Discrete Differential Evolution Particle Swarm Optimization Algorithm for Energy Saving Flexible Job Shop Scheduling Problem Considering Machine Multi States

TL;DR

The paper addresses energy-efficient scheduling in a flexible job shop when machines have multiple states, including speeds and setup times, formalizing EFJSP-M with dual objectives: minimize makespan $f_1=C_{max}$ and total energy consumption $f_2=TEC$. It introduces D-DEPSO, a discrete PSO framework augmented with differential evolution operators and a critical-path–driven local search, featuring a two-layer OS/MV encoding, ADM-S decoding, hybrid initialization, a novel learning scheme (TPOF), and CP-based refinement. Extensive experiments on extended benchmarks (DPs, MKAs) show EFJSP-M feasibility and that D-DEPSO yields superior Pareto fronts, convergence, and coverage compared with multiple baselines and variant configurations. The work demonstrates the practical potential of energy-aware, multi-state machine scheduling and provides insights for deploying hybrid metaheuristics in complex discrete optimization problems with energy considerations.

Abstract

As the continuous deepening of low-carbon emission reduction policies, the manufacturing industries urgently need sensible energy-saving scheduling schemes to achieve the balance between improving production efficiency and reducing energy consumption. In energy-saving scheduling, reasonable machine states-switching is a key point to achieve expected goals, i.e., whether the machines need to switch speed between different operations, and whether the machines need to add extra setup time between different jobs. Regarding this matter, this work proposes a novel machine multi states-based energy saving flexible job scheduling problem (EFJSP-M), which simultaneously takes into account machine multi speeds and setup time. To address the proposed EFJSP-M, a kind of discrete differential evolution particle swarm optimization algorithm (D-DEPSO) is designed. In specific, D-DEPSO includes a hybrid initialization strategy to improve the initial population performance, an updating mechanism embedded with differential evolution operators to enhance population diversity, and a critical path variable neighborhood search strategy to expand the solution space. At last, based on datasets DPs and MKs, the experiment results compared with five state-of-the-art algorithms demonstrate the feasible of EFJSP-M and the superior of D-DEPSO.

Figures (16)

• Figure 1: The Gantt Diagram of the sample.
• Figure 2: The sample's machine states during the whole cycle:(a)$M_1$,(b)$M_2$.
• Figure 3: The framework of D-DEPSO.
• Figure 4: The illustration of two-dimensional extended coding scheme.
• Figure 5: The illustration of ADM-S.