2. GA for Solving FJSP
Job shop scheduling problem (JSP) is the basis of FJSP, and does not consider the flexibility of machine selection. With minimizing makespan of JSP, Zhang et al.
[17][8] proposed an effective hybrid GA, Xie et al.
[18][9] developed a new improved GA that combines GA and tabu search (TS), and Goncalves et al. designed a random-key based GA. With regard to FJSP with minimizing makespan, Pezzella et al.
[19][10] designed a GA with different rules for generating individuals, Zhang et al. proposed a combined GA that takes variable neighborhood search into consideration, Gutiérrez et al. designed a hybrid GA that combines GA and repair heuristics, and Fan et al.
[20][11] developed an improved genetic algorithm, in which problem-specific encoding and decoding strategies are designed.
3. FJSP-AGV
JSP with a limited number of AGV is named as JSP-AGV. With regard to JSP-AGV, the existing works have been focused on minimizing makespan. Bilge and Ulusoy
[21][12] designed an iterative algorithm and a set of benchmark instances. Erol et al.
[22][13] developed a multi-agent-based algorithm, which includes four agents, namely manager agent, staff agent, AGV agent, machine agent, and AGV-machine resource agents. Deroussi et al.
[23][14] designed a novel neighboring method, which includes three intelligent algorithms, namely iterated local search, simulated annealing, and their hybridization. Kumar et al.
[24][15] developed a novel differential evolution algorithm, whose encoding only considers the operations sequencing sub-problem. Moreover, the machine selection sub-problem and the AGV selection sub-problem are determined in the decoding with specific heuristics. Zheng et al.
[25][16] designed a tabu search algorithm and first presented a mixed integer linear programming (MILP) model to obtain optimal solutions. Fontes and Homayouni
[26][17] proposed an improved MILP by considering more constraints for minimizing makespan of JSP-AGV. Abdelmaguid et al.
[27][18] proposed a hybrid GA/heuristic approach, while the heuristic is to determine the AGV selection in the decoding scheme. Lacomme et al.
[28][19] designed a disjunctive graph-based framework for modeling JSP-AGV and an improved memetic algorithm. Ham
[29][20] first developed a constraint programming model and a new set of benchmark instances.
In order to simultaneously optimize makespan, mean flow time, and mean tardiness of JSP-AGV, an improved multi-objective GA was designed
[30][21], which determines the AGV selection sub-problem in the decoding. With regard to JSP-AGV simultaneously making makespan, AGV travel time, and minimized penalty cost, a multi-objective GA was designed, which used the fuzzy expert system to adjust crossover operators
[31][22]. With consideration of the battery charge of AGV, three intelligent algorithms, namely GA, particle swarm optimization (PSO), and hybrid GA-PSO were developed to simultaneously make makespan with the number of AGV being minimized
[32][23].
With only one AGV in a flexible manufacturing system, Caumond et al.
[33][24] proposed a MILP for scheduling problems. Moreover, the maximum number of jobs, the limited input/output buffer capacities, and the no-move-ahead trips were taken into consideration simultaneously. With regard to FJSP-AGV on minimizing makespan, Ham
[29][20] extended the constraint programming model of JSP-AGV and proved the optimality of ten benchmark instances
[34][25]. Homayouni and Fontes
[3] proposed the first MILP model for solving small-sized instances to optimality and a local search-based heuristic for solving small to large-sized instances. Chaudhry et al.
[35][26] presented a Microsoft Excel spreadsheet-based solution and GA, and Homayouni et al.
[11][27] proposed a multi-start biased random key genetic algorithm (BRKGA). In BRKGA, the encoding only considers the operations sequencing sub-problem, and the machine selection and AGV selection sub-problems are determined by several different greedy heuristics. Zhang et al.
[36][28] designed a hybrid algorithm GATS that combines GA and tabu search algorithm (TS) for minimizing makespan and of FJSP-AGV with bounded processing times. In GATS, the GA decides the machine-AGV selections of all operations and TS optimizes the operations sequencing. In order to fast and accurately estimate the makespan of FJSP-AGV, Cheng et al.
[37][29] designed an adaptive ensemble model of back propagation neural networks. Yan et al.
[38][30] first studied the FJSP-AGV in a digital twin workshop and developed a three-layer -encoding based GA. Moreover, in order to implement the optimized schedules to a digital twin system, an entity-JavaScript Object Notation method was designed. As we know, Li et al.
[12][31] first studied dynamic FJSP-AGV with simultaneously minimizing makespan and total energy consumption and developed a hybrid deep Q network (HDQN)-based dynamic scheduling method.