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at - Automatisierungstechnik

Quantum computer-aided job scheduling for storage and retrieval systems

Stefan Windmann

Published Jan 1, 2024• 3 citations
Publisher

Abstract

Abstract In this paper, a quantum computer-aided approach to job scheduling for automated storage and retrieval systems is introduced. The approach covers application cases, where various objects need to be transported between storage positions and the order of transport operations can be freely chosen. The objective of job scheduling is to arrange the transport operations in a sequence, where the cumulative costs of the transport operations and empty runs between subsequent transport operations are minimized. The scheduling problem is formulated as an asymmetric quadratic unconstrained binary optimization (QUBO) problem, in which the transport operations are modeled as nodes and empty runs are modeled as edges, with costs assigned to each node and each edge. An Quantum Approximate Optimization Algorithm (QAOA) is used to solve the QUBO. Evaluations of the quantum computer-aided job scheduling approach have been conducted on the IBM Q System One quantum computer in Ehningen. In particular, the running time for the solution of the QUBO has been investigated, as well as the scalability of the approach with respect to the required number of qubits.

DOI
10.1515/auto-2023-0072

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Abstract In this paper, a quantum computer-aided approach to job scheduling for automated storage and retrieval systems is introduced. The approach covers application cases, where various objects need to be transported between storage positions and the order of transport operations can be freely chosen. The objective of job scheduling is to arrange the transport operations in a sequence, where the cumulative costs of the transport operations and empty runs between subsequent transport operations are minimized. The scheduling problem is formulated as an asymmetric quadratic unconstrained binary optimization (QUBO) problem, in which the transport operations are modeled as nodes and empty runs are modeled as edges, with costs assigned to each node and each edge. An Quantum Approximate Optimization Algorithm (QAOA) is used to solve the QUBO. Evaluations of the quantum computer-aided job scheduling approach have been conducted on the IBM Q System One quantum computer in Ehningen. In particular, the running time for the solution of the QUBO has been investigated, as well as the scalability of the approach with respect to the required number of qubits.
Quantum optimization which is the use of quantum computers and algorithms for solving complex optimization problems, is one of the topics in quantum computing with the highest potential. Two types of approaches are generally used to solve combinatorial optimization problems with quantum computers: exact methods such as the Grover’s search algorithm, and meta-heuristics such as the Quantum Annealing and the Quantum Approximate Optimization Algorithm (QAOA). Exact methods and variational methods like QAOA make use of universal gate-based quantum computers, such as the ones developed by the IBM company.Quantum annealing is designed for analogic quantum computers developed by D-Wave. Solving a combinatorial optimization problem with heuristics generally requires a transformation of the problem to a format suitable for the quantum computer. While some existing frameworks can cope with Constrained Quadratic Models (CQM), Quadratic Unconstrained Binary Optimization (QUBO) is the best option to map an optimization problem to a quantum computer or simulator. We consider in this paper the job shop scheduling problem.
As systems become more complex and large-scale, there is a need for more effective scheduling algorithms to maximize resource usage and minimize job completion times. The older methods of scheduling like First-Come-First-Serve (FCFS) and Round Robin (RR), although easier to compute, tend to perform poorly in dynamic scenarios because they cannot manage intricate constraints and multi-objective optimization efficiently. As traditional methods approach their limit of performance, quantum computing presents a potentially fruitful avenue for conquering combinatorial challenges based on its ability to examine many states at once. This work proposes a quantum-aided scheduling framework that employs Quadratic Unconstrained Binary Optimization (QUBO) formulations and quantum solvers for the purpose of improving job scheduling in distributed environments. The original contribution is the marrying of quantum optimization (with IBM Qiskit's QAOA and D-Wave's hybrid solvers) with traditional distributed computing frameworks such as Apache Spark. Google Cluster Workload Traces are employed to mimic real-world situations, and jobs are described by CPU, memory requirements, and arrival times. Once the scheduling problem has been formulated into a QUBO model, quantum algorithms produce the optimized job-to-machine assignments. The outcomes are compared against baseline classical schedulers on performance metrics including make span, throughput, and resource utilization. The experiment demonstrates that quantum-assisted scheduling significantly improves makespan and enhances resource utilization, particularly under high workloads. It also provides evidence of the feasibility of integrating quantum solvers with existing big data infrastructures.
Flexible job-shop scheduling problems (FJSPs) represent one of the most complex combinatorial optimization challenges. Modern production systems and control processes demand rapid decision-making in scheduling. To address this challenge, we propose a quantum computing approach for solving FJSPs. We propose a quadratic unconstrained binary optimization (QUBO) model to minimize the makespan of FJSPs, with the scheduling scheme encoded in the ground state of the Hamiltonian operator. The model is solved using a coherent Ising machine (CIM). Numerical experiments are conducted to evaluate and validate the performance and effectiveness of the CIM. The results demonstrate that quantum computing holds significant potential for solving FJSPs more efficiently than traditional computational methods.
Abstract Airline itinerary and scheduling represent some of the most difficult computational problems that exist in transportation. The problems require choosing the best flight routes while determining schedules and allocating resources through various constraints which include regulatory requirements and maintenance schedules and dynamic demand patterns. The solution of small and medium-scale instances has been achieved through mixed-integer programming and heuristic methods including simulated annealing and genetic algorithms and branch-and-price but these methods become impractical for larger real-world instances due to exponential scaling issues. Quantum computing has introduced fresh solutions which enable the resolution of these problems. Quantum mechanical phenomena particularly superposition and entanglement enable optimization algorithms to examine an exponentially expanded solution space simultaneously. Our research applies a basic airline scheduling problem to the Traveling Salesman Problem (TSP) before converting it into a Quadratic Unconstrained Binary Optimization (QUBO) problem. The Quantum Approximate Optimization Algorithm (QAOA) serves as a hybrid quantum-classical method to solve this formulation. The experimental evaluation of a 4-city scenario shows that quantum-based optimization generates performance levels comparable to traditional methods and indicates that improved quantum hardware development will provide computational benefits for complex airline scheduling problems. This research holds dual importance because it can minimize operational expenses and improve scheduling performance and it establishes fundamental principles for complex combinatorial problem optimization across the transportation industry. The research establishes fundamental principles for quantum-enabled applications that will revolutionize airline operations and other transportation networks by solving critical scalability and solution quality problems.
Despite quantum computing is revealing an increasingly promising technology that has the potential to introduce a significant speed-up in many areas of computation, the number of problems that it can represent and solve is currently rather limited. Therefore, one of the current challenges faced by the quantum computing community is to broaden the class of problems that can be tackled. Among these problems, scheduling problems are a class of particularly interesting and hard combinatorial problems; in this paper, we present a novel solution for representing and solving the Flexible Open Shop Scheduling Problem (FOSSP) to optimality by minimizing the makespan. We firstly present a compact formulation of this problem as a Quadratic unconstrained binary optimization (QUBO), which can be used to solve this problem with a quantum annealer. Then, we proceed to the Quantum Approximate Optimization Algorithm (QAOA) problem formulation, thus producing both the cost and mix Hamiltonians related to the problem. From the Hamiltonians, we provide the complete description of the quantum circuit that can be used to tackle the FOSSP within the QAOA framework. This second approach can be used to solve the optimization problem with a general-purpose quantum gate-based hardware.
In planning and scheduling, large-scale optimization problems often have complex limits and a lot of factors, which makes them hard to answer with standard methods. Quantum annealing has become a hopeful way to deal with these problems because it can quickly look into a lot of possible solutions. This essay looks into how quantum annealing might be used to solve optimization problems in transportation and scheduling, with a focus on how it could be used for route planning, inventory management, and arranging workers. To do these optimization jobs, quantum annealing is used. This is a quantum computing method that gets the global minimum of a cost function. We use the D-Wave quantum annealer in this method. It turns the problem's limits and objective function into a quadratic unconstrained binary optimization (QUBO) model. The quantum annealer then works on this model to find the best answers. The suggested method combines traditional preparation methods with quantum annealing to get the best results for big schedule and transportation issues. We use quantum annealing to solve difficult multi-objective optimization problems, like reducing shipping time, cost, and resource use all at the same time. Preliminary results show that quantum annealing can make solutions much better and use computers much more efficiently than traditional methods for optimizing supplies and schedules. Quantum annealing works especially well with problems that have a lot of dimensions. It can provide scalable answers that sometimes work better than standard methods.