You are a quantum computing researcher tasked with developing a quantum algorithm to solve a complex optimization problem in logistics - the Vehicle Routing Problem with Time Windows (VRPTW). This is NP-hard and becomes computationally intractable for classical computers with more than 100 nodes. Design a hybrid quantum-classical algorithm using the Variational Quantum Eigensolver (VQE) approach. Provide a detailed explanation of how to encode the VRPTW into a Hamiltonian, design an appropriate ansatz (parameterized quantum circuit), and select a classical optimizer. Compare your approach to classical algorithms like simulated annealing and genetic algorithms in terms of solution quality and computational complexity. Implement your algorithm using a quantum computing framework like Qiskit or Cirq. Analyze the noise resilience of your algorithm and discuss how it would perform on near-term quantum hardware versus fault-tolerant quantum computers. Include circuit diagrams, mathematical formulations, and performance analysis.