Nearest neighbor classification of pareto dominance in multi-objective optimization

This study investigates the nearest neighbor classification of predicting Pareto dominance relationships in multi-objective optimization. A similarity measurement called the sum of ranked dimensional sequential number is proposed. It transfers the original domains of each decision components into the same integer interval [0:N-1], where N is the size of sample set. Each decision component of a sample candidate solution is assigned an integer between 0:N-1 according to the relative distance from the component to the same dimensional component of a observed candidate solution. The sum of the integers of all decision components of a sample candidate is defined as the similarity measurement. The nearest neighbor classification algorithms using different similarity measurements are tested. The experiments show that the sum of ranked dimensional sequential number is more efficient similarity expression than the Euclidian distance. The nearest neighbor classification uses the proposed similarity is a competent method for predicting Pareto dominance.