An Original Theoretical Investigation of Quantum-Inspired Optimization Algorithms for Large-Scale Mechatronic System Design Under Multi-Objective Uncertainty

Large-scale mechatronic system design problems encompassing thousands of interacting design variables, multiple conflicting objectives, and pervasive parameter uncertainties exceed the scalability of classical deterministic and metaheuristic optimization algorithms, motivating the investigation of quantum-inspired computational approaches that exploit quantum mechanical principles within classical computing architectures. This dissertation presents an original theoretical investigation of quantum-inspired optimization algorithms for multi-objective mechatronic system design under uncertainty, developing novel algorithm formulations and convergence theory tailored to the structural characteristics of mechatronic design optimization problems. A quantum-inspired multi-objective evolutionary algorithm is developed in which candidate designs are represented as quantum bit superposition states evolved through quantum rotation gate operations, enabling simultaneous exploration of exponentially larger design space regions per evaluation compared to classical binary-encoded evolutionary algorithms. A robust design extension of the proposed algorithm is formulated that minimizes the Pareto front of expected objective values and objective variance simultaneously under parameter uncertainty represented by probability distributions derived from manufacturing tolerances and operational condition variations. Theoretical scalability and convergence rate analyses are conducted using Markov chain theory, providing the first analytical convergence results for quantum rotation gate-based multi-objective algorithms applied to continuous engineering design problems. The algorithm is applied to the multi-objective robust design of an industrial exoskeleton actuation system for ergonomic load-carrying assistance in Nigerian port cargo handling operations in Apapa, Lagos. Compared to NSGA-III and conventional QIEA baselines, the proposed algorithm identifies Pareto solutions with 21 percent better hypervolume indicator within the same computational budget. Keywords: quantum-inspired optimization, multi-objective design, mechatronic systems, robust optimization, evolutionary algorithm