Hippopotamus Optimization for Dynamic Flexible Job Shop Scheduling under Machine Tool Breakdowns

Abstract

Dynamic flexible job shop scheduling under machine tool breakdowns represents a complex and highly constrained combinatorial optimization problem in modern manufacturing systems. This research paper proposes an integrated optimization framework that simultaneously determines operation sequencing, machine tool assignment, tool selection, and tool orientation with the objective function of minimizing makespan. A unified multi-string solution representation is developed to simultaneously model all decision layers. Three biologically inspired metaheuristic algorithms, Genetic Algorithm (GA), Particle Swarm Optimization (PSO), and Hippopotamus Optimization (HO), are implemented using the proposed encoding scheme. A rescheduling strategy is introduced to preserve completed operations while rescheduling the affected operations after machine tool failures. Experimental verification demonstrates that the integrated framework effectively handles dynamic disturbances and significantly improves scheduling performance. Comparative analysis shows that the hippopotamus optimization algorithm achieves superior convergence behavior and better objective function values than the other approaches. The proposed method provides a robust framework for resilient scheduling under multiple resource constraints