20xx數學建模美賽f題論文-文庫吧在線文庫

　　

【正文】 after adjustment, etc.2) The result of the superior optimization procedure indicates the most rational distribution of refugees on the links and the nodes of the network according to the most rational policies. Introduction of advanced algorithm Brief introductionAs for the theoretical value, we used special algorithm.The main algorithm of us is the advanced Dijkstra algorithm. Dijkstra algorithm is designed for the single source problem. With the inspiration from Edmondkarp algorithm, we extended the Dijkstra algorithm to solve this multiple source and multiple targets. matrix introductionTo apply this algorithm, we introduced two conceptions: weighting factor matrix and resource factor matrix. The former matrix consists of different factors matrices and indicate the cost or degrees of difficulty of the various links on the network, while the resource matrix represents the resource of various nodes on the network for the consumption of transmission and settlement of refugees.The weighting factor matrix consists of different factors matrices:1) timeconsuming (pressure attenuation)matrix 2) leakage ratio (death rate) matrix3) the degree of social unrest (water pressure)matrix4) economic attraction (water demanding)matrix5) policy(node resistance)(number of entry points)matrix6) overloading of routes(pipe resistence)matrix7) Other special factor matricesThe resource factor matrix also consists of different factors matrices:1) welfare factor(negative pressure)matrix2) GDP factor(storage )matrix3) Religious resistance (evaporation)matrix4) Other special factor matrices Special extending for various conditionsThere are various extending parameters which will influence the final distribution of refugees. One of the most important advantages of our model is the excellent scalability of new parameters. As long as a proper parameter factor matrix is given and the rule to calculate every element of the matrix is rational, then, the result is rational.To adjust the importance and sensitivity of different factor matrices, we can use different power for different elements ing from different matrix. 5 The Model The basic model Assumptions and justificationPlease refer the above assumptions The process of model building basic establishmentTo evaluate the severity of refugee crisis, an indicator would be established: is the factor of transportation pressure of refugees. is the factor of resource consumption of refugees. is the factor of inequality, which represents the difference between the actual number of refugees each country has accepted and the ideal number of refugees should be acmodated considering the general economical policy, region and even the resisting pressure from nongovernmental aspects. is the factor of overload, which represents the degree of deviation pared total number of refugees with the capacity to acmodate refugees of all the receiving countries. is the allocation of refugees under the known condition without adjustment under the current policies (may not be reasonable enough). is the allocation of refugees with the reasonable adjustment of the policies. Before the adjustment, equals 1, and x represents the undetermined weight index represents the money each country could provide to refugeesare relevant coefficient, such as the coefficient of economic trend and people’s attitude on refugeesSuppose that the expenditure of each refugee in every receiving country is roughly equal and denoted as s. All the expense that all receiving countries could afford is denoted as S, while that of certain country (i represents the i th country). As a result, y represents the undetermined weight index represents the total reasonable number of refugees that all the receiving countries could acmodate. S is all the expense that all receiving countries could afford while s is the expense for each person. , represents the actual number of refugees on such a certain route. represents the ideal number of refugees on such a certain route. represents the number of all routes.z represents the undetermined weight index the route network(water pipe networks)To build such a network, the first and most important work is to select some nodes which represent crucial countries according to the 3rd assumption mentioned above. The principle of selecting is that your selection will represent the structure of the problem, and the node is influential enough that it can’t be ignored. By doing so, we get a pipe network where refugees can settle and transit.1) Weighting factor matrixa) Routes relationship(nodes and link)matrixIf there is n countries, then we can get a symmetric matrix A(n*n).If there is a route between two countries, then the element of the corresponding position is 1,or it is 0. Like the figure below.White means 1, other colors mean 0.b) Leakage ratio (death rate or degree of danger) matrixThe death rate on the land is much smaller than on the sea and the total number of the refugees, so the death rate can be regard as 0. When it es to the sea, the death rate can’t be ignored.a represents the undetermined weight index represents number of death people on the routes represents number of people on the routesc) Timeconsuming (pressure attenuation)matrixFirstly, identify the percentage,for the percent of walk, for the percent of bus, for the percent of rail way, for the percent of sea. Use the formula Then we get the average speed of European refugees on the land and on the sea.Identify the specific distance of each route (to gain the data, we use the google earth to measure the distance).Then we know the average time of each route t.The index we use here is .Here, b represents the undetermined weight indexd) Overloading of routes(pipe resistence)matrixThe number of refugees in Europe has gone over 1 million , so he