Advancing Quantum-Inspired Optimisation Algorithms for Large-Scale Combinatorial Problems in Nigerian Logistics

Large-scale combinatorial optimisation problems arising in Nigerian logistics networks, including the nationwide petroleum product distribution system, the national postal delivery network, and the multi-commodity agricultural supply chain, are computationally intractable for exact methods but require solution quality guarantees that standard metaheuristics cannot provide theoretically. This dissertation develops and analyses a family of quantum-inspired optimisation algorithms, drawing on the mathematical principles of quantum annealing and quantum tunnelling, to address this theoretical and computational gap. The first contribution develops a novel quantum-inspired simulated annealing algorithm with a theoretically analysed cooling schedule that provably converges to the global optimum of the combinatorial problem in finite time under conditions weaker than classical simulated annealing. The second contribution proposes a quantum tunnelling-inspired operator for genetic algorithm crossover that escapes basin boundaries in fitness landscapes characterised by many local optima, with a proof of improved expected hitting time to global optimum for landscape classes arising in vehicle routing. A third contribution derives polynomial-time approximation guarantees for the proposed algorithms on a class of structured combinatorial problems including the k-facility location problem relevant to agro-logistics hub design. The framework is benchmarked on real instances from NNPC distribution data and produces solutions averaging 7.3 percent closer to known optimal bounds than leading metaheuristic comparators. Keywords: quantum-inspired optimisation, combinatorial algorithms, Nigerian logistics, quantum annealing, approximation algorithms.