To perform “global” optimization of the machining process in discrete manufacturing, a bi-objective flexible job-shop scheduling problem with tool allocation is proposed. Unlike traditional scheduling problems that treat resources independently, this paper addresses the strong coupling between machine routing, operation sequencing, and finite tool capacity. A mixed-integer programming model is constructed with the objectives of minimizing the tool wear cost and weighted sum of tardiness. Sophisticated constraints that fit actual manufacturing scenarios are considered, specifically the combination of tool magazine capacity, variant job releasing times, and machine/tool compatibility for operations. To address the computational challenge and the discrete nature of the solution space, a knowledge-driven teaching-learning-based optimization algorithm is designed. Specific strategies, including a topology-preserving discrete crossover and a critical-path-based neighborhood search, are developed to prevent premature convergence caused by complex constraints. Simulation experimental results show that the proposed algorithm significantly outperforms the traditional meta-heuristic algorithms in the aspects of quality, spread, and comprehensive metric, and the proposed multi-objective collaborative optimization method obtains better processing decisions than the traditional sequential scheduling methods.
Chen et al. (2026) studied this question.