Fuzzy linear regression with global continuous optimization

Finding the global optimum of an unknown system has attracted a great deal of interest in many engineering problems. In this setting, meta-heuristics are very common and efficient approaches for solving complex real-world problems in Global Continuous Optimization Problems (GCOPs) as they can approximate solutions without any need for mathematical assumptions such as differentiability. The application of global continuous optimization methods is essential in many engineering applications where an optimization problem has certain properties such as unreliable derivatives and/or black-box nature. Meta-heuristic based optimizations, as one of the promising approaches in global continuous optimization, have a slow rate of convergence. Hybridization frameworks are investigated as a potential way of enhancing the optimization speed, and the quality of solutions. -- Fuzzy linear regression analysis is a powerful tool to model the input-output relationship for forcasting purposes or studying the behavior of the data. The existing challenges in fuzzy linear regression are, dealing with non-transparent fitness measures, outlier detection and spread increasing problem. The application of global continuous optimization is investigated to tackle these issues. We propose an Unconstrained Global Continuous Optimization (UGCO) method based on tabu search and harmony search to support the design of Fuzzy Linear Regression models (FLR). The proposed approach offers the flexibility of using any kind of an objective function based on the client's requirements or requests and the nature of the data set, and then attains its minimum error. -- Fuzzy linear analysis may lead to an incorrect interpretation of data in case of being incapable of dealing with outliers. Both basic probabilistic and least squares approaches are sensitive to outliers. In order to detect outliers, we propose a two stage least squares approach based on global continuous optimization which outperforms some issues that exist in other methods. In both the first and second phases, the minimization of the model fitting measurement is achieved by hybrid optimixation which gives us the fliexibility of using any type of model fitting measures regardless of being continuous, differentiable, or transparent. -- Some of the fuzzy linear regression models suffer from constantly increasing spreads of the outputs with the increase in the magnitude of the inputs. Such models are known to have the so-called spread increasing problem. We introduce a model, obtained by the application of hybrid optimization, which is capable of having variable spreads for different input variables regardless of their magnitude. The proposed approach is also compared and contrasted with other models in terms of the number of parameters, the flexibility of spreads, and errors.