, MOO supports sustainable production patterns (SDG 12). Moreover, by reducing energy consumption and emissions, it contributes to climate action (SDG 13), while simultaneously enhancing public health through the development of healthier food products (SDG 3) [36; 37]. The practical applications of MOO in the food industry are diverse, reflecting its flexibility and broad relevance. In supply chain management, MOO optimizes logistics to balance costs, delivery times, and environmental impacts. In manufacturing, it enhances production processes to maximize yield and energy efficiency while maintaining product quality. MOO also supports product development by optimizing formulations for sensory attributes, nutritional value, and shelf life. Additionally, it plays a crucial role in designing sustainable packaging solutions and identifying optimal materials that balance cost, durability, and environmental impact. These applications underscore MOO's ability to address complex challenges across the food value chain [37; 38]. The integration of MOO with advanced technologies, such as artificial intelligence (AI), machine learning, and digital twins, has further expanded its capabilities. These technologies enable MOO to handle large datasets, predict outcomes with high accuracy, and adapt to dynamic conditions. For example, digital twins--virtual replicas of physical systems--allow food manufacturers to simulate and optimize processes in real-time, reducing risks and costs associated with experimentation. Similarly, the integration of machine learning models enhances MOO's predictive power, making it particularly valuable for real-time process control, quality assurance, and supply chain optimization [34]. In the long term, the value of MOO lies in its ability to create adaptive systems that respond to evolving circumstances. As consumer preferences, regulatory requirements,and environmental conditions change, MOO provides the flexibility to re-optimize processes and products. This adaptability is critical for ensuring the competitiveness and sustainability of the food industry in an uncertain future. Multi-objective optimization is a cornerstone of modern food industry practices, addressing economic, nutritional, environmental, and societal goals in a comprehensive manner.