Multi-Objective Optimization in Manufacturing: From Evolutionary Algorithms to Quantum Variational Methods

Abstract Modern manufacturing increasingly demands the simultaneous optimization of multiple, often conflicting responses, such as mechanical performance, energy efficiency, cost, and sustainability. These challenges are more pronounced in advanced material systems, including biopolymers and fiber-reinforced composites, where nonlinear process–property interactions govern the final performance. This review presents a structured and analytical examination of multi-objective optimization strategies in manufacturing, tracing their evolution from classical evolutionary algorithms to deterministic parameter-free methods and, more recently, to quantum variational approaches. Genetic algorithms and Rao-based techniques are discussed in terms of convergence behavior, computational complexity, and robustness in handling nonlinear, multi-parameter systems. The emerging role of the quantum approximate optimization algorithm is then examined within a variational framework capable of exploring high-dimensional solution landscapes through hybrid quantum–classical computation. By comparing these methodologies under a unified mathematical formulation, the review highlights their suitability for complex manufacturing problems, particularly in sustainable composite processing. Current limitations, benchmarking gaps, and scalability concerns are critically analyzed. The study concludes by outlining future research directions toward quantum-enabled smart manufacturing systems capable of adaptive, multi-response optimization in environmentally responsible material design. Keywords: multi-objective optimization, manufacturing systems, genetic algorithm, Rao algorithm, QAOA, quantum optimization, biopolymer composites, sustainable manufacturing, and variational methods.