Bilevel Optimal Production Scheduling of Heating Furnaces with a Practical Production Simulator Using Integer Form of Population-Based Incremental Learning with an Initial Probability Matrix Setting Method and Local Search with a Surrogate Model

This paper proposes bilevel optimal production scheduling of heating furnaces with a practical production simulator using integer form of population-based incremental learning (IF-PBIL) with an initial probability matrix setting method and local search with a surrogate model. In batch production factories, it is essential to generate a high-quality production schedule within a limited time. In other words, a highquality solution must be obtained with a limited number of objective function evaluations. This paper presents two proposals. Proposal 1 is the initial probability matrix setting method for IFPBIL especially for batch production and it is applied to the optimization of production ratios. The method configures the initial probability matrix of IF-PBIL using a high-quality solution. By applying the method, the likelihood of obtaining a high-quality solution increases with fewer objective function evaluations. Proposal 2 is local search with a surrogate model for IF-PBIL applied to the optimization of production start time. Local search is applied to the solutions obtained by IF-PBIL. Therefore, since the method can improve the solutions to high-quality ones without using the simulator, the likelihood of obtaining a high-quality solution increases even if the number of objective function evaluations is reduced. The effectiveness of each proposal, as well as the entire proposed method incorporating all proposals, is confirmed using the optimal production scheduling problem of actual heating furnaces. In addition, the Mann-Whitney U test is applied to verify the effectiveness of the proposed method.