A Quantum Optimization Algorithm for Single Machine Total Weighted Tardiness Minimization

TL;DR

This paper introduces a novel quantum optimization algorithm leveraging Grover's search and Trugenberger's methods to efficiently solve the NP-hard single machine total weighted tardiness minimization problem, which is infeasible with classical algorithms.

Contribution

The paper proposes a new quantum algorithm specifically designed for the NP-hard TWTM problem, combining Grover's search and quantum optimization techniques for improved solution probability.

Findings

The quantum algorithm effectively finds solutions with high probability.

It demonstrates potential advantages over classical methods for NP-hard scheduling problems.

The approach is theoretically efficient for the TWTM problem.

Abstract

A single machine total weighted tardiness minimization (TWTM) problem in operational planning is considered. The problem is formulated as an NP-hard constrained combinatorial problem, which has no known deterministic polynomial complexity solution using classical computing. Based on efficient Grover's quantum search and Trugenberger's quantum optimization algorithms, a novel efficient quantum optimization algorithm is proposed to solve the NP-hard single machine TWTM problem, which makes the desired solution satisfying the searching constraints and showing the minimal TWT value be measured with the highest probability.