# A Survey on Variable Neighborhood Search for Sustainable Logistics
## 1 Introduction
To address these complexities, a system's approach is essential, one that acknowledges the dynamic interplay and trade-offs among these dimensions. In addition, sustainability is closely aligned with the principles of a circular economy, which seeks to minimize waste and optimize resource utilization across the entire value chain--from production to consumption. By closing the loop through strategies such as recycling, reuse, and remanufacturing, the circular economy supports the Sustainable Development Goals (SDGs) adopted by the United Nations [1; 2]. These goals emphasize rational resource use, reduced environmental impact, and improved social well-being. Embedding such principles into sustainable logistics not only addresses immediate challenges but also creates long-term strategies for resilient and efficient systems. Given the growing importance of sustainable logistics, optimization techniques like Variable Neighborhood Search (VNS) have gained attention in recent years due to their ability to solve complex, combinatorial optimization problems. VNS is a powerful meta-heuristic framework widely used for solving large-scale global optimization problems across various domains, including logistics. It operates by systematically exploring different neighborhood structures to diversify the search and enhance intensification, making it highly effective in identifying high-quality solutions. VNS has shown particular promise in solving logistics-related problems, where finding optimal or near-optimal solutions is critical to improving efficiency, minimizing costs, and achieving sustainability goals. The connection between VNS and sustainable logistics lies in its ability to address the three core dimensions of sustainability--economic, environmental, and social--through optimization techniques. VNS contributes to sustainable logistics by enabling decision-makers to optimize critical operations, such as minimizing carbon emissions in transportation, reducing energy consumption in warehouses, and improving resource allocation across supply chains. Moreover, its capacity to handle multiobjective problems, especially when it is hybridized with other optimization methods, ensures that economic efficiency can be balanced with environmental and social considerations, such as integrating renewable energy sources into logistics networks or improving worker welfare. VNS can also guide the development of sustainable logistics goals by offering a structured approach to explore and evaluate potential trade-offs between conflicting objectives. For instance, it can prioritize solutions that reduce costs while maintaining low environmental impacts, thus supporting organizations in meeting sustainability targets. Additionally, the adaptability of VNS allows it to incorporate specific constraints and scenarios, such as uncertainty in demand or dynamic changes in logistics networks, making it a practical and versatile tool for achieving long-term sustainability goals. The versatility and robustness of VNS make it an ideal tool for addressing the optimization challenges that arise in sustainable logistics, particularly those that involve complex decision-making, such as routing, scheduling, and location. By applying VNS to these logistics problems, it is possible to simultaneously consider economic, environmental, and social factors, providing solutions that balance efficiency with sustainability. Furthermore, VNS can be adapted and hybridized with other optimization methods to enhance its effectiveness in solving multiobjective problems, which is particularly relevant in sustainable logistics, where multiple conflicting objectives must be considered. This study aims to investigate the use of VNS in sustainable logistics in a deeper way by addressing the following key research questions:  
* In which specific areas of sustainable logistics is VNS most commonly applied, and what types of problems does it address most effectively? * Which VNS variants are utilized most frequently to solve these sustainable logistics problems?