Single- and Multi-Objective Stochastic Optimization for Next-Generation Networks in the Generative AI and Quantum Computing Era

Next Generation (NG) networks move beyond simply connecting devices to creating an ecosystem of connected intelligence, especially with the support of generative Artificial Intelligence (AI) and quantum computation. These systems are expected to handle large-scale deployments and high-density networks with diverse functionalities. As a result, there is an increasing demand for efficient and intelligent algorithms that can operate under uncertainty from both propagation environments and networking systems. Traditional optimization methods often depend on accurate theoretical models of data transmission, but in real-world NG scenarios, they suffer from high computational complexity in large-scale settings. Stochastic Optimization (SO) algorithms, designed to accommodate extremely high density and extensive network scalability, have emerged as a powerful solution for optimizing wireless networks. This includes various categories that range from model-based approaches to learning-based approaches. These techniques are capable of converging within a feasible time frame while addressing complex, large-scale optimization problems. However, there is currently limited research on SO applied for NG networks, especially the upcoming Sixth-Generation (6G). In this survey, we emphasize the relationship between NG systems and SO by eight open questions involving the background, key features, and lesson learned. Overall, our study starts by providing a detailed overview of both areas, covering fundamental and widely used SO techniques, spanning from single to multi-objective signal processing. Next, we explore how different algorithms can solve NG challenges, such as load balancing, optimizing energy efficiency, improving spectral efficiency, or handling multiple performance trade-offs. Lastly, we highlight the challenges in the current research and propose new directions for future studies.