Curve Fitting-based Performance Measurement for Decision Making at Noisy Multiobjective Optimization Problems

Abstract

Engineering problems ae generally contains real life systems that can measure with sensors or contains some factors which can be modelled as noise with probabilistic and statistical properties. In real life, Noise is inherent to engineering problems. As one of the toolsets for engineering problems, the optimization problems like multiobjective optimization problems can be under noise thread. For this reason, to handle the noise, multiobjective optimization algorithms should be improved and additional techniques should be defined/introduced. However, another problem arises at the obtained solution set from the optimization algorithm which is the performance measurement and therefore selecting the solution by decision maker. Since the obtained objective values contains measurement the position of the objectives on the objective space do not represent their true position. For this reason, it is not easy -not possible- for the decision maker to select the proper solution. Also using the conventional the performance measurements on this noisy data is not represent the exact or supportive information for the decision maker. For these reasons in this research a method which is based on curve fitting is proposed. In the proposed method by using the obtained solutions an average -fitted- function is obtained and it is sampled with respect to the position of the obtained solution, and then the shadows of obtained solutions are generated. This shadow set is used to measure the performance and used as indicator for the decision maker.