# Hybrid Algorithms for Inbound and Outbound Truck Scheduling in Cross-Docking Systems
## 2 Literature Review
[9] developed five metaheuristics including Simulated Annealing (SA), the Genetic Algorithm (GA), the Keshtel Algorithm (KA), stochastic fractal search (SFS), and a hybrid SA-PSO. The Taguchi approach is conducted to obtain the algorithm parameters. In addition, 22 problems were tested and compared for the heuristic efficiency. [PERSON] and [PERSON] [10] considered a bi-objective identical truck scheduling problem, which is to assign containers into batches in order to minimize the makespan and the total weighted earliness and tardiness cost. An MIP model is introduced, and a bi-objective gray wolf algorithm is conducted to solve it. [PERSON] et al. [11] introduced the concept of the inventory level of temporary storage and considered truck scheduling and dock assignment at the same time. Three minimizing objective functions, including the makespan, maximum inventory level, and total material handling distance, are covered in the inbound and outbound truck scheduling. A genetic algorithm is used and compared among the four crossover strategies. [PERSON] et al. [12] explored multi-dock cross-dock truck scheduling problems for minimizing the makespan. The authors conducted a parallel machine-based heuristic and obtained better results than the time-indexed mathematical model and the previously developed heuristic algorithms. [PERSON] et al. [13] considered the uncertainty of trucks' arrival and operational times for a cross-dock truck scheduling problem. A two-stage math model is developed, and an extended model based on K-means clustering is introduced. A column and constraint generation algorithm is proposed and designed to solve this problem. [PERSON] et al. [14] developed a structured integer linear model for the truck scheduling problem with multi-products, no temporary areas, and single dock door. The Lagrangian heuristic algorithm is utilized to decompose into three subproblems. Effective solution algorithms and repairing mechanisms for all such problems are provided and solved. [PERSON] et al. [15] mentioned that perishable product distribution has not received enough attention in academia, although cross-docking behaviors in the cold chain have been widely adopted. The authors considered the decay of perishable products and introduced a new MIP model for truck scheduling. In addition, an evolutionary algorithm is developed to solve this problem, and the computational results showed that this algorithm outperforms the other metaheuristics. [PERSON] et al. [16] considered a time window and deadline for shipping trucks and developed a new math model. A hybrid metaheuristic algorithm based on KA and SA is proposed to compare with other algorithms in order to prove its efficiency. [PERSON] [17] mentioned that the inbound and outbound truck scheduling at cross-docking terminal (CDT) doors is one of the complicated decision problems faced by the CDT operators. A new memetic algorithm called APMA is proposed for scheduling CDT trucks and outperforms some of the well-known heuristic algorithms. The particle swarm optimization algorithm (PSO) was proposed by [PERSON] and [PERSON] [18], and its principle comes from observing the method of information transmission when bird groups in nature are foraging. According to the observation, when the flock is looking for food in a certain search range, the individual bird will move towards the individual bird in the flock that successfully finds food, that is, the behaviors of learning, sharing, and memory. In general, the direction of movement of individual birds depends on the information sharing between their own experience and neighboring birds. PSO is a global optimal solution search algorithm based on the concept of population. Each bird in the flock is regarded as a particle, the flight area is regarded as the particle search range, and the current position of each particle will be based on its own experience and neighboring birds to make changes.