Solving the Examination Timetabling Problem in GPUs

Vasileios Kolonias,Efthymios Housos,Christos Gogos,Panayiotis Alefragis,George Goulas

doi:10.3390/a7030295

Abstract

The examination timetabling problem belongs to the class of combinatorial optimization problems and is of great importance for every University. In this paper, a hybrid evolutionary algorithm running on a GPU is employed to solve the examination timetabling problem. The hybrid evolutionary algorithm proposed has a genetic algorithm component and a greedy steepest descent component. The GPU computational capabilities allow the use of very large population sizes, leading to a more thorough exploration of the problem solution space. The GPU implementation, depending on the size of the problem, is up to twenty six times faster than the identical single-threaded CPU implementation of the algorithm. The algorithm is evaluated with the well known Toronto datasets and compares well with the best results found in the bibliography. Moreover, the selection of the encoding of the chromosomes and the tournament selection size as the population grows are examined and optimized. The compressed sparse row format is used for the conflict matrix and was proven essential to the process, since most of the datasets have a small conflict density, which translates into an extremely sparse matrix.

Highlights

Optimization is the process of finding the best solution from a set of available alternatives, taking into account all of the required problem constraints [1]
Optimization problems with discrete variables are called combinatorial optimization problems [1], and the examination timetabling problem (ETP) that is solved in this work belongs to this class of problems
All of the parts of the algorithm are executed in the Graphical processing units (GPUs), and the results show a speedup of about 7,000× compared to a CPU single-threaded implementation

Summary

Introduction

Optimization is the process of finding the best solution from a set of available alternatives, taking into account all of the required problem constraints [1]. The variables of optimization problems can be either continuous or discrete. Optimization problems with discrete variables are called combinatorial optimization problems [1], and the examination timetabling problem (ETP) that is solved in this work belongs to this class of problems. Mathematical programming [3], artificial intelligence [4] and meta-heuristic techniques [5] are some of the algorithmic families for the solution of these problems. The class of evolutionary algorithms (EA) [6,7,8], which is used in this paper, is based on Darwinian theory [9] and is usually included in the computational intelligence family

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