Scheduling is one of the problems that has attracted the attention of many researchers over the years. The University Course Timetabling Problem (UCTP) is a highly constrained real-world combinatorial optimization task. Designing course timetables for academic institutions has always been challenging, because it is a non-deterministic polynomial-time hardness (NP-hard) problem. This problem attempts to assign specific timeslots and rooms to the events considering a number of hard and soft constraints. All hard constraints must be satisfied to achieve a feasible solution, whereas satisfying all soft constraints is not necessary. Although the quality of the solution is directly related to the number of soft constraints that are satisfied. One of the recent innovative methodologies for solving UCTP is the hybrid algorithm, which attempts to automate the timetabling design process so that it would be able to work with different instances of problem domains. In this paper, we present a hybrid method based on the Improved Parallel Genetic Algorithm and Local Search (IPGALS) to solve the course timetabling problem. The Local Search (LS) approach is used to strengthen the Genetic Algorithm (GA). The IPGALS has applied a representation of the timetable, which ensure the hard constraints would never be violated. Hard constraints are measured by Distance to Feasibility (DF) criterion. In fact, applying the DF criterion leads to achieving feasible solutions and promotes the performance of our algorithm. Due to the wide range of problem constraints, the proposed algorithm is performed in parallel to improve the GA searching process. The IPGALS algorithm is tested over BenPaechter and ITC-2007 standard benchmarks and compared with the state-of-the-art techniques in this literature. The experimental results confirm the effectiveness and the superiority of the proposed algorithm compared to other prominent methods for solving UCTP.

A hybrid algorithm for the university course timetabling problem using the improved parallel genetic algorithm and local search

Developing Compact Course Timetables with Optimized Student Flows

This paper presents a review pertaining to assignment problem within the education domain, besides looking into the applications of the present research trend, developments, and publications. Assignment problem arises in diverse situations, where one needs to determine an optimal way to assign subjects to subjects in the best possible way. With that, this paper classified assignment problems into two, which are timetabling problem and allocation problem. The timetabling problem is further classified into examination, course, and school timetabling problems, while the allocation problem is divided into student-project allocation, new student allocation, and space allocation problems. Furthermore, the constraints, which are of hard and soft constraints, involved in the said problems are briefly elaborated. In addition, this paper presents various approaches to address various types of assignment problem. Moreover, direction and potential paths of problem solving based on the latest trend of approaches are also highlighted. As such, this review summarizes and records a comprehensive survey regarding assignment problem within education domain, which enhances one’s understanding concerning the varied types of assignment problems, along with various approaches that serve as solution.

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An Assignment Problem and Its Application in Education Domain: A Review and Potential Path

As an important administrative task in the area of education, course timetabling is a complex optimization problem that is difficult to solve by conventional methods. The paper adapts a new nature-inspired metaheuristic called ecogeography-based optimization (EBO), which enhances biogeography-based optimization by equipping the population with a neighborhood structure and designing two new migration operators named global migration and local migration, to solve the university course timetabling problem (UCTP). In particular, we develop two discrete migration operators for efficiently evolving UCTP solutions based on the principle of global and local migration in EBO, and design a repair process for effectively coping with infeasible timetables. We test the discrete EBO algorithm on a set of problem instances from four universities in China, and the experimental results show that the proposed method exhibits a promising performance advantage over a number of state-of-the-art methods.

University course timetabling using a new ecogeography-based optimization algorithm

In this paper, we present a web-based group decision support system for the Academic Term Preparation problem faced at a business school of a large Middle Eastern university. This multi-stage problem involves several stakeholders that need to coordinate for the course offerings, instructor assignments, and the preparation of the relevant timetables. This coordination is facilitated through a web application that implements all stages of the workflow. It further automates the timetabling task through an optimization module using a new multi-objective mixed integer programming model. The model is based on curriculum and student sectioning requirements; academic and administrative policies; and, the present capacity situation. The new system replaces a semi-automated spread sheet tool, resulting in improved quality of timetables, efficient workflow coordination, customized reporting, significantly reduced lead times, and eradication of human errors.

A web-based group decision support system for academic term preparation

A new hybrid algorithm for university course timetabling problem using events based on groupings of students

Sudoku is an interesting number placement puzzle with some simple rules. For some positive integer n, the puzzle involves an n2 × n2 grid partitioned into n2 distinct blocks each of size n × n such that the integers 1 through n2 appear exactly once in each row, each column and each block of the grid. Often some static numbers known as givens are placed according to the difficulty rating in the puzzle and then the rule is to place the numbers from 1 to n2 in the partially filled grid such that the conditions of the puzzle are satisfied. The aim of this paper is to propose a new algorithm for enumerating all possible Sudoku squares of size n2. It is based on the concepts of permutations derived from n2 × n2 S-permutation matrices termed as S-permutations. There is a one-to-one correspondence between Sudoku squares and the set of those S-permutation matrices which are mutually disjoint to each other. The proposed algorithm uses the set of all S-permutations generated by some permutation generation algorithm as input and then enumerates all the subsets of cardinality n2 of all S-permutations which are mutually disjoint to each other. The correctness of the algorithm is established. Its worst-case time complexity is O(ωn2 +2logω), where ω = (n!)2n. A mathematical formula involving the total number of the sets of (n2 − 1) mutually disjoint S-permutations is also derived. Experimentally, the proposed algorithm is verified for the Sudoku squares of size 9 × 9. It is observed that our algorithm is more systematic and better in terms of computational efficiency.

Pallavi Mishra

Papers

A new hybrid algorithm for university course timetabling problem using events based on groupings of students

A new algorithm for enumerating all possible Sudoku squares