Energy-efficient job shop scheduling problem with transport resources considering speed adjustable resources

Abstract

Due to stricter environmental regulations, volatile energy prices, and the increasingly growing energy demand, manufacturing companies need to reduce their energy consumption. Therefore, energy efficiency has recently become the research focus in manufacturing systems, particularly regarding scheduling problems. Although energy efficiency in manufacturing systems can be addressed in many ways, such as adopting renewable resources, using improved machinery, and redesigning products and production processes, researchers have proved energy-efficient scheduling to be an effective way of reducing energy consumption. Additionally, scheduling optimization is easier to apply to existing systems and requires far less capital investment, if at all, making it more widely applicable; especially for small and medium enterprises (Fernandes, Homayouni, and Fontes 2022;Para, Del Ser, and Nebro 2022;Gahm et al. 2016).Two solution methods were developed to solve the proposed EEJSPT-MS: a bi-objective mixed-integer linear programming model (MILP), and a multi-objective multi-population biased random key genetic algorithm (mpBRKGA). MILP's can provide exact optimal solutions but are usually too computationally demanding and slow to solve large instances in a reasonable timeframe, and thus are deemed unsuitable for real-world applications for this problem. Thus, heuristic methods, such as the proposed mpBRKGA are employed to find good solutions for larger problems significantly faster.The proposed mpBRKGA is a multi-population algorithm based on the BRKGA initially proposed by Gonçalves and Resende (2011). The mpBRKGA uses a set Ω of single-objective populations and a set Π of multi-objective populations. It features one single-objective population per each objective in the problem (which are Makespan and TEC in this case), and a variable number of bi-objective populations minimizing both objectives (minimum of 1). Each population is initially generated through vectors of random keys uniformely drawn from [0,1], which are each decoded into feasible solutions for which the makespan and TEC are calculated.Each iteration, the populations are ranked by using a non-dominated sorting algorithm and, within each non-dominated set, according to crowding distance. Afterwards, for each population, the top 𝑁 𝑒 solutions are deemed the elite solutions for this iteration and the remaining ones are non-elite.