Traditional job shop scheduling problems often neglect the travel times or assume that unlimited transport resources are available. These cases are often inconsistent with engineering practice because vehicle transportation tasks are very common in the FJSS problem. If the vehicle transportation problem cannot be fully considered, the optimal solution to the job scheduling problem will not be obtained. The job shop scheduling problem with transportation constraints needs to decide the machine scheduling, vehicle scheduling, and transportation assignment. Ref. [2] designed a multistart biased random key genetic algorithm for the flexible job shop scheduling problem with transportation. Solving these interrelated problems is helpful in improving the operational performance of the job scheduling system. Refs. [4,16] proposed an integrated scheduling method of machines and automated guided vehicles in a flexible job shop environment based on genetic algorithms.

The use of mobile robots also brings transportation issues. The authors of [5] modeled the job shop scheduling problem as a mixed integer linear programming (MILP) model and considered the routing problem of mobile robots. A mixture of job shop scheduling systems and transportation scheduling systems also increases the factors considered during scheduling. Ref. [7] produced a job shop scheduling joint consideration of production, transport, and storage/retrieval systems. Ref. [9] addressed the energy-efficient job shop scheduling problem with transport resources, considering speed-adjustable resources. These works revealed that the benefits of integrating job shop scheduling and transportation scheduling can greatly improve the job completion time and operational performance.

Many research works often independently study job shop scheduling problems and vehicle transportation problems, such as dynamic job shop scheduling [12,17], interval job shop [13], energy-efficient distributed flexible job shop scheduling [14], limited waiting time constraint on a hybrid flowshop [18], embedded environment [19], and flexible job shop scheduling [20]. Ref. [21] presented a dynamic configuration method of flexible workshop resources based on an imperialist competitive algorithm hybrid neighborhood search (IICA-NS). Although doing so can reduce the difficulty of solving a problem, it leads to a lack of coordination since sub-optimal solutions and cannot reach global optimization. Recent research progress indicates that neglecting transportation scheduling in job shop scheduling may result in serious consequences [22], such as low resource utilization, unexpected bottlenecks, high intermediate inventories and operational costs, and low user satisfaction.

The integration of job shop scheduling and vehicle scheduling makes the scheduling problem more challenging since the multi-objective decisions and constraints become more complex [17]. Ref. [23] employed a multi-agent system simulation-based approach for collision avoidance in an integrated job shop scheduling problem with transportation tasks. Many researchers have demonstrated that there are a lot of conflicting factors in coordinating job shop scheduling and transportation scheduling. For example, ref. [24] introduced an approach to the integrated scheduling of flexible job shop scheduling, considering conflict-free routing problems. In engineering practice, a flexible job shop scheduling task often transports materials from one workstation to another or from a load/unload area to another, which are inevitably involved in vehicle transportation scheduling [25].

Now, current mainstream scientists consider this kind of FJSS problem to be multi-objective with many conflicting factors and NP-hard, so traditional, exact approaches can only be applied to solve small-sized cases [1]. It is very important and challenging to design efficient algorithms to address it in large-sized cases, such as simulated annealing (SA) [6] and fuzzy logic (FL) [11]. Among them, swarm intelligence (SI) algorithms have received great attention [23,26], i.e., genetic algorithms (GAs) [2,4,16], particle swarm optimization (PSO) [6,19], ant colony optimization (ACO) [8], deep learning (DL), artificial neural networks (ANNs) [12,27], artificial bee colony (ABC) [13], adaptive memetic algorithms (AMAs) [14], migrating birds optimization [17], grey wolf optimization (GWO) [20], quantum cat swarm optimization [22], artificial slime mold [28], artificial Physarum swarm [29], coronavirus herd immunity [30], artificial plant community [31,32], whale optimization [33], artificial algae [34], and the Jaya algorithm [35]. However, these swarm intelligence algorithms are also prone to fall into local optimization prematurely, and some scholars have tried to improve algorithm performance using hybrid algorithms [6,36].

In recent years, a unique creature has given us new inspiration. Natural Physarum polycephalum can generate countless mycelia for expansion and then shrink into the optimal network structure after finding food [15]. Some researchers have tried to simulate their search behavior [28,29], but the current research works have not fully explored the core functions of the Physarum polycephalum colony, i.e., swarm learning, expanding the population size to increase the search ability, and shrinking the population size to optimize solution results.