Binary Nearest Neighbor Classification of Predicting Pareto Dominance in Multi-objective Optimization

Abstract

A method of predicting Pareto dominance in multi-objective optimization using binary nearest neighbor classification (BNNC) is proposed. It encodes real value feature variables into binary bit strings with the same length. The similarity of two feature variables is directly measured by weighted sum of the binary bits. The analysis shows that when the orders of magnitude for various feature variables differ from each other, the similarity measured by scaled feature variables is able to more uniformly reflect the contribution of each feature variable to Pareto dominance relationship, and BNNC has computational complexity of O(N). Experiments results show that, in addition to remarkably increasing classification accuracy rate, it is more efficient and robust than the canonical nearest neighbor rule and Bayesian classification when used to classify those problems with unbalanced class proportions and feature vectors no less than 2 dimensions.