Finding feasible timetables using group-based operators.

This paper describes the applicability of the so-called "grouping genetic algorithm" to a well-known version of the university course timetabling problem. We note that there are, in fact, various scaling up issues surrounding this sort of algorithm and, in particular, see that it behaves in quite different ways with different sized problem instances. As a by-product of these investigations, we introduce a method for measuring population diversities and distances between individuals with the grouping representation. We also look at how such an algorithm might be improved: first, through the introduction of a number of different fitness functions and, second, through the use of an additional stochastic local-search operator (making in effect a grouping memetic algorithm). In many cases, we notice that the best results are actually returned when the grouping genetic operators are removed altogether, thus highlighting many of the issues that are raised in the stud

Identifying feasible schedules for elementary school gifted and talented education programs

Elementary school Gifted and Talented (GT) education programs enrich the quality and effectiveness of public school institutions by providing qualitatively different approaches to traditional classroom education and a more aggressively paced curriculum to children who exhibit high academic and creative ability. Typically, this is provided through enrichment classes which take place during the regularly scheduled class day. Due to this, schools which provide these services often encounter a series of complex scheduling challenges as students come from different classes and different grades to attend GT enrichment classes, each having varying schedules and varying availabilities. Using ad hoc techniques to address these challenges proves to be extremely time consuming and inefficient due to the tightly constrained nature of elementary school class scheduling. In this study, we model the problem as an integer-linear program in order to provide an accurate means of efficiently identifying feasible schedules for GT instructors

Reinforcement learning based local search for grouping problems: A case study on graph coloring

Grouping problems aim to partition a set of items into multiple mutually disjoint subsets according to some specific criterion and constraints. Grouping problems cover a large class of important combinatorial optimization problems that are generally computationally difficult. In this paper, we propose a general solution approach for grouping problems, i.e., reinforcement learning based local search (RLS), which combines reinforcement learning techniques with descent-based local search. The viability of the proposed approach is verified on a well-known representative grouping problem (graph coloring) where a very simple descent-based coloring algorithm is applied. Experimental studies on popular DIMACS and COLOR02 benchmark graphs indicate that RLS achieves competitive performances compared to a number of well-known coloring algorithms

Design, Engineering, and Experimental Analysis of a Simulated Annealing Approach to the Post-Enrolment Course Timetabling Problem

The post-enrolment course timetabling (PE-CTT) is one of the most studied timetabling problems, for which many instances and results are available. In this work we design a metaheuristic approach based on Simulated Annealing to solve the PE-CTT. We consider all the different variants of the problem that have been proposed in the literature and we perform a comprehensive experimental analysis on all the public instances available. The outcome is that our solver, properly engineered and tuned, performs very well on all cases, providing the new best known results on many instances and state-of-the-art values for the others

Incorporating Machine Learning to Evaluate Solutions to the University Course Timetabling Problem

Evaluating solutions to optimization problems is arguably the most important step for heuristic algorithms, as it is used to guide the algorithms towards the optimal solution in the solution search space. Research has shown evaluation functions to some optimization problems to be impractical to compute and have thus found surrogate less expensive evaluation functions to those problems. This study investigates the extent to which supervised learning algorithms can be used to find approximations to evaluation functions for the university course timetabling problem. Up to 97 percent of the time, the traditional evaluation function agreed with the supervised learning regression model on the result of comparison of the quality of pair of solutions to the university course timetabling problem, suggesting that supervised learning regression models can be suitable alternatives for optimization problems’ evaluation functions

An effective hybrid local search approach for the post enrolment course timetabling problem

We address the post enrolment course timetabling (PE-CTT) problem in this paper. PE-CTT is known as an NP-hard problem that focuses on finding an efficient allocation of courses onto a finite number of time slots and rooms. It is one of the most challenging resources allocation problems faced by universities around the world. This work proposes a two-phase hybrid local search algorithm to address the PE-CTT problem. The first phase focuses on finding a feasible solution, while the second phase tries to minimize the soft constraint violations of the generated feasible solution. For the first phase, we propose a hybrid of Tabu Search with Sampling and Perturbation with Iterated Local Search. We test the proposed methodology on the hardest cases of PE-CTT benchmarks. The hybrid algorithm performs well and our results are superior compared to the recent methods in finding feasible solutions. For the second phase, we propose an algorithm called Simulated Annealing with Reheating (SAR) with two preliminary runs (SAR-2P). The SAR algorithm is used to minimize the soft constraint violations by exploiting information collected from the preliminary runs. We test the proposed methodology on three publicly available datasets. Our algorithm is competitive with the standards set by the recent methods. In total, the algorithm attains new best results for 3 cases and new best mean results for 7 cases. Furthermore, it is scalable when the execution time is extended

How to pack trapezoids: exact and evolutionary algorithms

The purposes of this paper are twofold. In the first, we describe an exact polynomial-time algorithm for the pair sequencing problem and show how this method can be used to pack fixed-height trapezoids into a single bin such that interitem wastage is minimised. We then go on to examine how this algorithm can be combined with bespoke evolutionary and local search methods for tackling the multiple-bin version of this problem—one that is closely related to one-dimensional bin packing. In the course of doing this, a number of ideas surrounding recombination, diversity, and genetic repair are also introduced and analysed

Modifying Regeneration Mutation and Hybridising Clonal Selection for Evolutionary Algorithms Based Timetabling Tool

This paper outlines the development of a new evolutionary algorithms based timetabling (EAT) tool for solving course scheduling problems that include a genetic algorithm (GA) and a memetic algorithm (MA). Reproduction processes may generate infeasible solutions. Previous research has used repair processes that have been applied after a population of chromosomes has been generated. This research developed a new approach which (i) modified the genetic operators to prevent the creation of infeasible solutions before chromosomes were added to the population; (ii) included the clonal selection algorithm (CSA); and the elitist strategy (ES) to improve the quality of the solutions produced. This approach was adopted by both the GA and MA within the EAT. The MA was further modified to include hill climbing local search. The EAT program was tested using 14 benchmark timetabling problems from the literature using a sequential experimental design, which included a fractional factorial screening experiment. Experiments were conducted to (i) test the performance of the proposed modified algorithms; (ii) identify which factors and interactions were statistically significant; (iii) identify appropriate parameters for the GA and MA; and (iv) compare the performance of the various hybrid algorithms. The genetic algorithm with modified genetic operators produced an average improvement of over 50%