Preference-Based Multi-Objective Genetic Programming for Energy-Efficient Dynamic Flexible Job Shop Scheduling

Energy-Efficient dynamic flexible job shop scheduling (E-DFJSS) is a valuable real-world combinational optimisation problem. As an important variant of DFJSS, E-DFJSS aims to optimise trade-off between production effectiveness and energy consumption. Genetic Programming (GP) has been successfully used to learn dispatching rules in E-DFJSS. Nevertheless, different users have different preferences on the trade-off between production effectiveness and energy consumption, the studies of preference-based multi-objective optimisation algorithms are limited. These existing related preference-based methods face the issue of premature convergence in the early stage when solving E-DFJSS, which results in insufficient diversity. To address these challenges, we develop a preference-based multi-objective GP approach for E-DFJSS. A fusion r-dominance and achievement scalarising function dominance criterion is embedded into the proposed algorithm to solve E-DFJSS. Experimental results on training and test on three scenarios with four preferences show that the proposed method could improve the effectiveness of learned scheduling heuristics by balancing diversity and convergence of evolutionary progress.