Fine-tuned robust optimization: Attaining robustness and targeting ideality

Abstract

The paper provides a Robust Optimization framework with original concepts and fundamentals that combine ideals from relative regret models and static robust optimization with novel decision-making concepts. The algorithm uses a fine-tuning strategy to attain a robust solution close as possible to an ideal target, while simultaneously guarantees robustness according to a preset trade-off risk. The framework comprises original concepts, a mathematical approach, and an algorithm. Statistical treatment based on the original framework concepts supports short, middle, or long-term decision-making settings. The framework is highly tractable as the algorithm forces the creation of a setting for a robust optimization considering the specified risk. This manuscript provides an in-depth discussion of its philosophy, objective, original concepts, fields of application, as well as statistical and probabilistic fundamentals. The framework can be applied in linear and nonlinear mathematical models if the objective function is monotonic in the domain of the active convex region. In addition, it is needed to follow some axioms stated in the paper. The framework is recommended for discrete and continuous optimization problems, including SDP, LP, NLP, MILP or MINLP. Real-world applications regarding nonlinear models are restrict. Operations research are a great scope of application having a myriad number of linear models. Numerical simulations were done considering a planning of a sales problem, solving several examples to validate the study and to gain a better understanding of the framework. All results have showed high tractability and performance. The paper discusses real-world applications with references in fields such as supply chain planning, design optimization, MPC control theory, and portfolio optimization.