Modern industrial environments are evolving into data-intensive cyber-physical systems that require robust computational frameworks for performance prediction and optimization. While existing literature has addressed developments in statistical methods, artificial intelligence, and quantum computing individually, there remains a lack of systematic reviews examining the integrated evolution and data processing capabilities of these three paradigms. This review addresses the need to clarify the capabilities, limitations, and application domains of each approach to enable engineers to select appropriate data-driven methodologies for specific optimization challenges. In this review, we traced the historical development of optimization methodologies from design of experiments and response surface methodology through neural networks and generative models to variational quantum algorithms, presented chronological development tables documenting key milestones in each paradigm, and analyzed industrial implementation cases including conversion rate increases and emission reductions. The analysis reveals that statistical methods exhibit unique strengths in systematic data analysis, AI in complex pattern recognition, and quantum computing in high-complexity simulation, with their hybrid integration providing optimal performance. This study provides significance in offering a comprehensive framework necessary for connected industries to strategically deploy multi-paradigm optimization strategies within integrated network environments to achieve sustainability goals while maintaining global competitiveness.