Forming Reasonably Optimal Groups (FROG) Michelle Craig mcraig@cs.utoronto.ca Diane Horton dianeh@cs.utoronto.ca François Pitt fpitt@cs.utoronto.ca Department of Computer Science University of Toronto Toronto, ON, M5S 3G4, CANADA ABSTRACT Instructors often put students into groups for coursework. Several tools exist to facilitate this process, but they typi- cally limit the criteria one can use for forming groups. We have defined a general mathematical model for group forma- tion: a set of attribute types, group-formation criteria, and fitness measures. We have implemented an optimizer that uses an evolutionary algorithm to create groups according to the instructor’s criteria. Our experiments support the hypothesis that, even with a general model, reasonably op- timal solutions to the group-formation problem can be found in reasonable time. Several instructors have used the tool to form groups for their courses. In all cases, they were im- pressed by the expressiveness of the model and pleased with the quality of the groups produced. Categories and Subject Descriptors K.3.1 [Computers and Education]: Computer Uses in Education—collaborative learning ; K.4.3 [Computers and Society]: Organizational Impacts—computer-supported col- laborative work ; D.2.2 [Software Engineering]: Design Tools and Techniques—evolutionary prototyping ; I.2.8 [Ar- tificial Intelligence]: Problem Solving, Control Methods, and Search—heuristic methods General Terms Algorithms, Human Factors, Experimentation Keywords Group formation, courseware, evolutionary algorithms, op- timization, collaborative learning, group work 1. INTRODUCTION Instructors often put students into groups for coursework. Forming groups by hand can be very time-consuming, es- pecially with large classes and potentially complex criteria. Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. GROUP2010, November 7–10, 2010, Sanibel Island, Florida, USA. Copyright 2010 ACM 978-1-4503-0387-3/10/11 ...$10.00. For example, one could imagine wanting groups that are heterogeneous with respect to GPA, cover a range of skill sets, are homogeneous with respect to where students live, leave no woman alone in a group, and have students whose timetables include at least one free time-slot in common. Most instructors would not attempt to satisfy such require- ments by hand, opting to compromise on the criteria or to let students group themselves. Existing tools for group forma- tion are either customized to consider only specific student attributes and criteria or are otherwise constrained. Our primary goal is to define an expressive, general model that gives the instructor as much control as possible over the criteria to be used in group formation, the attributes on which they are based, the relative weighting of the criteria, and the size of the groups to be formed. By using the model in actual classes, we aim to demonstrate that it can express what instructors want, and do so naturally. Tractability of the group formation process is a significant concern, given that the number of possible partitions of a class grows explosively with class size. For example, there are more than 1.8 × 10 98 possible partitions of a class of 100 into groups of size 4. Like many other group-formation systems, we do not attempt to find an optimal solution, but instead aim to find a reasonably optimal one (hence the “R” in“FROG”); the user-interface can then allow the instructor to make adjustments to the groups. Others have demon- strated that optimization can be done effectively when the model is somewhat limited; we intend to show that it can also be done on our more general model in reasonable time. Furthermore, through real class use, we aim to show that instructors will actually use the groups that the FROG tool forms. 2. TERMINOLOGY, RELATED WORK There are two main categories of group-formation soft- ware. Some tools are used to assist online learners in form- ing their own support networks that may include students from other networks [11]. Groups are not necessarily non- overlapping and a given student may belong to zero or more groups. Many authors have studied this problem, e.g., [8, 19, 15]. In particular, Strnad and Guid [15] use a genetic algorithm working on fuzzy attributes to select good groups from a pool of employees, based on criteria specified by a company manager. Their optimizing algorithm is the closest to our own among the systems that we surveyed. Although we do not solve the same problem, our model could support this task because it provides a precise measure of fitness for each possible group. 141