# Composing Multiple Online Exams: The Bees Algorithm Solution
## 2 Background and Related Work
### The Single-Exam Generation Problem  
The demand for performing online exams has increased remarkably in recent times. As a result, there has been a growing interest in developing optimal and efficient methods to generate online exams. Several approaches have been employed to address the single-exam generation problem. One straightforward method is the randomization approach utilized in [14], in which a Shuffling Algorithm was employed to detect and prevent  
Figure 1: Information that appears in the waggle dance (inspired by [29]). the duplication or repetition of randomly generated questions. Additionally, Simulated Annealing (SA) has been employed in [9] to select test items in a web-based environment, aiming to achieve a balanced distribution of information, content coverage, and item exposure (i.e., a measure of the frequency with which a test question is selected), within the generated test. Nevertheless, more sophisticated metaheuristic optimization algorithms are the current trend for solving this problem, as evident by [2; 10; 11; 12; 13; 15; 31; 32; 33; 34]. Particle Swarm Optimization (PSO) is a widely used optimization algorithm that imitates a flock of birds to locate an optimal solution. In PSO, each bird is referred to as a particle that flies searching for nourishment, which then shares the location of a favorable site. By doing so, the rest of the flock, or the swarm, can profit until they locate the optimal spot or solution. PSO was used in [15] to generate exams based on an objective difficulty level, while satisfying several constraints, such as the required number of questions in the exam and the number of questions used per section. A fitness function for each particle, i.e., exam, was calculated. The swarm keeps moving towards the global best until it reaches an optimal solution or satisfies the termination condition. The results of this approach showed that PSO succeeds in finding the best test to fit the requirements from a question bank with great speed, accuracy, and stability. The Genetic Algorithm (GA) has also proven to be powerful for generating online exams [10; 15; 31; 32; 33]. GA is an algorithm based on natural selection, in which the best individuals are selected for reproduction. The offspring then inherit characteristics from their parents. At the start of each generation, several individuals are selected and sorted according to their respective fitness levels. If the individual with the best fitness satisfies the requirements, the algorithm will stop. Otherwise, crossover and mutation will take place. The algorithm keeps iterating this process until a satisfactory solution is found. Studies [31; 32; 33] used GAs to generate online tests. The work in [31] attempted to generate tests with many requirement constraints, such as the number of questions, question types, difficulty, answer time, and exposure. The fitness function measures the difficulty level of the test, the class distribution, the total time needed to complete the test and the average exposure to the test paper. This approach yielded reasonable, diverse test papers, with a fast-running time of approximately 10 s.  
The researchers in [32] developed two distinct models to generate tests, each considering a problem with a different objective. The first model solves the Specified Length of Assessment Time problem (SLAT), in which the generated exam must be solved in a fixed period of time. The second is the Fixed Number of Test Items (FNTI) problem, wherein the exam must consist of a specific number of questions. The proposed models are the Concept Lower Bound First Genetic (CLFG) approach, which addresses SLAT problems, and the Feasible Item First Genetic (FIFG) approach, used to solve FNTI problems. Both models attempt to make all questions in an exam meet the lower bound of the expected relevance of each concept to be addressed.