A Multi-Objective Hybrid Algorithm for the Casting Scheduling Problem with Unrelated Batch Processing Machine

The casting production process typically involves single jobs and small batches, with multiple constraints in the molding and smelting operations. To address the discrete optimization challenge of casting production scheduling, this paper presents a multi-objective batch scheduling model for molding and smelting operations on unrelated batch processing machines with incompatible job families and non-identical job sizes. The model aims to minimise the makespan, number of batches, and average vacancy rate of sandboxes. Based on the genetic algorithm, virus optimization algorithm, and two local search strategies, a hybrid algorithm (GA-VOA-BMS) has been designed to solve the model. The GA-VOA-BMS applies a novel Batch First Fit (BFF) heuristic for incompatible job families to improve the quality of the initial population, adopting the batch moving strategy and batch merging strategy to further enhance the quality of the solution and accelerate the convergence of the algorithm. The proposed algorithm was then compared with multi-objective swarm optimization algorithms, namely NSGA-II, SPEA-II, and PESA-II, to evaluate its effectiveness. The results of the performance comparison indicate that the proposed algorithm outperforms the others in terms of both quality and stability.