Transformation and Linearization Techniques in Optimization: A State-of-the-Art Survey

To formulate a real-world optimization problem, it is sometimes necessary to adopt a set of non-linear terms in the mathematical formulation to capture specific operational characteristics of that decision problem. However, the use of non-linear terms generally increases computational complexity of the optimization model and the computational time required to solve it. This motivates the scientific community to develop efficient transformation and linearization approaches for the optimization models that have non-linear terms. Such transformations and linearizations are expected to decrease the computational burden, allowing for more efficient problem solving while retaining the essential characteristics of the original models. This survey comprehensively reviews the current state-of-the-art methods, comparing their efficiencies and applicability across various optimization domains, thereby providing valuable insights for researchers and practitioners in the field of mathematical optimization. The findings advocate for further advancements in the development of innovative techniques that can simplify optimization models and enhance the effectiveness of solving complex decision-making problems.