# A Survey on Variable Neighborhood Search for Sustainable Logistics
## 5 Research Trends and Gaps  
The analysis of the current literature on the use of VNS in sustainable logistics reveals several trends and gaps that point to future opportunities for research in this area. Some trends are summarized in the following points. * Growth in publications. As illustrated in Figure 1, there has been a notable rise in the number of publications on VNS in sustainable logistics since 2019. This trend reflects the increasing awareness and recognition of optimization methods like VNS in addressing complex and pressing challenges in logistics systems while promoting sustainability. The rapid growth in interest highlights the broadening application of VNS techniques in response to the global demand for more sustainable and efficient logistics practices. * Dominance of operational research and computer science journals. The majority of studies in this field are published in journals related to operations research, computer science, and engineering. Journals such as _Computers & Operations Research_ and _Computers & Industrial Engineering_ are particularly prominent, as depicted in Figure 2.
* Focus on routing and scheduling. The optimization problems most frequently addressed in the reviewed studies are routing and scheduling. As shown in Figure 3, the majority of papers using VNS target these two areas, underlining their centrality in sustainable logistics. These problems are essential for reducing transportation costs, improving efficiency, and minimizing environmental impacts, all of which are core elements of sustainable logistics practices. * Multiobjective optimization. An expanding body of research focuses on multiobjective problems where VNS is applied to simultaneously optimize conflicting objectives. These studies are vital for developing logistics systems that not only minimize costs but also integrate sustainability considerations such as emissions reduction, energy efficiency, and resource conservation. Multiobjective approaches remain highly relevant as they enable decision-makers to balance economic, environmental, and social goals in logistics systems. * Hybridization with other methods. A significant trend is the hybridization of VNS with other optimization techniques. As indicated in Figure 5, methods such as SA, TS, and GA are commonly combined with VNS to improve solution quality. This hybridization enhances flexibility and facilitates the exploration of complex optimization problems. * Prevalence of VNS variants. GVNS and BVNS remain the most widely used VNS variants, with a growing interest in the use of AVNS over the past few years. Regarding research gaps and future research directions, we summarize the following points:
* Lack of focus on uncertainty and dynamism. While uncertainty and dynamism are critical factors in sustainable logistics, few studies incorporate these elements into VNS-based models. Uncertainty in demand, travel times, and environmental conditions, as well as the dynamic nature of logistics networks, can substantially impact optimization algorithms. Future research could explore robust optimization techniques and dynamic adaptation mechanisms to make VNS more applicable to real-world logistics challenges. * Limited exploration of social sustainability. Although economic and environmental sustainability are often addressed in VNS-based logistics optimization, the social dimension remains underrepresented. Social factors, such as worker well-being, job creation, and safety, require more attention in the literature. Including these social metrics in optimization models is essential to ensuring logistics practices are socially responsible and equitable. * Innovation in hybridization techniques. While VNS has been successfully combined with various methods, further innovation in hybridization strategies is needed. Incorporating emerging technologies such as machine learning and reinforcement learning into VNS frameworks has received limited attention but holds significant potential for advancing sustainable logistics. * VNS variants.