Hybrid quantum-classical computation for automatic guided vehicles scheduling

TL;DR

This study utilizes D-Wave hybrid solvers that implement classical heuristics with potential assistance from a quantum processing unit and demonstrates that the AGVs problem is better suited to quantum computing than its railway counterpart, the latter being denser in terms of the average number of constraints per variable.

Abstract

Motivated by recent efforts to develop quantum computing for practical, industrial-scale challenges, we demonstrate the effectiveness of state-of-the-art hybrid (not necessarily quantum) solvers in addressing the business-centric optimization problem of scheduling Automatic Guided Vehicles (AGVs). Some solvers can already leverage noisy intermediate-scale quantum (NISQ) devices. In our study, we utilize D-Wave hybrid solvers that implement classical heuristics with potential assistance from a quantum processing unit. This hybrid methodology performs comparably to existing classical solvers. However, due to the proprietary nature of the software, the precise contribution of quantum computation remains unclear. Our analysis focuses on a practical, business-oriented scenario: scheduling AGVs within a factory constrained by limited space, simulating a realistic production setting. Our approach maps a realistic AGVs problem onto one reminiscent of railway scheduling and demonstrates that the AGVs problem is better suited to quantum computing than its railway counterpart, the latter being denser in terms of the average number of constraints per variable. The main idea here is to highlight the potential usefulness of a hybrid approach for handling AGVs scheduling problems of practical sizes. We show that a scenario involving up to 21 AGVs, significant due to possible deadlocks, can be efficiently addressed by a hybrid solver in seconds.

Figures (7)

• Figure 1: Example of the AGVs scheduling problem given pre-defined AGVs paths as colour lines. First, AGVs are routed to travel between ports (colour rectangles), which is the input to our algorithm. The goal of the algorithm is to timetable AGVs to avoid collisions in zones. In our case zones $s_0, \ldots s_6$ are allegorically assigned spatial areas where AGVs paths intercept start or active ports are located. AGVs paths in terms of zones are AGV $s_0, s_1, s_2, s_3$, AGV $s_4, s_3, s_2, s_1$, AGV $s_6, s_5, s_4, s_3$$AGV s_5, s_6$ and AGV $s_2, s_3$
• Figure 2: Illustration of minimal passing time (upper panel) and headway (lower panel) Eq. \ref{['eq::min_pass_time']}
• Figure 3: Example network with $7$ zones derived from Fig. \ref{['fig:topology_stations']}
• Figure 4: Comparison of performance of Classical CPLEX exact and approximate (achieved by setting constant computational time) with hybrid quantum-classical solver, CQM in particular. All presented solutions were feasible. For CPLEX exact on the largest instance ($1302$ variables) the time limit of $30$ minutes was used, as it was not possible to achieve the certified output in a reasonable time, $6$h time limit CPLEX computation yields the same results. Error bars were computed by performing $10$ independent realizations of experiments of CQM computation and calculating the standard deviation over realizations.
• Figure 5: Histograms of objectives of feasible CQM solutions for various problem sizes: $6$ AGVs a), $7$ AGVs b), $12$ AGVs c), $15$ AGVs d). For each run, approximately a hundred samples were returned. Histogram spreads are measured by the standard deviation (std): $6$ AGVs std = $0.19$, $7$ AGVs std = $0.62$, $12$ AGVs std = $1.51$, $15$ AGVs std = $1.9$.