Abstract: In the area of reservoir engineering, the optimization of oil and gas production is a complex task involving a myriad of interconnected decision variables shaping the production system's infrastructure. Traditionally, this optimization process was centered on a single objective, such as net present value, return on investment, cumulative oil production, or cumulative water production. However, the inherent complexity of reservoir exploration necessitates a departure from this single-objective approach. Multiple conflicting production and economic indicators must now be considered to enable more precise and robust decision-making. In response to this challenge, researchers have embarked on a journey to explore field development optimization of multiple conflicting criteria, employing the formidable tools of multi-objective optimization algorithms. These algorithms delve into the intricate terrain of production strategy design, seeking to strike a delicate balance between the often-contrasting objectives. Over the years, a plethora of these algorithms have emerged, ranging from a priori methods to a posteriori approaches, each offering unique insights and capabilities. This survey endeavors to encapsulate, categorize, and scrutinize these invaluable contributions to field development optimization, which grapple with the complexities of multiple conflicting objective functions. Beyond the overview of existing methodologies, we delve into the persisting challenges faced by researchers and practitioners alike. Notably, the application of multi-objective optimization techniques to production optimization is hindered by the resource-intensive nature of reservoir simulation, especially when confronted with inherent uncertainties. As a result of this survey, emerging opportunities have been identified that will serve as catalysts for pivotal research endeavors in the future. As intelligent and more efficient algorithms continue to evolve, the potential for addressing hitherto insurmountable field development optimization obstacles becomes increasingly viable. This discussion on future prospects aims to inspire critical research, guiding the way toward innovative solutions in the ever-evolving landscape of oil and gas production optimization.