# A Survey on Variable Neighborhood Search for Sustainable Logistics
## 6 Discussion  
VNS offers several advantages when addressing sustainable logistics problems. Its metaheuristic nature allows it to tackle large-scale, combinatorial optimization problems efficiently. The systematic exploration of neighborhood structures ensures a balance between exploration and exploitation, making VNS particularly suitable for problems with complex, multimodal solution landscapes. Furthermore, VNS is flexible and can be hybridized with other optimization methods, enhancing its applicability to multiobjective problems and dynamic scenarios. However, VNS is not without limitations. One drawback is its dependency on the definition and size of neighborhood structures, which can significantly influence the algorithm's performance. Poorly chosen neighborhoods may lead to suboptimal solutions or increased computational time. Another limitation is that VNS is inherently heuristic, meaning that it does not guarantee finding the global optimum. Moreover, implementing VNS for real-world logistics problems requires domain-specific knowledge to properly adapt the algorithm, which can pose challenges for practitioners without sufficient expertise. When using VNS, practitioners must carefully define problem-specific parameters, such as neighborhood structures and shaking mechanisms, to achieve desired results. The method's reliance on computational power can also become a bottleneck for very large-scale problems or scenarios involving real-time decision-making. Recommendations for improving its application include integrating VNS with advanced machine learning techniques to enhance parameter tuning and combining it with robust optimization frameworks to address uncertainty in logistics data. While VNS is a powerful optimization tool, alternative methods such as GA, TS, and PSO are also widely used in sustainable logistics. GAs, for instance, offer strong exploratory capabilities due to their population-based approach, but they may struggle with convergence speed. TS provides effective intensification strategies but can become trapped in local optima without proper diversification. PSO, on the other hand, is efficient for continuous problems but may require additional adaptation for discrete or combinatorial problems. Compared to these methods, VNS stands out for its structured search and adaptability, although the choice of the method should ultimately depend on the problem characteristics and computational resources available. One noteworthy observation from our analysis is the prevalent approach to formulating optimization problems where the objective is often defined as the minimization of a composite function. Specifically, many studies focus on reducing a sum of diverse cost components, and in certain cases, this objective incorporates a linear combination of multiple cost factors and sustainability metrics to evaluate the solution's overall impact. In some studies, an economic valuation of some effect contrary to sustainability, such as emissions or other collateral effects, is used. Such optimization problems could, and in some cases should, be treated as multiobjective problems, where the optimization of a linear combination of objectives being only one of the possible alternatives to address it. There are not many articles in the literature on the application of VNS alone to address multiobjective problems, both in sustainable logistics and in other areas, but the use of hybrids of two or more metaheuristics is more frequent, with some VNS versions being one of them. A key issue in the design and application of VNS is the choice of the series of neighborhood structures to use and also the order in which they are applied. Originally, it was recommended to use them by size or in order of complexity, from smallest to largest size or from least to most complex [7]. Different strategies have also been studied to change the neighborhood structure different from the original sequential change step, such as the cyclic, pipe, and skewed change step ([11]).