Mathematical modeling and evolutionary generation of rule sets for energy-efficient flexible job shops

As environmental awareness grows, sustainable scheduling is attracting increasing attention. The purposes of this paper are obtain the lower bound of energy-efficient flexible job shops with machine selection, job sequencing, and machine on-off decision making via a new mathematical model and to discover more energy-efficient rules with easy implementation in real practice via an efficient Gene Expression Programming (eGEP) algorithm. This paper first formulates a novel mixed-integer linear mathematical model to achieve effective machine selection, job sequencing, and machine off-on decision making. Then for the purpose of avoiding the empirical combination, five attributes exerting direct influence on the total energy consumption are extracted and consequently involved in the evolutionary process of eGEP. Furthermore, diversified rule mining operations with multi-gene representation and self-study are designed to enhance the search space and solutions quality. And, unsupervised learning is utilized in which global best and current worst are set to guide evolution direction since the learning progress has no prior knowledge. Experimental results show that machine off-on decisions efficiently reduce the total energy consumption; and, the discovered rules reach the lower bound calculated by GAMS/CPLEX in small problems and have significant superiority over other dispatching rules in energy saving.