2012年美赛论文B题.docx

Team #12911 Page PAGE \* MERGEFORMAT22 of 21 Team #12911 Camping along the Big Long River Abstract In this paper, we try to solve the problem of scheduling river tourism which contains different tour durations and various speeds of propulsion. We propose a plan to utilize the camping sites as much as possible, and guarantee that two different teams do not meet during all their trips, in order to provide tourists with the wildness experience. In model construction, under a series of necessary assumptions including trip duration and campsite states, we make the discrete dynamic programming on the Big Long River operation using the constraints and objective functions. Moreover, a matrix form is introduced to describe the states of campsites succinctly and comprehensibly. We improve particle swarm optimization (PSO) to Integer-PSO algorithm which can solve the large-scale integer optimization problems. Then the optimum solution is obtained under our assumptions. Through careful calculation, we have proved that this optimum solution satisfies the basic requirement of the topic. When there are 20 campsites, we figure out that the optimal solution is 43 trips. With the further discussion about the different demands of tourists and managers, we improve the current model and take more factors into account such as utilization percentage and different campsite quantity. We make the schedule of teams and find the law of schedule topology structure which helps us certify our model and suggest a better theory. We test the  HYPERLINK dict://key.0895DFE8DB67F9409DB285590D870EDD/robustness \o 查找: robustness robustness and sensitivity of the models by accurate simulation above and obtain some theoretical conclusions of the arrangement for river tourism. The obtained optimal solution performs promisingly when considering different conditions. Therefore, the theoretical guarantee and the simulation result are consist