Basic study on aggregation of objective functions in Many-objective optimization problems

Recently, it has been reported that Genetic Algorithms (GAs) are applied to Multi-objective Optimization Problems (MOPs) in a lot of studies, which are called MOGA. It is generally important to search a set of Pareto solutions in MOPs which have plural fitness functions, and then GA is effective to apply because of the multi-point search. The performance of MOGA, however, decreases with increasing the number of objective functions because the solution space exponentially spreads. Therefore, effective search of MOGA is the important issue in many objective optimization problems. It is one effective approach to aggregate some objective functions and to reduce the number of them. However, it has not been studied appropriate ways to aggregate or the number of objective functions to be aggregated. The purpose of this study is to grasp the effects of aggregation of objective functions. This paper studies the effects of aggregation when MOGA is applied to a simplified Nurse Scheduling Problem (sNSP) in two aggregating ways based on the meaning of each objective function, and their correlation coefficients. This paper compares the difference of searching area and superiorities of solutions between two cases, i.e., whether objective functions of sNSP are aggregated or not, by the visualization. According to the experimental result, it is found that correlation coefficients are significantly useful to aggregate objective functions.