Quantum Optimization with Lagrangian Decomposition for Multiple-process Scheduling in Steel Manufacturing

Abstract

Steel manufacturing involves multiple processes, and optimizing the production schedule is essential for improving the quality, cost, and delivery of products. However, the corresponding optimization problems are usually NP-hard and generally intractable even for modern high-performance computers. Recent advances in quantum computers, such as those developed by D-Wave Systems, have opened new possibilities for handling this type of optimization problem. Nevertheless, a major obstacle to the application of currently available quantum computers is the relatively small number of quantum bits, which limits the feasible problem size. To overcome this obstacle, we propose an algorithm for solving optimization problems based on Lagrangian decomposition and coordination. D-Wave quantum computers can explore diverse solutions simultaneously, and we leverage this unique characteristic to obtain the upper bound for Lagrangian decomposition and coordination. We apply the proposed algorithm to a simplified problem of two-process production scheduling. By decomposing the problem into two stages for the processes, the number of steel products that can be handled increases from five to eight (60% increase). The optimal solutions are reached even for the extended case of the eight products. The proposed algorithm is a promising technique for enabling the application of quantum computers to real-world problems by thoroughly exploiting quantum bits. KEY WORDS: steel manufacturing; multiple-process scheduling; Lagrangian decomposition and coordination; quantum annealing, and quantum-digital hybrid algorithm. 300 tons, whereas the volume downstream when reaching surface treatment is approximately 10 tons. Therefore, a production unit in an upstream process includes different products or semi-products across downstream processes. Between all the process layers, the grouping of different sequence orders or semi-products should be jointly optimized. Such optimization problems must be solved under several constraints. For instance, two products or semiproducts requiring very different processes or different specifications, such as chemical components, widths, and thicknesses, cannot be grouped. On the other hand, grouping products obtained from similar processing conditions is favorable for quality, productivity, and cost. Nevertheless, excessive grouping may lead to stock accumulation and delay because grouping implies waiting for other products

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Exploration of new chemical materials using black-box optimization with the D-wave quantum annealer

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