Jordan Makansi | Searcharxiv

arXiv2024

A Set Cover Mapping Heuristic for Demand-Robust Fleet Size Vehicle Routing Problem with Time Windows and Compatibility Constraints

We study the demand-robust fleet size vehicle routing problem with time windows and compatibility constraints. Unlike traditional robust optimization, which considers uncertainty in the data, demand-robust optimization considers uncertainty in which constraints must be satisfied. This paper is the first to solve a practical demand-robust optimization problem at large scale. We present an MILP formulation and also propose a heuristic that maps the problem to set cover in polynomial time. We show that under modest assumptions the relative difference in time complexity from a standard branch-and-bound algorithm to the proposed heuristic scales exponentially with the size of the problem. We evaluate our heuristic using a simulation case study on the Solomon benchmark instances for a variety of practical problem sizes, and compare with Gurobi. The empirical approximation ratio remains below 2.0.

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arXiv2024

A Greedy Quantum Route-Generation Algorithm

Routing and scheduling problems with time windows have long been important optimization problems for logistics and planning. Many classical heuristics and exact methods exist for such problems. However, there are no satisfactory methods for generating routes using quantum computing (QC), for mainly two reasons: inequality constraints, and the trade-off of feasibility and solution quality. Inequality constraints are typically handled using slack variables; and feasible solutions are found by filtering samples. These challenges are amplified in the presence of noise inherent in QC. Here, we propose a greedy algorithm that generates routes by using information from all samples obtained from the quantum computer. By noticing the relationship between qubits in our formulation as a directed acyclic graph (DAG), we designed an algorithm that adaptively constructs a feasible solution. We prove its convergence to a feasible solution, and illustrate its efficacy by solving the Fleet Sizing Vehicle Routing Problem with Time Windows (FSVRPTW). Our computational results show that this method obtains a lower objective value than the current state-of-the-art annealing approaches, both classical and hybrid, for the same amount of time using D-Wave Hybrid Solvers. We also show its robustness to noise on D-Wave Advantage2 through computational results as compared to the filtering approach on DWaveSampler, even when the filtering approach is given a longer annealing time, and a larger sample size.

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