Generating Data for Testing Pareto Sorting Algorithms
Michael A. Yukish · 11th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference · 2006
Evolutionary algorithm and multi-dimensional visualization applications both have a need for algorithms that identify the Pareto frontier, and to Pareto sort the data into levels of dominance . To properly develop these Pareto algorithms one needs test data of varying dimension, total numbers of points, number of points that are nondominated, and number of points that are on each level. This paper presents three related approaches to generating the test data, and discusses some insights into the nature of multi-dimensional Pareto frontiers given by studying the problem. Nomenclature N = number of points in data set d = dimension of problem Q = number of nondominated points 12 {,,,} k N NN … = number of points in each Pareto layer R, R’ = rotation matrix ,, zw … = point in multi-dimensional space