Abstract:

If the mathematical model of an optimization problem contains input and/or response variables that take discrete and continuous values, the problem is called as a mixed data optimization problem. In this study, the modeling and the optimization phases of multi-response problems with mixed data in terms of input variables are discussed. In the modeling phase, estimated response functions are obtained using Generalized Linear Models (GLM). In the optimization phase, the estimated response functions are considered as an objective function and the problem is expressed as a multi-objective optimization (MOO) problem with simultaneous optimization. In this study, a new solution algorithm based on the Non-dominated Sorting Genetic Algorithm-II (NSGA-II), one of the most frequently used artificial intelligence optimization algorithms in MOO, is proposed. This algorithm, which was prepared by making various adaptations in the variable representation, initial population generation and application of genetic operators stages of the NSGA-II, is called MDNSGA-II (Mixed Data NSGA-II) in this study. In MDNSGA-II, each discrete variable value is assigned a positive integer value and an integer indexing is performed for the discrete variable values. It is ensured that the discrete variable takes values in support set of variables by using the indexing approach. In the application part of the study, it is shown that Pareto solutions can be obtained with the proposed MDNSGA-II by using the mixed data set on energy efficiency from the UCI Repository database and the experimental mixed data set available in the literature in the field of food.

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