Highly Efficient Encoding for Job-Shop Scheduling Problems and its Application on Quantum Computers
arxiv(2024)
摘要
Combinatorial optimization problems are considered to be an application,
where quantum computing can have transformative impact. In the industrial
context, job shop scheduling problems that aim at finding the optimal schedule
for a set of jobs to be run on a set of machines are of immense interest. Here
we introduce an efficient encoding of job shop scheduling problems, which
requires much fewer bit-strings for counting all possible schedules than
previously employed encodings. For problems consisting of N jobs with N
operations, the number of required bit-strings is at least reduced by a factor
N / log_2(N) as compared to time indexed encodings. This is particularly
beneficial for solving job shop scheduling problems on quantum computers, since
much fewer qubits are needed to represent the problem. Our approach applies to
the large class of flexible and usual job-shop scheduling problems, where
operations can possibly be executed on multiple machines. Using variational
quantum algorithms, we show that the encoding we introduce leads to
significantly better performance of quantum algorithms than previously
considered strategies. Importantly, the encoding we develop also enables
significantly more compact classical representations and will therefore be
highly useful even beyond applicability on quantum hardware.
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