## 2 Literature Review
### Multi-Objective Optimization Techniques  
Multi-objective optimization problems are complicated to solve compared to single-objective problems. In the cross-docking context, various objectives can be considered. Some performance indicators concern inbound and outbound trucks such as loading and unloading time, makespan and preemption cost. While other objective functions are more related to the internal handling of products such as travel distance, total product stay time and inventory level. More detailed performance indicators can be found in the literature review of [PERSON] and [PERSON] (2018). Optimizing all these objectives can be challenging especially in case of conflicting objectives, thus any improvement in a criterion will generate a loss in the other criteria. Multi-objective problems can be solved using different approaches based on aggregation techniques, for example: the weighted sum, goal programming, lexicographic method, weighted min-max and other Pareto based approaches such as Non-dominated Sorting Genetic Algorithm and Multi-Objective Particle Swarm Optimization (2018). As reported by [PERSON] et al. (2018), in the context of multi-objective optimization, population based meta-heuristics are widely used than single solution based meta-heuristics (also called trajectory based meta-heuristics). Indeed, single solution based meta-heuristics such as Tabu Search (TS) (SColony Optimization (ACO) [60], etc.) to solve multi-objective problems [52]. For instance, Genetic Algorithms and Particle Swarm Optimization were used to solve various multi-objective optimization problems [61; 62]. Moreover, authors in [63] found that Genetic and Evolutionary Algorithms are the most used, then Simulated Annealing and finally Tabu Search. However, in single solution based meta-heuristics, Tabu Search (TS) and Simulated Annealing (SA) received significant attention in solving multi-objective optimization problems [64; 65]. Another category of trajectory based meta-heuristics is Variable Neighborhood Search which is based on the dynamic changing of the neighborhood during the search. Few researches adapted the Variable Neighborhood Search to solve multi-objective optimization problems [52]. For instance, [PERSON] [66] proposed a randomized VNS to solve the multi-objective flow shop scheduling by applying different neighborhood operators. [PERSON] et al. [67] developed two Multi-Objective Variable Neighborhood Search algorithms (MOVNS1 and MOVNS2) for the single machine scheduling problem while minimizing two conflicting objectives: earliness/tardiness and total flow time. The results of their algorithm outperformed the MOVNS proposed by [PERSON] [66]. Pareto based approaches are also applied in infrastructure maintenance such as pavement preservation. In this context, [PERSON] and [PERSON] [68] addressed the pavement management multi-objective optimization problem by suggesting a simulated constraint boundary method (SCBM) to optimize conflicting objectives: minimizing the total cost and maximizing the smoothness of the pavements. The proposed SCBM provides Pareto solutions without requiring any preferences parameters for the objective functions and the decision maker does not have to convert the objectives' units to a cost or monetary unit to use the approach. The performance of the SCBM approach is then compared to the Genetic Algorithm which takes additional computational time to find the Pareto solutions. In a comparative study, [PERSON] [69] addressed the bi-objective set covering problem. The authors proposed a Pareto memetic algorithm (PMA) to find the set of Pareto-optimal solutions. The proposed PMA was compared to ten different multi-objective meta-heuristics. [PERSON] et al. [70] proposed a bi-objective fuzzy mixed integer nonlinear programming model for the hazardous materials routing problem in a Road-Rail multimodal transportation network under uncertainty and sustainability constraints. The problem was then solved using a three-stage exact solution strategy.