美赛O奖经验分享

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当我谈数学建模时我谈些什么——美赛一等奖经验总结

前言：2012年3月28号晚，我知道了美赛成绩，一等奖（Meritorious Winner），没有太多的喜悦，只是感觉释怀，一年以来的努力总算有了回报。

从国赛遗憾丢掉国奖，到美赛一等，这一路走来太多的不易，感谢我的家人、队友以及朋友的支持，没有你们，我无以为继。

这篇文章在美赛结束后就已经写好了，算是对自己建模心得体会的一个总结。

现在成绩尘埃落定，我也有足够的自信把它贴出来，希望能够帮到各位对数模感兴趣的同学。

欢迎大家批评指正，欢迎与我交流，这样我们才都能进步。

个人背景：我2010年入学，所在的学校是广东省一所普通大学，今年大二，学工商管理专业，没学过编程。

学校组织参加过几届美赛，之前唯一的一个一等奖是三年前拿到的，那一队的主力师兄凭借这一奖项去了北卡罗来纳大学教堂山分校，学运筹学。

今年再次拿到一等奖，我创了两个校记录：一是第一个在大二拿到数模美赛一等奖，二是第一个在文科专业拿数模美赛一等奖。

我的数模历程如下：2011.4 校内赛三等奖2011.8 通过选拔参加暑期国赛培训（学校之前不允许大一学生参加）2011.9 国赛广东省二等奖2011.11 电工杯三等奖2012.2 美赛一等奖（Meritorious Winner）动机：我参加数学建模的动机比较单纯，完全是出于兴趣。

我的专业是工商管理，没有学过编程，觉得没必要学。

我所感兴趣的是模型本身，它的思想，它的内涵，它的发展过程、它的适用问题等等。

我希望通过学习模型，能够更好的去理解一些现象，了解其中蕴含的数学机理。

数学模型中包含着一种简洁的哲学，深刻而迷人。

当然获得荣誉方面的动机可定也有，谁不想拿奖呢？模型：数学模型的功能大致有三种：评价、优化、预测。

几乎所有模型都是围绕这三种功能来做的。

比如，今年美赛A题树叶分类属于评价模型，B题漂流露营安排则属于优化模型。

对于不同功能的模型有不同的方法，例如评价模型方法有层次分析、模糊综合评价、熵值法等；优化模型方法有启发式算法（模拟退火、遗传算法等）、仿真方法（蒙特卡洛、元胞自动机等）；预测模型方法有灰色预测、神经网络、马尔科夫链等。

历年美赛题目解法

历年美赛题目解法全文共四篇示例，供读者参考第一篇示例：历年美赛是美国工程建模大赛的简称，每年都会赛出许多优秀的选手和团队。

这项比赛主要是针对工程、数学和科学领域的学生，通过一个实际问题来展开建模和解答。

在历年美赛中，团队们面对的题目各不相同，有些题目会比较复杂，需要综合运用多门学科知识进行解答，而有些则相对简单，更注重创新和解决问题的方法。

在历年美赛题目中，有一些常见的解法和技巧可以帮助团队更好地应对挑战。

要充分理解问题，深入分析问题背景和要求，确保对题目的理解没有偏差。

要根据问题的特点和要求确定合适的数学模型，并运用各种数学方法和工具加以求解。

要善于利用计算机编程技巧来实现模型的建立和求解，以提高工作效率和准确性。

解题过程中，团队成员之间要密切合作，充分发挥各自的专长和优势，共同攻克问题。

在解答过程中，要及时调整思路和方法，灵活运用各种技巧和工具，以找到最优解。

在完成模型和解答后，要进行有效的分析和讨论，检查模型的合理性和稳定性，确保解答的准确性和可靠性。

在历年美赛题目中，有一些经典的解题思路和方法，被广泛应用于不同领域的问题中。

运用线性规划方法求解最优化问题，采用动态规划算法处理序列型问题，利用离散事件模拟技术模拟系统行为，通过随机过程分析系统性能等。

团队在解答问题时，可以参考这些经典方法，并根据实际情况进行创新和调整，以获得更好的结果。

在参加历年美赛的过程中，团队可以积累丰富的经验和知识，不断提高解题能力和创新意识。

通过与其他团队的交流和比赛，也能够拓展视野，学习他人的优秀经验和做法。

在解题过程中，要保持耐心和坚持，不断克服困难和挑战，直至最终获得满意的解答。

在历年美赛题目解法中，关键的是全面理解问题，切实分析和建立数学模型，灵活应用各种方法和技巧，团队配合紧密，有效沟通和讨论，并不断实践和改进。

通过不断练习和磨炼，团队可以在历年美赛中取得优异的成绩，展现出自己的才华和实力。

希望各位参赛者能够在历年美赛中不断进步，取得更好的成绩，展现出自己的独特魅力和价值。

美赛Outstanding Winner作者经验分享

首页个人主页竞赛广场校园广场学神日志谢永意个性签名：Never say Never吕静我的竞赛二本民族院校也可以拿美赛Outstanding Winner 和 SIAM Award关联竞赛：数学建模数学关键字： 2014年美国大学生数学建模竞赛特等奖（Outstanding Winner ） SIAM Award2014年的美赛，我们队很荣幸地拿到了Outstanding Winner SIAM Award ，这也是我国第四所大学拿到这个单项奖，之前是华中科大、清华和浙大。

可喜的是今年的SIAM 奖都来自中国的学生，浙江大学和我们西南民族大学包揽了AB 题的SIAM 奖。

应赛氪邀请，写了这一篇类似经验的分享。

我也想借这个机会总结一下我们第一次参加美赛就拿O 奖和SIAM 奖的经历，希望能给数模爱好者们一些帮助。

团队成员：谢永意，章瑶，刘一平获奖时大二都来自西南民族大学计科学院信息与计算科学1201班本篇经验贴作者为本队刘一平一、2013年五一数学建模联赛五一数学建模联赛对我们来说是我们和数学建模的相识，我们队里只有章瑶和谢永意参加了，我有事没有参加，虽然比赛规模没有国赛美赛那么大，但是对于刚上大一的我们来说，这也是一次受益终生的经历。

我们三个都是好朋友，听他俩说那次比赛经历相当坎坷，虽然是数学系的但毕竟才上大一，对于一些数学软件还是很白菜的，他们都是在短时间内学习使用软件，论文书写，还有模型建立的，那次比赛也算是为国赛奠定基础了。

那次比赛他们两个的成绩都还是不错的，一个三等奖一个二等奖，也是那次比赛让他们对国赛又充满了渴望，毕竟三天都是神经紧绷着，这种感觉很爽的，只有经历过的人才会体会到。

而且能学到很多东西。

也是那次比赛我之后才知道原来还有SPSS 这种软件。

二、2013年国赛2012年放暑假之前我们学校就有老师在上数学建模的培训课，我那个时候还没有组队，就是每天去打酱油，记得培训结束的最后一天，老师让同学们自愿组队，我本来是想回家的，不想留在学校，但是谢永意想参加国赛，所以我们就问了几个同学，但是毕竟培训都结束了好多人都组好队了，我们真的已经不抱希望了，就在这个时候我看到了我们班的学霸章瑶，就问了一下她，结果她也是想如果没人组队就直接回家的，既然我和谢永意邀请都邀请了她那就留下来培训了。

2011美赛C题O奖

Putting the Spark Back in theElectric CarTeam#11422February14,20111Team#11422Page2of20Contents1Clariﬁcation of Problem3 2Plan of Attack3 3Assumptions3 4On Types of Cars4 5Model for Number of Cars4 6Microeconomic Model56.1Global Inﬂuence Model (5)6.1.1Strengths&Weaknesses (7)6.2Localized Behavior (8)6.2.1Cellular automata (8)6.3Strengths and Weaknesses (9)7Macroeconomic Model:Meeting the Energy Demand107.1Current Energy Source and Demand (10)7.2Current Pollution rates (11)7.3Quantizing Pollution (11)7.3.1Health (12)7.4Quantizing Cost (12)7.5αParameter (13)7.6Minimizing X:Genetic and Nelder-Mead Methods (14)7.7Using Alpha to Determine Cost,and Vice Versa (14)7.8Example Calculation (16)7.9Fossil Fuels Saved (17)7.10Strengths and Weaknesses (17)8Meshing the Micro and Macro Models18 9Conclusion19Team#11422Page3of201Clariﬁcation of ProblemWith the recent introduction of the Nissan Leaf and Chevy Volt to the world carﬂeet and the fading supply of petroleum,the possibility of electric vehicles replacing standard petroleum cars is increasing.Questions arise concerning the feasibility of such vehicles,speciﬁcally regarding the amount of fossil fuels saved through widespread use of electric cars,and the economic feasibility.It is of great concern to auto-manufacturers and environmentalists alike to determine how to cause electric cars to’catch on,’and of equally great concern to govern-ments to determine how to augment the power grid to meet the demand of the electric carﬂeet.The models proposed within this paper will oﬀer an insight to these problems.2Plan of AttackOur objective is to model the eﬀects of electric vehicles on the environment, public health,and economy.We need to determine which methods would be most eﬀective in causing widespread use of electric vehicles,within a reasonable time rge scale use of electric vehicles would also put an increased strain on the power grid,which would have to be corrected.To determine the most eﬃcient way to do this,we will proceed as follows:1.Create a model for the amount of electric cars at any given point in time.(Micro)2.Create a model that gives a single value to the eﬀect electric cars have onthe environment,health,and economy.(Macro)3.Connect these models so that,by giving setup conditions,we can deter-mine the cost to minimize the pollution values.3AssumptionsDue to the extrapolative nature of our model,and the diﬃculty in obtaining reliable global information,several assumptions were made in order to complete our model.These simplifying assumptions will be used throughout the paper and could feasibly be replaced with reliable data when it becomes available.•The cost of building more coal,oil,and natural gas plants is negligible to the cost of yearly fossil fuel production.That is to say,energy costs simply rely on production prices from the plants themselves,and not creation of the plants.•We assume100%eﬃciency of converting fossil fuels to energy for electric-ity.This makes the calculations for energy easier,removing the need to know the electric energy conversion rate for electric generators.•World Governments can control addition of power plants to determine the proportions of energy from each source.This is essential in changing theTeam#11422Page4of20 makeup of the power grid.By being able to change the ratio of the energy sources of our electricity production can we can change the ratio of the pollutants produced for each unit of electrical energy.•Ratios of energy sources into demand sectors for the US in2009is the same as the ratios across the world.This allowed us to generalize the information that we had to the world-wide energy system.•Price increases quadratically as demand increases for fossil fuels.This allows us to extrapolate the past data,allowing us to produce a prediction of the cost of fossil fuels in the future.•Population within the next50years can be modeled with a cubicﬁt.This allows us to extrapolate the past data as well,ensuring that we know the amount of cars in a given year.•A major factor in choosing which car to buy is what the people around you own.The movie”Who Killed the Electric Car?”suggested that the main reason that electric cars did not become popular was because many people did not know about them or their properties.This assumption is the basis in the models for the spread of electric cars throughout a population.[9]•It is economically and environmentally infeasible to increase current en-ergy contribution to the electric power grid for each power source by more than%25percent.This is to establish upper bounds for the Nelder-Mead methods,and can be replaced with projected maximum contribution for 2060if/when these values become available.4On Types of CarsWe have decided to base our model solely on electric vehicles versus gasoline vehicles,instead of including hybrid vehicles.We have chosen to do this because we are concerned with the widespread usage of electric vehicles.If electric vehicle usage is widespread,then the idea of a hybrid car is useless,since electric cars can be used for most transportation usages and gas cars can be used for any transportation that electric cars cannot do.Hybrid models were created to transition from gas cars to electric cars.However,if we are to consider widespread usage of electric vehicles,hybrids won’t be necessary.It is worth noting that electric vehicles do have limited range,causing some range anxiety. Modern estimates suggest that90%of automobile users do not have needs that exceed the limitations of electric cars,however,so the range anxiety will only aﬀect10%of the population[9].5Model for Number of CarsIn order to model the change towards electric cars and its impact on the environment,we need a model for the number of cars in the future.We found an estimated134motor vehicles per1000people in the top130developed countries. From this,an estimate of120vehicles per1000people in the world can be made.Team#11422Page5of20 Using this and population data,we can expect to have C cars in t years after 1950based on the following equation[10]:C(t)=.002t(2.55·109+3.91·107t+1.1·106t2−9.38·103t3)We decided upon a cubicﬁt to model the population because itﬁtted popu-lation data very well.However,thisﬁt will only accurately model population data until2060,due to the cubic nature of the function.We have a multiplier of .002t because the number of cars per capita will increase over time,as data has shown[1].We are going to let E equal the proportion of cars which are electric. The following2equations give the number of electric and gasoline vehicles over time in terms of E.E(t)=E·C(t)G(t)=(1−E)·C(t)In our microeconomic model,we examine how E will change50years in the future based on an initial proportion of electric cars.This will allow us to see what must be done to make electric vehicle usage widespread.For our macroeconomic model,we let E=.9since we wish to examine the eﬀects of widespread electric vehicle usage.6Microeconomic ModelThrough examination of how individuals react to electric car usage we can model the change from petroleum vehicles to electric vehicles.Our small-scale model needs to be based on the likelihood that individuals will switch to electric vehicles.We propose two models.Both of these models require a government subsidy for electric cars in order to”jumpstart”their production,and explosion in popularity.Theﬁrst model is based on coupled diﬀerential equations for how one might expect the number of electric vehicles and the number of gasoline vehicles will change over a continuous time interval.The second model is a 2D cellular automata simulation to model the local inﬂuence as well as global inﬂuence of the number of electric vehicles,over a discrete time interval.6.1Global Inﬂuence ModelThis model assumes that individuals are inﬂuenced by the global proportion of people who have electric cars.An individual who is going to buy a new car or replace a broken down gas car will buy an electric car with a probability equal to the proportion of people who have electric cars.This is because the more people who have electric cars,the more likely an individual is to hear about electric cars and be persuaded to switch to an electric car.This allows us to deﬁne the following coupled diﬀerential equations where BDE and BDG is the probability that an electric and gas car will break down during one year.Since gas cars last for about8years and electric cars last for about20years,we letBDE=120and BDG=18[4].E (t)=E(t)E(t)+G(t)·(C (t)+BDG·G(t))−BDE·E(t)·1−E(t)E(t)+G(t)Team#11422Page6of20G (t)=1−E(t)E(t)+G(t)·(C (t)+BDE·E(t))−BDG·G(t)·E(t)E(t)+G(t)Since our C(t)and is only valid forﬁfty years in the future,solving these equations outright is unnecessary.We use Euler’s Method to approximate E(t) and G(t).To do this,we need two points,one for E(t)and one for G(t).Since t is measured in years after1950,we let G(60)=C(60).We cannot let E(60)=0 since the only way for the number of gas cars to grow is from the probabilityE(t) C(t).This model requires that a certain number of electric cars be seeded intothe population to jump start the growth of electric cars.In order to seed these cars,the government could pay the diﬀerence in cost between an electric vehicle and an average gas car to give people an incentive to buy an electric car.By spending this money to encourage people to use electric cars,the government would save money later by spending less money for fossil fuels,such as oil.We will examine how this works after we have built our macroeconomic model.To determine the seeding cost,we assume that the government will pay the diﬀer-ence between the cost of an electric vehicle and a gasoline vehicle.We decided this cost per car would be$41,000−$28,400=$12,600.The following graphs demonstrate the rate at which the proportion of electric vehicles grows(with seeding values of.05and.3)and the following table summarizes this data with varying proportions of seeding in2011.Team#11422Page7of20Seed Proportion Seeding Cost E in20600.011.0327·10110.2670.055.16348·10110.6670.11.0327·10120.8150.151.54854·10120.8770.22.06514·10120.9120.252.58174·10120.9330.33.09834·10120.948The more money spent on jumpstarting electric vehicles,the larger E will be50years in the future.In order to determine which proportion of seeded cars would be most proﬁtable in the future,we would need to know the make up of the power grid,which we determine in our macroeconomic model.We will connect this model to the macroeconomic model later.6.1.1Strengths&WeaknessesA strength of this model is that it allows the government to see what would need to be done in order for people to want to buy electric cars.By basing this model on the proportion of people who have electric cars,this model can realistically model an individual’s likelihood of switching to an electric car.A weakness in this model is that seeding only occurs in one year,instead of a range of years.Another weakness of this model is that it does not include locality,which misses out on what seems to be a crucial point in the rise of electric vehicles.Another weakness of this model is it does not consider current sources of energy.Currently,electric cars are not better for the environment because the largest source of electrical energy is coal;this will be considered and changed in the macroeconomic model.Team#11422Page8of206.2Localized BehaviorThe previous model assumes that the total percentage of electric cars inﬂuences the chance of a single person purchasing one.However,a person is aﬀected by the people closest to them in addition to the global behavior.This is why we decided to model the spread of electric cars using2-dimensional cellular automata.First,we decided that a cell’s percentage to pick either electric or gas is based on the8cells that are adjacent,known as the Moore Neighborhood. The inﬂuence from locality is converted into a chance of buying an electric car based on the number of your neighbors who are electric cars(N)according to the following equation:P(if electric stay electric)=18·(.1N+.1)P(if gas become electric)=120·(.1N+.1)Global inﬂuence is also considered with this model,and is incorporated with what we call the”snowball constant.”The diﬀerential equations given above can be applied to cellular automata rules by setting C (t)=0,since the number ofcells is constant,which allows us to substitute E(t)E(t)+G(t)with E p t,the proportionof electric vehicles.Ultimately we can rewrite our diﬀerential equations as:E pn+1(t)−E pn(t)=3E p(t)40·(1−E p(t))G pn+1(t)−G pn(t)=3E p(t)40·(E p(t)−1)To consider both the local and globalized behavior(L and W),we can simply weight these with the relative importance of localized behavior(due to the snowball eﬀect)with that of global behavior.Exact values of snowball constants will have to be determined through real world observations,and will likely vary throughout the population.For our data,we used a snowball constant k=4, assuming that localized behavior is responsible for80%of buying patterns.Our ﬁnal proportion looks like this:P=k·L+W 1+kThe amount of electric cars that are placed initially is changed in order to model the seeding program that the government has put in place.The output of the model gives the percentage of electric cars out of the total population of cars.This percentage can be traced from year to year to give you the eﬀect of governmental electric car seeding,both in theﬁnal percent as well as the year when government seeding no longer plays a role in the percentage of cars.6.2.1Cellular automataInitial seeding is important as there is no point to seeding more cars if fewer cars will get you to your goal percentage of electric cars on the road by a certain year.By using both the global and the local model,we determined that theﬁnal percentage of cars that are electric,for a given number ofTeam#11422Page9of20 seeding,is less in the local model than in the global model,meaning that these local interactions seem to slow down the distribution of cars.Theﬁnal state of one simulation and a chart of the proportion of electric vehicles versus timeare shown below:6.3Strengths and WeaknessesThe beneﬁts of a cellular automata model are many:this model diﬀers from all others in this report int that there is no population increase,which means that this model is independent of theﬂawed population model,and is free from allﬂaws that come with that.This means that this model can more accurately model years after1960.Modiﬁcations can be made to increase the chances of buying an electric car as time goes on,due to improvements in technology and the decrease in electric car cost.Furthermore,the eﬀects of localized behav-ior are well documented,and completely overlooked with diﬀerential equation models.The eﬀects of these localized behavior can be combined with the diﬀer-ential equation model with the snowball constant–an option unavailable to theTeam#11422Page10of20 diﬀerential equation model.This localized model is not without it’s weakness. Because of theﬁnite number of cells,it is diﬃcult to incorporate growth of the population(of total cars)into the CA model.Much of our values for proba-bilities rely on rough probabilities and assumptions of the snowball constant. These can be adjusted on a product-by-product,or even a cell-by-cell basis,but it complicates the model greatly.We also could have overlooked crucial values in our probability models percentages needed to factor into the lifetime cost of a car,relative usability values like the average range an electric car can go without recharging,and more qualitative values like sticker shock.7Macroeconomic Model:Meeting the Energy DemandWhereas our microeconomic model focused on the necessary parameters to en-sure a large number of electric cars in the future,our macroeconomic model focuses on the changes that need to be made to accommodate the increased demand of electricity.It is important to consider both the costs required to produce these new amounts of electric energy,and the”hidden”costs of pollu-tion.Without considering these”hidden”costs,our model would simply gener-ate the cheapest solution to the increased power demand,which could possibly just trade one fossil fuel(gasoline)for another(coal,etc.).Thus,we’ve gener-ated an equation to determine the cost associated with the increased electricity demand,depending upon how much of each energy source we utilize,and a variable parameter equating pollution to cost.7.1Current Energy Source and DemandData from the EIA has shown that38.075quadrillion BTU was used for elec-tricity in2009,producing11.159trillion kWh[7].The breakdown of energy sources contributing to this statistic is summarized in the following chart.Since it is assumed that this breakdown is roughly equal for all highly-developed coun-tries,the countries who will have the largest number of electric cars,and thus increased demand for electricity.[7]Team#11422Page11of20 The most recent electric cars from Li-ion Motors Corp have a range of120 miles and require8hours of charging from a110V source[4].This means that 52.8kWh are needed for a full charge,or.44kWh per mile of travel.This translates to1501.3BTU needed a mile in an electric vehicle.The average pas-senger car can travel31miles on a gallon of gasoline.Since a gallon of gasoline contains roughly116,090BTU,the average gas car runs on3744.84BTU per mile[1].This is more than twice as much energy required by electric cars,so switching to electric cars decreases the amount of energy required worldwide for transportation purposes,but also requires a switch from the100%gasoline power source for gas cars,to the medley of power sources used for electricity.7.2Current Pollution ratesBurning fossil fuels creates pollutants that damage the environment,increasing acid rain,respiratory illness,and photochemical ing current energy source quantities,the pounds per mile of use of electric and gas cars is sum-marized in the following table.Though nuclear power sources have not gained widespread popularity due to social fears of nuclear accidents and the relative cost of creating a network of reactors,their carbon footprints are negligible.It also goes without saying that the footprint of renewable energy sources are also negligible.Pollutant Electric Car Gasoline Car Diﬀerence Carbon Dioxide0.1839693020.614153760.430184458Carbon Monoxide0.0001611950.00012358−3.76149·10−5Nitrogen Oxides0.0003609130.0016776880.001316776Sulfur Dioxide0.0018842520.004201710.002317459Particulates0.0019805450.000314567-0.001665978Mercury1.16351·10−82.62139·10−81.45788·10−8 From our equation of the number of cars in terms of years since1950,C(t),and the proportion of those which are electric E,we create the following equations for the pounds of pollutant reduced each year.Pollutant Pounds SavedCarbon Dioxide0.430·12,200·E·C(t)Carbon Monoxide−3.76·10−5·12,200·E·C(t)Nitrogen Oxides0.00132·12,200·E·C(t)Sulfur Dioxide0.00232·12,200·E·C(t)Particulates-0.00167·12,200·E·C(t)Mercury1.46·10−8·12,200·E·C(t)7.3Quantizing PollutionThe pollution value is a metric that determines how good for the environment having a certain percentage of electric cars are.Theﬁrst value that determines this metric is the amount of pollution that is being saved in pounds per year. The second value is the percent pollutant decrease,which describes how muchTeam#11422Page12of20 control of that pollutant is had.For example,if you could either cut50%of the total carbon monoxide emissions or25%of the total carbon dioxide emis-sions,that50%decrease is weighted heavier,regardless of the actual pounds of emissions you are eliminating.A third,hypothetical,value would be the bad-ness of each pollutant.Since not all pollutants damage the environment and peoples health as much as others,this badness relates to the degree to which the current yearly amounts of pollutants are damaging the environment.In the trials we ran,we assumed that the total yearly emissions of every pollutant were equally bad,so each badness value was set at1.Given the set of pollutants, {CO2,CO,NO x,SO2,P articulate},where the subscripts,G,E,and T corre-spond to the amount emitted from gas cars,the amount saved by electric cars, and total emissions,respectively,our pollution can be deﬁned as follows:P ollution=pollutantsjj G+E·j Ej T7.3.1HealthIn examining the eﬀects of pollution,we should also consider the eﬀects on health.This is incorporated in our Pollution function because if we can only change a small percent of the quantity of a pollutant,it will have a smaller eﬀect on health,whereas if we can change a larger percent of the quantity of a pollutant,it will have a larger eﬀect on health.However,some pollutants may be more damaging to the environment than others,meaning that eliminating 50%of one pollutant would not be equivalent to eliminating50%of another. By analyzing data concerning the eﬀects of the pollutants on health and the environment,a badness factor could be determined by which each pollution percentage change could be multiplied with.By minimizing X,which is a func-tion for cost and pollution,we will also be minimizing the eﬀects.However in this model,we assumed that the badness factor,or the relative damage each pollutant causes to the environment and health,of each pollutant is the same.7.4Quantizing CostOnline sources can be used to estimate the small-scale cost of each BTU of each power source,in addition to the current production in the US[3].Bereft of data of the maximum production limits of each power source,it can be assumed that it would be economically infeasible to increase the current production limits for each power source to electricity by a factor greater than25%.This can be modiﬁed if more accurate statistics were obtained.Since widespread use of electric cars will require a major revamping of the power grid,demand will rise dramatically,potentially with no increase in supply.The prices of commodities increase with their scarcity,as seen by supply and demand curves.Again lacking data of supply and demand curves for power sources,we’ll be forced to make several assumptions.Given our maximum production limits,m,and our current production limits(deﬁned to be0here)and prices,i,we can deﬁne the price of a commoditiy to be ten times it’s current cost when we reach maximum production.We’ll also deﬁne the price to be2.5times current cost when weTeam#11422Page13of20 are halfway between current and maximum production ing these data points,we can set up a quadraticﬁt to model the price p(L)of one quadrillion BTU’s of a particular energy source per quadrillion BTU(L)more than current production as:p(L)=i−3i·Lm+12i·L2mto determine the total cost to increase production from current values to pro-duction l,we can simply integrate from0to l:P tot(l)=l0P(l)dl=l−3i·l22m+4i·l3m2So total cost for all power sources is equivalent to:Cost=P ower Sourcesjl j−3i j·l2j2m j+4i j·l3jm2jThe current production,cost,and maximum values are shown in the following table,where all productions are in QBTU,and cost in dollars per QBTU[3].Power Source Current Production Max Production Current Cost Petroleum0.383.4793.63∗1010 Natural Gas 6.8948.61751.47∗1010 Coal18.38422.988.7∗109 Renewable Energy 4.213 5.2662.2∗1010 Nuclear Energy8.42610.53255.9∗109 7.5αParameterWith cost and pollution both quantized,we can deﬁne an objective function asX=Cost+α·P ollutionWhere the number of electric cars,and hence their energy demand,is held constant.X is dependent on the number of quadrillion BTU’s we add to each power source and the alpha value,because cost is dependent on the power sources,and pollution is dependent on both power sources andα.Since wewant to minimize both cost and pollution,our goal is to minimize X.Theαvalue simply serves as a constant deﬁning how much the government values costto environment.For example,ifα=0,damage to the environment is not takeninto eﬀect and minimizing X is simply minimizing Cost.In and of itself,αis a relative value,as the relationship between it and pollution is very messy (again,dependent on all power sources).However,given a maximum amountof allowable pollutants,anαcan be determined.Possible values forαand their meaning will be discussed further in this report.Team#11422Page14of207.6Minimizing X:Genetic and Nelder-Mead Methods With X being a function of six variables(ﬁve power sources,and alpha),there are several methods that we can use search for global minimum,subject to the constraints that each power source is never to decrease from current pro-duction standards(under the assumption that removal of production facilities is both costly and creates largescale unemployment),and is never to exceed previously deﬁned maximum production standards.However,the nonlinear of nature eliminates the possibility of linear algebra techniques.Instead,we’ll rely heavily upon a Nelder-Mead iterative search technique and a genetic algorithm to deﬁne global minima.Though both of our techniques warrant equivalent so-lutions,we found that the Nelder-Mead search was much more computationally eﬃcient,so the genetic methods were ruled out.Thus,we run a minimiza-tion of X=Cost+α·P ollution subject to the following constraints,with variables{P etr,Nat,Coal,Ren,Nuc}deﬁning the amount of qBTU’s added to the power grid for petroleum,natural gas,coal,renewable energy and nuclear power,respectively:Minimize X=Cost+α·P ollution Subject toP etr+Nat+Coal+Ren+Nuc≤T otal Energy DemandCurrent P roduction≤P etr≤Current P roduction·1.25With theﬁnal constraint repeated for all power sources.7.7Using Alpha to Determine Cost,and Vice Versa Sinceαsimply refers to the amount to which we care about the environment, something that is diﬃcult to assign a concrete value to,we’ve allowed forαto vary.By iterating the Nelder-Mead optimization for a range ofαvalues,we can generate plots of each of the Power sources versus alpha.In plainspeak,that is to say that by choosing someαvalue(e.g.,we care x much about damage to the environment),we can locate the values of each power source qBTU by simply reading the graph.Since Cost is simply a function of the power sources and is monotonically increasing withα,we can generate a graph showing cost versus alpha,by simply repeating the above procedure,and then calculating the cost from the values of each power source,plotting this to a particular alpha value. Shown below are graphs of’cost Vs.α’and’Power Sources Vs.α’with90%of the motorﬂeet being electric cars,50years from today:Team#11422Page15of20These graphs allow us to oﬀer some insight into the behavior of the relation-ship betweenα(how much we care about the environment)and how we should augment the power grid.As is intuitive,a high reliance on coal and natural gas are necessary withα=0.Nuclear power seems constantly limited by our maxi-mum production value,suggesting that nuclear power,if production levels could be raised high enough,could be utilized in generating a low-cost,low-footprint power grid.Also intuitive is the monotonic behavior of the cost vsαgraph. The piecewise behavior is likely a result of certain’feasible pockets’within the polytope scanned with the Nelder-Mead method.。

参加美国大学生数学建模竞赛 - 知乎

5.制胜点
纵观整篇论文，没完成的模型（论文引用）不少，编程总共就两个，一个人口增长，一个层次分析。但是我们有条理的解决了这个问题，并且排版相当美观，图表制作的非常好看。
我觉得美赛并不是考你有多少数学知识，或者编程多么牛逼，或者队员背景多么生猛。而是你们是否能够好好合作，理清解决问题的思路，并有条理的写出来。你不一定要数学好编程好，也不需要有庞大的知识储备，而是要会尽可能的找到你要的资料和数据，尽可能全面的思考问题，在可选范围内，挑你能做好的去做。网上资料那么多，只是看你会不会发掘利用。
比赛报名：提前准备好visa或master card，名字和地址不要写错；
作息：要看各队情况了，原则是保证效率、不打乱节奏。前期都很亢奋，但如果打乱节奏可能导致后面疲劳期时效率过低，其实美国赛截止时间并不是很严格，前期利用好亢奋期和每天的高效率时间的话，到了疲劳期还能继续坚持下去，否则就是给你再多时间都无法持续下去。对那些想尝试达芬奇睡眠法的同学，建议先在之前比赛和练习时充分适应，避免临时改变作息方式，打乱节奏，降低效率；引用：如果copy了整段的原始论文，一定要注明来源——07年就出过outstanding奖因为引用的问题被收回的事。这是原则问题，千万注意！邮寄论文：提前联系邮局/快递，确认好邮局每天邮寄时间，以倒推截止时间，事实上这么多时间，很少有人能用满——这给了慢热队伍一个优势，之前练习也应先关注深度和质量，再考虑速度和效率；之前比赛的时候，交完论文的几天别闲着，继续魔鬼训练——对做到极致的模型再完善深化，对论文结论再推广演绎，甚至
必须保证团队里每个人都有共同的愿景和强大的动力，否则内耗是迟早的事。
高手和好导师都是稀缺资源，下手越早收获可能越大，想找高手：
你必须也是个高手，至少某方面特长能给人信心；必须保证团队间能衷诚合作，互相鼓励/配合——这点与谈恋爱一样，要经一定时间的磨合和考验，才能看得清；保证每个人的弱点能有效弥补，即便是高手全才也不多，对其弱点如果没有合适的人弥补，结果可能还不如实力平均的队伍；要能顶得住本校其他队的竞争，比如挖人、争导师、抢机房等等——人才太多没办法，哎～

数学建模美赛须知

加强数学建模综合能力培养——数学中国2011年美赛工作总结华晓帅（数学中国网站CEO）马壮（数学中国网站站长）2011年2月15日——2月19日，美国大学生数学建模竞赛与美国大学生交叉学科数学建模竞赛如期举行，作为中国最大的数学建模交流基地“数学中国”来讲，与参加美赛的中国内地同学共同度过了四天四夜。

对于本次竞赛，数学中国网站作了以下的总结。

希望能同大家交流一下比赛经验。

一、保持新闻的敏感度：在每次举办国内外数学建模竞赛之前，我们数学中国都事先做好心理准备，压一下比赛题目。

在春节前，数学中国论坛发表了《2011年数学建模十大热门研究课题》，第一个研究课题便压中了美赛的A题。

当然这里不是教大家如何猜题目。

我们想告诉大家要多关心国内外的时事、政治、经济。

为什么这样讲呢？道理很简单，学习数学建模，参加竞赛的最终目的不是拿奖，而是为了掌握一门社会科学技能。

大家学习数学建模后，可以用数学的眼光看问题。

比如说这次的A题，2007年2月联合国政府间气候变化专门委员会（IPCC）发表了第四次评估报告，在国际上引起了轩然大波。

报告预测指出，从人类工业时代开始到2100年，全球平均气温的“最可能升高幅度”是1.8至4℃，海平面升高幅度是19至58厘米，北冰洋的海冰将在本世纪后半段融化消失。

这个报告引出的问题很多，事实也得到了验证。

比如2007年至2011年的冬天，我们国家遭受了50年不遇的特大雪灾，美国南部又一次遭遇了飓风。

有证据显示这些都可能是由全球气候变暖引发的极端恶劣天气。

全球气候变暖考察的问题很多，A题选取了一个佛州的例子，意在让全球气候变暖得到大家足够的重视。

当然所有的时事不可能在一次竞赛里全部体现出来。

但是当大家看新闻的时候，应该多思考一下如何使用数学模型来处理新闻热点中提到的问题，经常和队员交流一下思路，增强对新闻的敏感度，提高对数学建模的应用能力。

我们数学中国论坛将在近期成立“数学建模研究组”（暂定名称）。

美赛写作材料模板及参赛经验分享

Tittle of paperSummary/Abstract Key words:I.Introduction（引言）Organ transplantation is a preferable treatment for the most serious forms of end-stage diseases. In recent years, advances in medical science and technology have made solid organ transplantation an increasingly successful and common medical procedure, a literal ''second chance at life". Not only does it offer the best hope for complete rehabilitation, but it has also proved to be the most cost-effective of all treatment options, including dialysis. Consequently, more and more people are benefiting from organ transplants and their survival rates are steadily improving. The surgical techniques involved have been mastered for half a century and are now considered as routine. The two main sources of kidneys for transplantation are deceased-donor kidneys and live-donations from family and friends. However, unfortunately, there is a considerable shortage of donor organs, compared to demands. As a matter of fact, efficient matching and allocation of organs donated has become an exigent problem.The United Network for Organ Sharing (UNOS), as the operator of the Organ Procurement and Transplantation Network (OPTN), is responsible for transplant organ distribution in the United States. UNOS oversees the allocation of many different types of transplants, including liver, kidney, pancreas, heart, lung, and cornea.Focusing on kidney transplantation, based on UNOS Kidney Allocation Model, we develop a mathematical model for US transplant networks. First, incomingorgans are matched with waiting candidates by medical institutions considering the factors as ABO blood compatibility, the degree of recipient major HLA mismatch in order to obtain a matching degree applied on the allocation part. After that, from the patients’perspective, on the basis of linear regression, priority weight is defined by pondering age, disease severity, time on waiting, PRA level, and region. Applying this mechanism of ranking, we realize MWBM (Maximum Weight Bipartite-graph Matching) and SMGS (Stable Matching based on Gale-Shapley algorithm). MWBM focuses on the optimal assignment of donors following the algorithm of bipartite-graph maximum weight matching; SMGS emphasizes the process of exchanges in order to obtain the stable exchanges between donors and candidates on the waiting list.II.The Description of Problem（问题重述)III.Basic Assumptions●The level of mismatch is only relative to the number of antigens.●The data and information are accurately registered according to the medicalmeasures●The data and information are refreshed in time according to the status of thepatients●No differences in the quality of the donor kidneys●The quality of the donor kidney is constantIV.Definitions and Notations●Kidney transplantation: A kidney transplant is a surgical procedure to implant ahealthy kidney into a patient with kidney failure.●Prioritization●MD: Matching Degree●PW: Prioritization weight●MWSM: Maximum Weight Bipartite Matching●SMGS: Stable Matching based on Gale-Shapley algorithm或V.ModelsThrough the investigation of US transplantation network, we draw a general picture of the mechanism. With reference to some resources available on the website of UNOS, a flow chart (Figure 1) is developed showing the procedure of the network.Currently, the initial waiting list is composed of patients who are waiting for a kidney or combined kidney-pancreas transplant. For the first time, the patients arerequested to show the correct and scientific information to the US kidney transplant network which is needed for donor-recipient matching, the ranking of patients on the waiting list, and determining the outcome of those transplanted. The patients’waiting lists are composed of initial patients, historical patients and unsuccessful recipient after transplantation. Historical patients refer to registered patients whose status have changed and have an influence on the procedure. A patient is taken off the waiting list when a graft is offered and accepted by that patient or the patient is dead while waiting for a transplant. Unsuccessful recipients refer to the patients who have a bad result of transplantation calling for transplantation again, as it is so-called relistFigure 1. A schematic depicting the steps occurring in the transplantation networks......Table 1.Survival rate involving HLA mismatchVI.Conclusions.Our model for the optimal allocation of the donor organs is established by three modules, procurement of MD and PW, optimal assignment by MWBM model and Stable Matching of Gale-Shapley algorithm. The model has offered a convincing procedure of the allocation with the ……VII.Strengths and weaknesses(模型优缺点)Strengths●……Weaknesses●VIII.References注意文献的积累，不要等到文章写完再去重新寻找文献。

数学建模美赛经验

不知道大家有没有看过《越狱》，呵呵，一般思路缜密的人都比较喜欢看这部戏。

这部戏很长，也历时了4年才放完大结局。

《越狱》共分为4季，另外还包括一部电影版！今天的主题我们也从越狱的角度开始，阐述美赛！做什么事情都要讲目的，我们不能像中国国家足球队那样每次比赛完都说一句最没骨气的话：我们是来交学费的！《越狱》从第一季开始男一号Michael帮助男二号Lincoln逃离监狱，如同中国的肥皂剧一样，每一季都是一个目的，逃出监狱！而目前在座的400多位学生，都是来参加美赛的，每个人的目标都不一样，有人要拿Outstanding，有人希望拿个SP就满足了。

而目的都是一样的。

就是要完美的完成竞赛论文，交出一份无悔于青春的答卷。

还记得《越狱》里的Michael在进入监狱前的准备工作吗，从第一季一直到第二季结束，他把所有的准备工作全部都纹在了身上。

可以说贯穿了前两季的所有的一切行动都是和他前期准备工作密不可分！我曾经在群里面说过一句话：机会都是留给有准备的人。

既然我们目的明确了，那么我们要进行充分的准备！What , Where , How , Why. 历年参加美赛的同学在竞赛中都会用到这4个词。

1. What：大家选什么题目？比赛开始、结束时间是什么时候？2. Where：参考资料那里去找？数据、文献在哪里找？数学中国的参考资料哪里可以找到？3. How：竞赛时间怎么分配？怎么建立模型？怎样建立思路？怎样书写求解程序？4. Why:：数据为啥不提供？为什么我想不出来？为什么这个题那么难？诸如此类的问题还有很多。

我们很是奇怪：为什么问题都要拿出来问？自己不去独立思考，不去独立解决。

这可是竞赛呀！假如说越狱中的Michael，把问题都拿出来问狱警、拿出来问同室狱友，还不被直接K.O.！后来我们也想明白了，这些情况的出现源于国内的应试教育，源于大家的被动学习！更具体一点说，大家在赛前没有做好充分的准备！但是怎么准备？问题又来了。

美赛特等奖经验分享

美赛特等奖经验分享清华大学的钟耀峰:我们的数模故事——14年美赛清华大学O奖非常感谢校苑数模的邀请，邀请我把自己美赛O奖的经验分布在论坛上。

这篇经验总结在5月份的时候就已经写好了，当时确实还不知道校苑数模论坛，后来一次偶然的机会在网上看到了校苑数模这个论坛，才开始偶尔来逛一下。

记得第一次逛论坛就看到了校苑寄语——banner广告“有些事不是看到了希望才去坚持，而是坚持了才会看到希望”，被这句话深深地折服，也被校苑数模这个富含文化的论坛所打动。

近期受论坛负责人赵松师兄邀请，将自己的经验分享写在论坛上，感到十分荣幸！第一次知道美赛是差不多去年的这个时候，当时觉得这比赛好像挺合我胃口，就想趁着大三带着那还残存着的激情好好干一把，也就图个经历嘛。

组队的过程挺意外的，以至于我还不清楚什么情况呢就组好了队，可能因为我们三个（我，张云翼，赵晓）本来就很熟悉。

后来想想我们三个确实是个不错的组合。

大三上期中考试之后，开始对某些专业课慢慢地厌倦了起来orz，于是开始找来美赛的论文看，也就是这个时候我才开始真正了解美赛。

我看的第一篇论文In the Zone: Novel Approaches to Airplane Boarding让我对美赛有了一个直观的概念。

读这篇文章时，我惊叹于它层层推进的模型，恰如其分的解释，清晰严密的逻辑框架以及漂亮的图表和美观的排版。

它让我了解了一个看起来棘手的问题的是如何被解决的。

这篇文章对我的影响很大，以至于我们参赛论文和这篇文章在架构上有不少相近之处。

这段时间我和赵晓、张云翼还联系了两位参加过美赛的学长，希望他们能给我们一些建议。

靠谱的学长们详细地解答了我们的疑惑。

我们得知了数学模型能够解决哪些问题，有哪些基本的方法，需要学习哪些知识。

我们也清楚了比赛的4天内时间应该大致怎么分配，三个人如果出现了意见不合的时候应该怎么处理等等。

之后用零零散散的时间看了几篇文章也逛了逛数模论坛，也就快到期末考试了。

美国数学建模大赛经验

一般人都认为美赛比国赛要难，这种难在思维上，美赛题目往往很新颖，一时间想不出用什么模型来解。

这些题目发散性很强，需要查找大量文献来确定题目的真正意图，美赛更为注重思想对结果的要求却不是很严格，如果你能做出一个很优秀的模型，也许结果并不理想也可能获得高奖。

另外，美赛还难在它的实现，很多东西想到了，但实现起来非常困难，这需要较高的编程水平。

除了以上的差异，在实践过程中，美赛和国赛最大的区别有三点：第一点区别当然是美赛要用英文写作，而且要阅读很多英文文献。

对于文献阅读，可以安装有道词典，开启截屏取词功能，这样基本上阅读英文文献就没什么障碍了。

对于写作，有的组是写好中文再翻译，有的是直接写英文，这两种方式都可行。

对于翻译一定至少要留出8小时来，摘要可能就要修改1小时。

如果想快点翻，可以直接使用有道词典，翻出来后再修改，虽然可能不地道，但至少比较准确，这样可大量节省翻译时间。

另外word要打开纠错功能，绿线代表拼写错误，红线代表语法错误，完成论文后整体浏览时要多注意这两种线，很可能会发现疏漏之处。

我一直认为翻译不是美赛的重点，只要能把意思表达清楚就行了，不必在翻译上浪费太多时间。

第二点区别是美赛大量的用到了启发式算法，如遗传算法、模拟退火、粒子群等等。

如果说你在国赛时还认为这些算法遥不可及，那么到了美赛你就必须掌握它了。

其实我认为对于搞编程实现的队员只要弄懂一种启发式算法就好，因为启发式算法是用来解决优化问题（多数为NP问题）的，不同算法间有很大的相似性，所以只要把一种学精了，这一类的问题就都能解了。

个人认为粒子群算法还是不错滴，遗传与模拟退火有些老套了，不过选择什么还是由你个人的接受程度决定，甚至你也可以自创算法。

第三点区别是美赛论文的排版不少人会使用Latex，一款用代码编辑的排版软件，它多用在对书籍和论文的排版上，效果美观但是操作很复杂，尤其是插入图片与表格，不是一般的麻烦。

而且，学习这种软件必须是一次性全部学完不能间断（据说完整的学习时间大概是几十个小时），只学某部分是没有用的。

关于一些美赛的技巧

查找文献的办法，各个学校可能都有自己购买的数据库，我在这里想提一下谷歌一个很厉害的功能，当然如果大家已经知道了就跳过吧。

那就是在关键词后边加上filetype:pdf，会有很多意想不到的收获！我们当时在找tipping point的时候查了很多数据库，但是垃圾信息也很多，谷歌的这个功能帮我们节省了不少时间，最后有用的数据也是从这里面找到的。

1. 论文的最前面一定要有assumptions，这个真的非常重要，只有宇宙无敌马克思主义是没有任何假设绝对正确的，如果大家的假设写的很专业很make sense，评委一定会想继续看下去的。

2. 格式一定要新颖，可以参照我发的链接里的O奖论文，大家可以发现这几篇论文的格式差别非常大，但是都有一个共同点：新颖，不死板。

我觉得老外还是挺在乎逼格的，你写的太中国风人家会觉得你不够creative，当然我说再多都没用，大家下载了那个文档一看就懂了。

3. 图片一定要fancy！不要把eviews等低端软件的统计报告图复制粘贴到你的论文里，这样做真的非常low！一定要自己画出很fancy但是很浅显易懂的图，真的很加分，journal里面的评委也是这样说的。

4. 最让人无语的是把代码写到论文里的同学，这个就不吐槽了，总之美赛的思想>算法>代码，你结果做不出来编一个都行（不过这样好像不太诚信，但是身边真有M奖的结果是编的，所以好像不是很重要），最重要的是你的想法，为什么要用这个方法？为什么方法是可行的？你是怎样做的？至于结果能做出来当然最好，没做出来也要想办法让你的论文显得很完整。

通过一周对美赛体制及outstanding论文的分析，得出了以下几个结论，希望与各位共同探讨：（1）美赛获奖覆盖率相当之大，只要你不作弊，三等奖就能到手，只要你摘要清晰明了，思路创新有依据，就能拿二等奖，其实拿一等奖最大的困扰就是英语，要拿一等奖必须要把最简单的道理全都说出来，力求用外国人欣赏的英语风格，尽量多的而有效率的叙述说明；当然把以后几点都做到，再配上点创新及参考文献标注地严格规范，你就是O奖得主；（2）美赛查资料问题：美赛题所需的资料基本上都能用谷歌实现，所以建议各位多去找一些谷歌全攻略来学习一下，但是有一点的是，就是你所参考过的资料，你都要在论文参考文献中或论文中有所提及，即便你只抄了6个单词，美赛对于版权问题查的是非常之严格的，不像国赛；（3）美赛算法创新及实现问题：如果你能从基本算法入手，把几种算法组合起来，并通过在美国教授看来比较权威的软件实现，这就是创新，权威点的软件当然是指多用美国出产的数学或制图软件。

大神美赛建模经验谈

牛人建模经验谈虽然也提到了全国赛，但主要是针对美赛的。

搞数学建模时间也算是不短了，也参加了大大小小好几次比赛了，也获了大大小小的不少奖，在参加建模竞赛中积累了不少的经验。

尤其是参加了两次全国赛愈加感到要在全国赛中取得好成绩经验第一，运气第二，实力第三，这种说法是功利了点，但是在现在中国这种科研浮躁的大环境中要在全国赛中取得好成绩经验是首要的。

这并不说明美赛中经验不重要，在美赛中经验也是首位的，但是较之全国赛就差的远多了，这是由于两种比赛的不同性质造成的。

全国赛注重"稳"，与参考答案越接近，文章通顺就可以有好成绩了，美赛则注重"活"，只要有道理，有思想就会有不错的成绩，这个也体现了两个国家的教育现状，这个就不扯开去了。

在数模竞赛中经验会告诉我们该怎么选题，怎么安排时间，怎么控制进度，知道什么是最重要的，该怎么写论文......，或许有人会认为选题也需要经验吗？经过参加了多次比赛后觉的是有技巧的，选个好题成功的机会就大的多，选题不能一味的根据自己的兴趣或能力去选，还要和全体参赛队互动下（这个开玩笑了，不大容易做到，只能是在极小的范围内做到），分析下选这个题的利弊后决定选哪个题，这里面道道也不少，后面会详细的展开谈谈。

写这个东西当做是回忆下以前的点点滴滴，希望自己的经验能帮助一些新手（这样的说法不大好，暂时想不出更好的，凑活着先用着）能尽快的成长，尽快的发挥自己的能力，体验数学在应用中的作用，爱上数学，甚至和数学打一辈子交道。

组队和分工数学建模竞赛是三个人的活动，参加竞赛首要是要组队，而怎么样组队是有讲究的。

此外还需要分工等等一般的组队情况是和同学组队，很多情况是三个人都是同一系，同一专业以及一个班的，这样的组队是不合理的。

让三人一组参赛一是为了培养合作精神，其实更为重要的原因是这项工作需要多人合作，因为人不是万能的，掌握知识不是全面的，当然不排除有这样的牛人存在，事实上也是存在的，什么都会，竞赛可以一个人独立搞定。

美赛冲刺课8 美赛注意事项及获奖技巧

赛题。各队可于EST时间2018年2月8日周四下午5:00，（北京时间是2018年2月9日凌晨6点）登录竞赛网站查看赛题。
• ① 2018年竞赛日期和时间：
报名截止时间：北京时间2018年2月9日周五凌晨4:00 竞赛开始时间：北京时间2018年2月9日周五上午6:00）竞赛结束时间：北京时间2018年2月13日周二上午9:00 电子邮件提交截止时间：北京时间2018年2月13日周二上10:00 控制页提交截止时间：北京时间2018年3月3日周六上午6:00 竞赛结果：预计2018年4月29日公布
完成模型检验和优缺点的工作。完成大部分中文论文的写作。完成摘要的写作。工作特点：一个人完成模型检验工作，两个人完成论文写作工作。
（4）邮件检查清单
• ① 邮件主题是正确的 (COMAP#控制号)。 • ② 邮件附件 (一个文件) 命名是正确的(Team #控制号) ，而
且已附加到邮件中。 • ③ 发送到的邮件地址是正确的(forms@)。
4 竞赛结束时
赛前提示
• 在竞赛结束时间之后，论文电子版的状态将会更新。通常情况下，在竞赛结束24－48小时后，论文电子版的状态都将会更新。
• 摘要页需要清楚描述使用的方法和问题，以及最重要的结论，而不应仅仅是问题的重述、剪切或者粘贴引用内容。
• 摘要页需涵盖的内容：问题重述与说明，用自己的话表示你想做什么；
解释假设和理由，清楚列出模型中使用的所有变量；使用的模型；模型测试和灵敏度分析，包括误差分析；模型和方法的劣势和优势等。
• ⑤ 论文必须为英语书写，使查清单：
① 邮件主题是正确的 (COMAP#控制号)。 ② 邮件附件 (一个文件) 名字是正确的(Team #控制号) ，而且已附加到邮件中。 ③ 发送到的邮件地址是正确的(solutions@)。

如何备战美赛MCM

美赛备战攻略各位校苑会员，你们好！我是校苑数模论坛的赵松，截止目前，2014年“校苑数模高校巡回讲座”已经接近尾声了，我有幸参加了清华站、北航站、武汉理工站、西大站以及西南民大站的现场讲座，聆听了包括美赛赛题专家周老师、美赛O奖获得者华科熊风以及西南民大谢永意等众多嘉宾的精彩报告。

大学期间，我参加了美赛、国赛、Mathorcup、电工杯、苏北赛、校赛等大大小小的赛事，共9次。

这篇帖子的内容融合了自己的参赛经验、两年的科研经验（包括英文论文写作）以及嘉宾们的经验；题目定义成《美赛如何获奖》，我觉得一点都不为过，只要做好文章提到的内容，可以说至少可以获得美赛二等奖。

1. 对美国大学生数学建模竞赛的错误认识<1> 不是数学专业的同学能否参加数学建模竞赛？这个问题由来已久，不仅仅限于美赛，对国赛、Mathorcup 以及其它数模赛事，某些非数学专业的人都会望而生畏。

与其说望而生畏，不如说是望文生义，很多同学只要看到“数学”二字，心里都会产生一种高大上的感觉。

造成对数学建模的错误认识的原因是各方面的，比如数模指导教师都是理学院的、教高数的，还比如学长们的经验分享中明确提出需要具备一定的数学功底等等。

第一，数学建模竞赛对数学确实有一定的基础性要求，我个人认为高等数学、线性代数以及概率论与数理统计这三门课，基本可以构成数学建模的数学门槛。

有些学校明确要求不让大一或者大三以下的学生参赛，也是考虑到低年级的学生没有系统地学习过这三门课。

这些基本知识在进一步的了解基本数学模型的过程中会经常遇到。

第二，数学建模竞赛涉及的领域远远超出了理论数学的范畴，它属于应用数学范畴，涉及到物理、化学、计算机、医疗以及控制等等各大门类。

一种很现实的现象是，高校在组队的过程中，往往将不同专业的学生组成一队，也是考虑到这个因素。

总结来说，不是数学专业的同学也非常适合参加数学建模竞赛，数学成绩不好的同学并非不适合参加数学建模竞赛。

2023美赛建模经历总结

2023美赛建模经历总结引言我参与了2023年的美赛建模比赛，并在比赛中取得了一些经验和收获。

在本文档中，我将总结我的经验，并分享我的观点和方法。

赛前准备参加美赛建模比赛需要进行一系列的准备工作。

首先，我们需要熟悉比赛的规则和要求。

这包括了解比赛的主题、时间要求、评分标准等等。

其次，我们需要组队，并明确每个队员的职责和分工。

每个队员都应该负责自己擅长的领域，这样可以充分发挥大家的优势。

最后，我们还需要制定一个详细的计划，以确保我们按时完成各个阶段的任务。

队内协作队内协作是美赛建模比赛中至关重要的一环。

在我们的队伍中，我们通过定期的会议和讨论来促进团队合作。

每个队员都有机会分享自己的想法和观点，并提出改进的建议。

我们建立了一个有效的沟通渠道，以便及时解决问题和调整计划。

此外，我们还利用在线协作工具共享文件和资源，方便队员之间的合作和交流。

数据收集和处理在比赛中，数据收集和处理是一个重要的环节。

我们需要收集相关的数据，并进行合理的处理和分析。

对于大规模的数据集，我们采用了并行计算和分布式处理的方法，以提高效率和准确性。

此外，我们还利用数据可视化工具，将数据以图表的形式展示出来，使得我们可以更直观地理解和分析数据。

模型构建和验证在美赛建模比赛中，我们需要构建一个有效的模型，并对其进行验证。

在模型构建过程中，我们采用了多种方法和技术。

我们首先对数据进行预处理，包括数据清洗、特征提取等等。

然后，我们尝试了多个模型，并比较它们的性能。

最后，我们选择了一个最好的模型，并进行了交叉验证和参数调优，以确保模型的准确性和稳定性。

结果分析和总结在比赛结束后，我们对结果进行了分析和总结。

我们回顾了我们的方法和策略，并评估了我们的模型的性能。

我们还比较了我们的结果和其他队伍的结果，以了解我们在比赛中的竞争力。

最后，我们总结了我们的经验和教训，并提出了改进的建议。

结论通过参与2023年的美赛建模比赛，我学到了很多知识和经验。

美国大学生数学建模竞赛赛20160719

美国大学生数学建模竞赛的命题与评阅
天津大学边馥萍 fpbian@
美国大学生数学建模竞赛
热烈祝贺山东大学荣获2016年美赛O奖
参赛命题评阅获奖培训
1. MCM/ICM 简介
美国大学生数学建模竞赛创始人 Ben Fusaro 1984年向美国教育部申请到一笔为期三年的基金，并于1985年开始正式举办。竞赛由COMAP组织和管理竞赛的命题、组织形式、宗旨、评审原则 MCM参赛情况：第1届：1985年参赛队158个队（美国），交卷90队，70所大学第32届：2016年参赛队7421个队，919所大学， 12个国家及地区，中国学生参赛队超过93.5%
初评标准
对题目的解读，赛题中没有明确给出的模糊概念是否澄清。建模所需的前提条件及假设及其合理性的说明。通过对赛题的分析论证建模的合理性。建立有效解答赛题的模型。对模型的稳定性、敏感性进行测试，检验。讨论模型的优缺点，给出清晰的结论。符合要求的摘要：应包含以下内容用自己的语言描述要解决的问题，强调建模所用的假设，指出所用的模型类型或构造的新模型，模型检验及误差分析和优缺点讨论。
2016 ICM Contest Outstanding Teams
2训资料（高教出版社出版）
美国大学生数学建模竞赛题解析与研究 2007-2008 第一册 2005-2006 第二册 Mathematical Modeling for the MCM/ICM Contest , Volume 1, 2 正确写作美国大学生数学建模竞赛论文 …..
UMAP数学建模案例精选1、2册，3册即将出版
UMAP 案例精选—1、2测已出版，3册即将出版特点：案例及习题有具体解法，有些适合做教学案例配套PPT正在制作中

2023年美赛B题O奖分析报告

2023年美赛B题O奖分析报告1. 简介本报告针对2023年美赛B题中获得O奖的团队进行了分析。

本次分析旨在从队伍技术实力、解决问题的方法和创新思维等方面，对O奖团队进行综合评估和详细说明。

2. 背景2023年美赛B题是关于某个复杂系统的优化问题。

该题涉及到多个变量并且存在多个约束条件，在给定的限制下，需要找到最优解。

解决这样的问题需要综合运筹学、统计学、计算机科学等多个学科的知识和技能。

3. O奖团队的技术实力O奖团队在技术实力方面表现出色，他们充分运用了运筹学、统计学和计算机科学的知识，对问题进行了深入的分析和研究。

他们使用了合适的数学模型来描述问题，并基于此构建了相应的优化算法。

此外，他们还通过编程实现了算法，并使用计算机进行模拟和验证。

在具体的技术实现上，O奖团队采用了高级的优化方法，如整数规划、线性规划等。

他们利用Matlab、Python等工具进行数值计算和算法实现，并通过可视化的方式展示结果。

团队成员还具备良好的编程能力和数据处理能力，能够高效地处理大量数据并进行分析。

4. O奖团队的方法与思路O奖团队在解决问题的方法和创新思维方面展示了高水平的能力。

他们不仅仅满足于表面的分析和求解，而是通过深入挖掘问题本质，提出了独特的解决方案。

首先，O奖团队充分理解了题目要求，并从整体上进行考虑。

他们对问题进行了全面的分解，找出了其中的关键要素和关联因素。

在建模过程中，他们充分考虑了系统的复杂性，对每一个关键因素进行详细的分类和分析，以便更好地把握问题的本质。

其次，O奖团队通过结合不同的优化方法和算法，形成了针对性强的解决方案。

他们对问题的特点进行了充分的理解，并进行深入地优化和改进。

在优化算法选择上，他们采用了综合考虑效率、准确性等因素的方法，确保了解法的可行性和可靠性。

最后，O奖团队在创新思维方面也有突出表现。

除了传统的优化方法，他们尝试了一些新的技术手段和方法。

例如，他们采用了机器学习和人工智能的技术，辅助解决问题。

给参加MCM同学的一些建议——如何在短时间内争取最大可能性拿奖

给参加MCM同学的一些建议——如何在短时间内争取最大可能性拿奖彭子未本文主要探讨如何在明天就比赛的情况下，增大获奖的几率。

另外还要先对我去年写的《当我谈数学建模时我谈些什么——美赛一等奖经验总结》做一些解释。

去年我写的《当我谈数学建模时我谈些什么——美赛一等奖经验总结》/blog/296254215/855386875 授权给上海交大数协转载后，到今天已经有超过10000的浏览量了，全站评论也有上千条，说实话，我没想到这篇文章能传播这么广，着实吃了一惊。

今天抽空看了看评论，觉得毕竟这文章是去年写的了，有的地方今天看来也觉得表述不很到位，这里统一做一下解释，别误导了大家。

1、我写此文的目的——这篇文章的阅读对象写此文是在去年美赛结束后第二天开始的，为的是能够详实而完整的记录整个比赛过程。

文中提到了我的背景只是一个文科专业的双非院校学生，因此此文的对象是那些和我一样在普通大学、读普通专业渴望逆袭而又觉得自己实力不足的同学。

我记录下比赛的全流程是想给我们学校的师弟师妹一个参考：如果失败了，没拿奖，那这么做就不可取；如果成功了，他们可以如法炮制，增加获奖几率。

所以某些牛大的骄子们，此文本来的对象就不是你们，喷此文好比批评幼儿园教材太幼稚一样，没有意义。

如果你们的目标是F奖或者O奖，像这里的爷一样：请你们戳这里：https:///file/d/0B5dLYzw7XIleZ2poRWhSSV9ubGc/edit 去年O奖大神的经验总结，我的这篇文章你读到这里就可以了。

2、关于睡眠与LaTeX评论里讨论最多的就是这个问题。

去年美赛4天我只睡了10小时，现在我自己都觉得夸张，而且肯定也做不到了。

其实，这个睡眠时间因人而异，你什么时候想睡就睡好了，只要不耽误做题，一切睡眠安排都OK。

我想去年很可能是因为实力不行，心里没底，导致想以压缩睡眠时间来做题，其实现在觉得这样也不可取。

后来我还参加了2012年的国赛，这次睡眠充足，作息规律，结果是我们队成为了广东省推荐国家一等奖并参与答辩的6支本科队之一，这也弥补了我前年国赛的遗憾。

美赛经验交流分享

MCM/ICM 经验分享
IE 07 张莹
yingzhang8996@
Content
1 背景分析 2 准备工作 3 团队合作 4 文献资料 5 时间安排
Introduction
• MCM
– Mathematical Contest in Modeling – 数学建模竞赛
• ICM
组队分工
• 参加美赛前，每一名队友必须要考虑自己在团队中扮演什么样的角色，承担什么责任。 • 假如你是队长，需要找到两名队友共同完成本次比赛任务，必须把每个人的分工进行明确。 • 如果一个队中有两个人具有较强的编程能力，那是一个非常不错的组合！！
团队精神
• • • • 每一个人在每一分钟都能发挥作用保持每个人的参与敢于质疑 Initiative
做事积极主动，担负起自己在团队中的责任主动找事情做，做完自己的事在那闲着对其他成员的积极性是一种打击
• How to deal with conflict
赛前就应该考虑比赛过程中出现冲突问题的解决方案：投票，组长决定，折中等
Summary Sheet
• The summary is a very important part of your MCM paper. • The judges place considerable weight on the summary, and winning papers are sometimes distinguished from other papers based on the quality of the summary. • Imagine that a reader may choose whether to read the body of the paper based on your summary. • A summary should clearly describe your approach to the problem and, most prominently, what your most important conclusions were. • Your concise presentation of the summary should inspire a reader to learn the details of your work.