Abstract
During the peak tourist season, large theme parks often experience a simultaneous influx of visitors, resulting in prolonged waiting times for popular attractions. This extended waiting significantly reduces tourists' satisfaction and may negatively impact their willingness to revisit the theme park. In Taiwan, schools at all levels often plan graduation trips to theme parks for their students. Students are divided into groups and must enter and exit the theme park at the same time. This article presents a new theme park problem with multitype facilities (TPP-MTF) for student groups. Based on the group's preference for theme park facilities, multitype reserved tickets with popular facilities are designed for groups, so groups do not need to wait for the reserved facilities. Since the waiting time for groups can be reduced, the theme park can also obtain ticket fees in advance and estimate the number of visitors to the theme park, so the theme park and the group can achieve a win-win situation. This article proposes a new decoding approach for a random permutation of integer sequence and embeds it into an immune-based algorithm, genetic algorithm, and particle swarm optimization algorithm to solve the TPP-MTF problem. A theme park in Taiwan was taken as an example and numerical results of the three algorithms were analyzed and compared to verify the effectiveness of the proposed algorithms.