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20xx數(shù)學(xué)建模美賽f題論文(完整版)

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【正文】 re we take 10 thousand of people as unit. We set a base constant , should be selected properly to adjust the sensitivity.e) Policy factor(node resistance)(number of entry points)matrixThis is the most important factor and also the hardest to define. So to give a practical criterion, we adopt a Fuzzy Synthetic Evaluation model. we define the indicator p.We select as a standard number, the assessment level ranges from 0 to 1.The evaluation system involves the number of entry points and the open degree of government for refugees.The indicator p is largest value 1 means absolute open while 0 means totally refuse.f) Degree of social unrest (water pressure)matrix We define r as an indicator of the degree of social unrest Like the procedure above, we adopt a Fuzzy Synthetic Evaluation model.The lager the gap between the degree of social unrest of two countries, the smaller the r is. So r ranges from 0 to 1.g) Economic attraction (water demanding)matrixWe define u as an indicator for economic attraction between two countries.The lager the gap between the degree of economic states of two countries, the smaller the u u ranges from 0 to 1.2) the resource arrayMake a list of the GDP of the countries involved in the problem.Set a series of factors to represent different influence factors, like economic state, religious factor. To identify them, we also use a Fuzzy Synthetic Evaluation model. And will be discussed during the algorithm explanation.6 The Unstoppable Refugee Algorithm The background introductionAs we concentrate on the main map of Europe relative to the route of refugee flow, we can figure out the major and minor nations that re directly infected by methods of both taking settlement and passingby. So we regard them as the nations that re “on the way”, as for those not directly infected, such as Iceland, we made the assumption that they re not on the way.Abstractly we build a network of this relationship, just as the following diagram presented, each country were regarded as one single point and the connection, or saying ,the traffic path between two different lands were summarized as one line in the networking, and each path were confirmed no ignorancethat means where there lies a mon boundary between two countries ,there should be one path. The only difference is that the difficulties of travelling on that path, which varies under condition of the nature or mathematical distance, dangerous rankings, traffic system, etc. There’s no need to discuss every detail about the route but we can provide a single factor that can inflect and summarize the difficulty of one single route.Under the specific situation and assumption we made, we can build a explicit network of Europe expressing the relationship and the condition of all the possible routes and destinations refugees may take. Graphing the EuropeWe define that there is the Graph G(V, E), and each country should be regarded as one Vertex ,the connection from country 1 to country 2 ,to simplify the model, the Graph should be the Undigraph, that means if , and furthermore, we made the assumption that the difficulties between the two way path were of the same size. The difficulty of the single path between countryshould be expressed by the weight of the specific path.For the total explanation of the geographical relationship as well as the path between countries, we summarize the matrix we discussed before and then store the result of each path into one adjacency matrix, if there is a path between, we store the weight of path into the matrix, the less difficulty of the path, the lower value it should be. And if there is no direct path or not accessible (like from Russia to Spain we must take the way of Poland, France), the value of the path should be regarded as 0 for no relationship ,but stored as INFINITY for most difficult. For example, if there’re 4 countries , the difficulty of the path between , is , and , while there is no direct path from 1 and 4, 2and 4, we can draw the diagram and the matrix below. And that for the program language (c++ for example) we store them into a dyadic array arc[i][j]. So for single refugee, the initial task for him should be finding a way leaving the battlefield as soon as possible and settle down at the peaceful place. And the best way to do that is to find a quickest way to other country. Let’s assume that there is recently a battle taken place at country and one homeless refugee was searching for the way to the peace country , and the difficulties of the travel route are explained in the following what will that refugee do? He will probably find the way of least difficulty and get rid of the disaster as soon as possible, because it is not the trekking but fleeing. So every refugee are at the same dilemma, that he should find a quickest way of the network. The following shows that the best way from to is ,.So if states for Syria and states for Germany, the refugee find a most efficient way from Syria to Germany, experiencing less difficulties. Basic path finding algorithmThen the problem es out that how to find the most efficient way? It is simplified to the model that in Graph we should find a shortest way from to and make sure . And there is the famous algorithm called Dijkstra, or the Shortest Path Algorithm, fitting the condition of finding a shortest way from single start vertex to ending vertex in the graph stored in the adjacency matrix.So after the calculation before, here es the 32*32 matrix stored with information of 32 relative countries on the 6 major routes with the weight explaining the difficulties of each path, but the Dijkstra algorithm can only find the single short way from one start point. The disadvantage of the original algorithm is explicit:1) Dijkstra can only find the shortest way once.2) Dijkstra algorithm can only define the start point , and the system
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