Measuring Human Performance on Clustering Problems: Some Potential Objective Criteria and Experimental Research Opportunities
Journal of Problem Solving
The study of human performance on discrete optimization problems has a considerable history that spans various disciplines. The purpose of this paper is to outline a program of study for the measurement of human performance on discrete optimization problems related to clustering of points in the two-dimensional plane. I describe possible objective criteria for clustering problems, the measurement of agreement of solutions produced by subjects, and categories of experiments for investigating
... n performance on clustering problems. To facilitate future experimental testing of human subjects on clustering problems, optimal partitions were obtained for 233 two-dimensional clustering problems ranging in size from 10 to 70 points. For each test problem, an optimal solution was obtained for each of three objective criteria: (a) maximizing partition split, (b) minimizing partition diameter, and (c) minimizing within-cluster sums of squares, and similarity of the solutions among these criteria has been computed. Parker and Rardin (1988, chapter 1) characterize discrete optimization as a particular class of problems within the much larger field of combinatorics. The defining principle of discrete optimization is the minimization or maximization of some criterion measure over a finite set of mutually exclusive alternatives. There are many relevant discrete optimization problems, and such problems can vary significantly with respect to their computational tractability. A partial list of some of the most familiar discrete optimization problems is as follows: minimum spanning tree, shortest-route, traveling salesperson problem, graph coloring, p-median problem, set-covering problem, knapsack problem, bin-packing problem, and quadratic assignment problem. These problems have many important applications in areas such as facility location, vehicle routing, electrical circuitry, assembly line design, telecommunications network architecture, and the analysis of psychological data.