Travel time optimization on multi-AGV routing by reverse annealing

TL;DR

This study extends a use of optimization with general problem solvers in the application of multi-AGV systems and reveals the potential of reverse annealing as an optimizer.

Abstract

Quantum annealing has been actively researched since D-Wave Systems produced the first commercial machine in 2011. Controlling a large fleet of automated guided vehicles is one of the real-world applications utilizing quantum annealing. In this study, we propose a formulation to control the traveling routes to minimize the travel time. We validate our formulation through simulation in a virtual plant and authenticate the effectiveness for faster distribution compared to a greedy algorithm that does not consider the overall detour distance. Furthermore, we utilize reverse annealing to maximize the advantage of the D-Wave's quantum annealer. Starting from relatively good solutions obtained by a fast greedy algorithm, reverse annealing searches for better solutions around them. Our reverse annealing method improves the performance compared to standard quantum annealing alone and performs up to 10 times faster than the strong classical solver, Gurobi. This study extends a use of optimization with general problem solvers in the application of multi-AGV systems and reveals the potential of reverse annealing as an optimizer.

Figures (5)

• Figure 1: Calibration of reversal distance. We performed reverse annealing on 10 random nontrivial QUBO problems that appeared while running the algorithm with $20$ AGVs and analyzed the energies of each of the $1000$ samples. For a given reversal distance, the height of the red, green, and gray areas represents the mean probability of attaining the same state, the ground state, and the other state, respectively.
• Figure 2: Annealing schedule of forward and reverse annealing. The red and blue lines indicate the chronological changes in annealing parameter $s$ in forward and reverse annealing, respectively.
• Figure 3: Virtual plant we used in this study. The network shows the roads on which AGVs can move. Each circle represents a node, which is an intersection or a mid-point. Each arrow represents the directed connection between two nodes. The length of each arrow is one meter. The square nodes indicate the pick-up or drop-off points that can be the source and destination of AGVs. In the plant, 20 AGVs are active on their task.
• Figure 4: Comparison of TTS performance The orange circle and purple triangle show mean value of TTS(0.99) of Gurobi and reverse annealing, respectively. The error bars indicate the standard error.
• Figure 5: Comparison of residual energy. The purple triangle, red cross, and green circle show mean residual energy of samples on 10 problems solved by reverse annealing, forward annealing, and the greedy algorithm, respectively. The error bars indicate the standard error.