# Composing Multiple Online Exams: The Bees Algorithm Solution
## 2 Background and Related Work
### Bees Algorithm (BA)  
Bee-inspired algorithms are commonly employed as metaheuristic optimization techniques, leveraging the intelligent behavior of honeybees [19]. These algorithms belong to the category of swarm intelligence optimization methods, drawing inspiration from the cooperative foraging behavior of natural bee colonies [20]. The Bee Algorithm (BA) and its closely related variant, the Artificial Bee Colony (ABC), have demonstrated successful applications in various optimization problems. They have been particularly effective in domains such as vehicle routing and transportation, as exemplified by [21; 22; 23; 24], as well as in timetabling and scheduling problems, as demonstrated in [25; 26; 27].  
In nature, a bee colony is characterized as a collective entity that exhibits a wide-ranging presence, extending over significant distances (often exceeding ten kilometers) in multiple directions simultaneously to explore a vast area in search of food. The success of a colony's foragers relies on their ability to be directed towards productive food sources. In theory, flower patches that can attract a large number of bees are expected to offer abundant nectar and pollen, making them easily accessible with minimal energy expenditure. Conversely, flower patches that provide limited nectar or pollen tend to attract fewer bees [28].  
In a bee colony, foraging begins with scout bees searching for suitable flowers. These scouts explore their surroundings in a random manner, moving from one patch to another. When a scout bee discovers a source of nectar or pollen, it returns to the hive and performs a unique behavior known as the waggle dance on the dance floor. This peculiar dance holds significance in colony communication, as it conveys three essential pieces of information about the flower patches: direction, distance, and source quality, as depicted in Figure 1.  
Equipped with this information, the colony can effectively guide its bees without the need for external supervision or a predetermined blueprint. Follower bees inside the hive, who have been awaiting the dance, as well as the scout bees, then return to the flower patch. While collecting food from the patch, the bees assess its quality and continue to refine the waggle dance, if necessary, upon their return to the colony. This iterative process ensures that the colony continues its search for the most suitable patches, with bees performing additional waggle dances to recruit more individuals if the patch still contains ample food and requires additional workers [28]. The BA tries to mimic this process by applying the following steps [28]:  
* Initialize the population with random solutions.
* Evaluate the fitness of the population.
* While (stopping condition not met):
* Select the best sites for neighborhood search.
* Select elite sites from the best sites.
* Recruit bees around selected sites and evaluating fitness.
* Select the fittest bee from each site.
* Assign the remaining bees to a random search and assessing their fitness.
* End While.
* Return the best bee as the final solution.  
The BA begins with a population of solutions as its initial starting point. During the first iteration, bees make numerous local moves in order to explore potential solutions to the problem. This process is repeated until a predetermined number of solutions have been discovered. The best solutions, determined by their fitness, are retained. Subsequently, new neighboring solutions are generated around these top-performing solutions. These newly generated solutions are then evaluated to estimate the solutions that should be aimed for. The process continues iteratively until the algorithm satisfies a specified termination condition, ultimately returning a satisfactory solution to the problem [30].