## 2 Related Work
### Salp Swarm Algorithm
#### 2.2.2 Characteristics and Application Fields of SSA  
SSA has the following advantages:  
1. Few parameters and easy to implement:  
SSA only needs to adjust a few parameters such as population size and iteration times. The algorithm structure is simple and the implementation difficulty is low. 2. Strong global search capability:  
Through the leader follower chain structure, SSA can effectively explore the global optimal solution in the solution space. 3. Highly self-organizing:  
The group dynamic update mechanism does not require manual intervention and is suitable for complex optimization problems. 4. Good compatibility with other algorithms:Flexible integration with genetic algorithms [16], simulated annealing [17] and other algorithms to improve performance. Due to the advantages of SSA, it has been applied to solve problems such as target classification [18], photovoltaic system optimization [19], feature extraction [20], image processing [21], and biomedical signal processing [22]. Some scholars have also applied SSA in the field of production scheduling, but it is not very common and is still in its infancy. [PERSON] et al. [23] proposed an improved SSA based on firefly algorithm to solve parallel machine scheduling problems. [PERSON] et al. [17] proposed an improved SSA based on Levy flight integrated simulated annealing strategy to solve FJSP. [PERSON] et al. [24] developed collaborative group search strategies and population diversity maintenance mechanisms to enhance the SSA optimization capabilities in addressing hybrid flow shop scheduling problems with setup operators. The FJSP involves multiple coupled constraints such as process sequence and machine selection., Solving algorithms for FJSP must balance global and local optimization. Traditional Particle Swarm Optimization (PSO) tends to become trapped in local optima due to its single information-sharing mechanism, leading to degraded solution quality. Similarly, traditional Genetic Algorithms (GA) face challenges where crossover and mutation operations often compromise solution feasibility. When the fitting function in GA is poorly designed, the algorithm tends to favor locally superior individuals, causing rapid decline in population diversity and premature convergence to local optima. In contrast, the SSA inherently establishes a dynamic equilibrium mechanism through leader-guided global exploration and follower-driven local refinement, naturally balancing global and local search capabilities. In Reference [15], the SSA outperformed seven algorithms, including PSO and GA. Existing research demonstrates the potential of SSA in solving workshop scheduling problems. However, SSA has the following limitations:  
1. The multi-objective FJSP is a discrete optimization problem. The position update formula for leaders and followers in SSA are designed for continuous optimization problems and cannot be directly applied to discrete problems. Among the studies mentioned above, only reference [24] mentioned a method to solve this problem, while others did not specifically address how to discretize the position formula in SSA. Reference [24] implemented discretization through threshold segmentation and probabilistic distribution sampling, which presets fixed threshold intervals to partition continuous spaces into non-overlapping discrete regions. Their method establishes probability distribution models for each interval, utilizing 8 parameters (with two assumed to follow normal distributions). However, this approach exhibits high dependency on manually configured thresholds and parameter sensitivity. 2. When SSA approaches the potential optimal solution region, it requires excessive time to thoroughly search these areas. Weak exploitation capability leads to slow convergence speed. Regarding the solution of FJSP, current improvements in SSA have primarily focused on either modifying the position update formula [23], unilaterally strengthening local search capabilities [25], or singularly enhancing population diversity [24].