Building and Solving a Small LP Model in C++

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外刊每日精读 Making trouble

外刊每日精读 | Making trouble文章脉络【1】看重制造业的国家都有工业战略，但是英国没有。

【2】英国对自己的可再生能源产业非常自满。

【3】安迪·霍尔丹称英国很可能在这场再工业化军备竞赛中落后。

【4】与中国相比，西方在绿色技术方面觉醒地太晚了。

【5】英国想要成为一个制造业“超级大国”还有一段路要走。

【6】英国不再是一流的制造业经济体，而且几十年以来都不是。

【7】戴森最近宣布将把电池工厂建在新加坡，这也完美诠释了英国现在正面临的挑战。

【8】戴森没有选择在英国建厂有多重原因。

【9】英国进行高价值的脑力劳动，其他国家负责生产的想法已经不再符合实际。

【10】国家相关战略的缺失让制造商处于竞争劣势。

【11】缺少合适的、有规划的工业战略是英国的致命弱点。

【12】从行动来看，英国似乎并没有参与竞争。

经济学人原文Making trouble：UK needs an industrial strategy to compete in manufacturing【1】Countries that are serious about manufacturing have industrial strategies.The US and China have one. So do Germany and France. Britain does not . Rishi Sunak talks about turning the UK into a “science and technology superpower” but that’s all it is: talk. It is a PR strategy masquerading as an industrial strategy.【2】Faced with the challenge presented by Joe Biden’s inflation reduction act (IRA), the government says it has no need to respond to the package of green subsidies being provided by Washington because Britain has already established a thriving renewables sector and the Americans are playing catch up. The complacency is staggering.【3】Andy Haldane , once the Bank of England’s chief economist and now the chief executive of the Royal Society of Arts, last week said: “The world is facing right now an arms race in re-industrialisation. And I think we’re at risk of falling behind in that arms race unless we give itthe giddy-up.”【4】China, Haldane added, had been focusing on green technology for many, many years and had forged ahead in tech such as solar and batteries. “The west has belatedly woken up,” he said. “The IRA is throwing cash to the wall on that. The cost of that [is] almost certainly north of half a trillion dollars. Possibly north of $1tn. The EU is now playing catch up, [and] the UK currently is not really in the race at any kind of scale.”【5】A quick glance at the latest trade figures shows Britain has some way to go to be a manufacturing“superpower”.manufacturing’s share of the economy shrank from more than 30% to less than 10% of national output in Elizabeth II’s reign. The goods deficit, last in surplus in the early 1980s, stood at £55bn in the first three months of this year, with imports more than 50% higher than exports. A £40bn quarterly surplus in services was not enough to close the trade gap.【6】Those who supported Brexit say the UK now has the freedom to export more to faster growing parts of the world economy . Those who opposed it say exporting to the EU has become more burdensome. Both are right, but both are missing the point. Before Britain can take advantage of export opportunities it has to have stuff to export. The fact is the UK is no longer a firstrank manufacturing economy and hasn’t been for decades.【7】Dyson’s recent announcement that it will build a battery factory in Singapore is a perfect illustration of the challenge facing the UK. There was never the remotest possibility that the plant would be in the UK due to what its founder James Dyson, a prominent Brexit supporter, called in a letter to the Times, t he “scandalous neglect” of science and technology businesses.【8】Only part of the company’s reluctance to manufacture in the UK is due to the recent jump in corporation tax, though that wipes out any benefit from tax breaks for research and development. It is also the planning system, the lack of trained engineers, the disdain shown for science and technology, and government interference in the way businesses are run.【9】The company says the UK will remain a centre for R&D, and it will invest £100m in a new tech centre in Bristol for software and AI research. But the idea that Britain can do all the high-value brain power stuff while other countries do the production is an illusion. Increasingly, Dyson’s R&D happens in Singapore, the site of its global HQ, and in the Philippines.【10】Dyson is by no means alone. A report by the lobby group Make UK found that six in 10manufacturers thought government had never had a longterm vision for manufacturing, while eight in 10 considered the absence of a strategy put their company at a competitive disadvantage compared with other manufacturing nations. It is no surprise that AstraZeneca recently announced it was building its new factory in Ireland .【11】Stephen Phipson, Make UK ’s chief executive , said last week the US was spending 1.5% of national output on its IRA. The equivalent sum in the UK would be £33bn. It was not just the money, though. “A lack of a proper, planned industrial strategy is the UK’s achilles heel ,” Phipson said. “Every other major economy, from Germany, to China, to the US, has a long-term national manufacturing plan, underlying the importance of an industrial base to the success of its wider economy. The UK is the only country to not have one.“If we are to not only tackle our regional inequality, but also compete on a global stage, we need a national industrial strategy as a matter of urgency.”【12】One option is to concentrate instead on sectors where the UK does have global clout: financial and business services, for example. In that case, the pretence has to stop that levelling up will be delivered by new factories turning out world-beating products.The government can either make Britain an attractive place for manufacturing companies to invest or it can decide not to compete. Judged by its actions rather than by its rhetoric, it seems to have chosen the latter option.。

Gurobi最优算法和启发式算法的融合

Gurobi 最优算法和启发式算法的融合顾宗浩GUROBI CTO, 联合创始人深圳, 2018年7月13日Outline•MIP Algorithm•Heuristics and (vs.) optimization •Gurobi heuristics•Non-LP based•LP based•Reformulation•Improvement•SubMIP and recursive•Features helping heuristics •Gurobi heuristic parameters •User input for Gurobi heuristics •MIP start/Multiple MIP starts•MIP hint•Partition heuristic•Heuristic callback•What to do with too big/hard models•MIP算法•启发式和（vs.）优化•Gurobi启发式算法•基于非LP•基于LP•模型改建•改进型•子MIP和递归•有助于启发式的功能•Gurobi 启发式参数•Gurobi启发式的用户输入功能•MIP 起始值/多个MIP起始值•MIP提示•分区启发式•启发式回调•如何处理太大/太难的模型概要Gurobi MIP Algorithms Gurobi 混合整数规划算法MIP Building Blocks 模块•Presolve•Tighten formulation and reduce problem size•Solve continuous relaxations•Ignoring integrality•Gives a bound on the optimal integral objective•Cutting planes•Cut off relaxation solutions•••Primal heuristics•Method, NodeMethodPresolve, PrePasses, AggFill, Aggregate, DualReductions, PreSparsify, ...Cuts, CutPasses, CutAggPasses, GomoryPasses, CliqueCuts, CoverCuts, FlowCoverCuts, ...预优化求解连续松弛模型切平面MIP Presolve预优化•Reduce problem size•Strengthen LP relaxationDisconnected•Identify problem sub-structures••Similar to LP presolve, but more powerful: 与LP 预优化类似，但更强大•Exploit integrality•Round fractional bounds and right hand sides•Lifting/coefficient strengthening•Probing•Does not need to preserve duality•We only need to be able to uncrush a primal solution•Neither a dual solution nor a basis needs to be uncrushedMIP –LP Relaxation LP 松弛问题MIP –Branching 分支LP based Branch-and-Bound 基于LP的分支定界法Upper BoundGAPLower BoundSolving a MIP Model 求解混合整数模型O b j e c t i v ePresolving Node SelectionNode PresolveLP Relaxation Cutting PlanesHeuristicsBranchingPresolving Node Selection LP Relaxation Cutting PlanesNode Presolve BranchingHeuristics Read MPS format model from file /models/mip/roll3000.mps.bz2Reading time = 0.03 secondsroll3000: 2295 rows, 1166 columns, 29386 nonzerosOptimize a model with 2295 rows, 1166 columns and 29386 nonzerosCoefficient statistics:Matrix range [2e-01, 3e+02]Objective range [1e+00, 1e+00]Bounds range [1e+00, 1e+09]RHS range [6e-01, 1e+03]Presolve removed 1308 rows and 311 columnsPresolve time: 0.08s Presolved: 987 rows, 855 columns, 19346 nonzerosVariable types: 211 continuous, 644 integer (545 binary)Root relaxation: objective 1.112003e+04, 1063 iterations, 0.03 secondsNodes | Current Node | Objective Bounds | WorkUnexpl | Obj Depth IntInf 0 0 11120.0279 0 154 -0 0 11526.8918 0 207 -0 0 11896.9710 0 190 -Presolving Node SelectionNode PresolveLP RelaxationCutting PlanesHeuristicsBranchingWhich open node should be processed next?Presolving Node SelectionLP RelaxationCutting PlanesNode PresolveBranching HeuristicsPresolved: 987 rows, 855 columns, 19346 nonzerosVariable types: 211 continuous, 644 integer (545 binary)Root relaxation: objective 1.112003e+04, 1063 iterations, 0.03 secondsNodes | Current Node | Objective Bounds | WorkDepth IntInf | Incumbent BestBd 0 0 11120.0279 0 154 -11120.0279 -0 0 11526.8918 0 207 -11526.8918 -0 0 11896.9710 0 190 -11896.9710 -H 327 218 13135.000000 12455.2162 5.18% 42.6 1sPresolving Node SelectionLP Relaxation Cutting Planes Node Presolve BranchingHeuristics Root relaxation: objective 1.112003e+04, 1063 iterations, 0.03 seconds Nodes | Current Node | Objective Bounds | WorkExpl Unexpl | Obj Depth IntInf 0 0 11120.0279 0 154 -0 0 11526.8918 0 207 -0 0 11896.9710 0 190 -0 0 12151.4022 0 190 -0 0 12278.3391 0 208 -5485 634 12885.3652 52 143 12890.0000 12829.0134 0.47% 54.5 25sCutting planes:Learned: 4Cover: 39Implied bound: 8Clique: 2MIR: 112Flow cover: 27GUB cover: 11Zero half: 91Explored 6808 nodes (357915 simplex iterations) in 27.17 secondsThread count was 4 (of 8 available processors)PresolvingNode Selection LP Relaxation Cutting Planes Node Presolve BranchingHeuristicsRoot relaxation: objective 1.112003e+04, 1063 iterations, 0.03 seconds0 0 11120.0279 0 154 -0 0 11526.8918 0 207 -0 0 11896.9710 0 190 -0 0 12448.7684 0 181 -H 0 0 16129.000000 12448.7684 22.8% -H 0 0 15890.000000 12448.7684 21.7% -0 2 12448.7684 0 181 15890.0000 12448.7684 21.7% -H 142 129 15738.000000 12450.7195 20.9% 43.8 1sH 212 189 14596.000000 12453.8870 14.7% 42.3 1sH 217 181 13354.000000 12453.8870 6.74% 42.6 1s * 234 181 40 13319.000000 12453.8870 6.50% 42.1 1sH 254 190 13307.000000 12453.8870 6.41% 41.3 1sH 284 194 13183.000000 12453.8870 5.53% 42.6 1s H 286 194 13169.000000 12453.8870 5.43% 42.7 1sBranch-and-Cut 分支切割Presolving Node SelectionLP Relaxation Cutting Planes Node PresolveBranchingHeuristics Presolved: 987 rows, 855 columns, 19346 nonzerosVariable types: 211 continuous, 644 integer (545 binary)Root relaxation: objective 1.112003e+04, 1063 iterations, 0.03 secondsNodes | Current Node | Objective Bounds | Work| Obj Depth IntInf | Incumbent BestBd 0 0 11120.0279 0 154 -0 0 11526.8918 0 207 -0 0 11896.9710 0 190 -H 0 0 15890.000000 12448.7684 21.7% -0 2 12448.7684 0 181 15890.0000 12448.7684 21.7% -...1066 702 12956.2676 31 192 13087.0000 12629.5426 3.50% 37.2 5s1097 724 12671.8285 8 147 13087.0000 12671.8285 3.17% 41.6 10s1135 710 12732.5601 32 126 12890.0000 12727.1362 1.26% 44.6 15s3416 887 12839.9880 46 136 12890.0000 12780.7059 0.85% 49.7 20s 5485 634 12885.3652 52 143 12890.0000 12829.0134 0.47% 54.5 25sHeuristics and (vs.) optimization 启发式和(对立)优化•优化是NP-hard•我们只应考虑启发式，但可行性问题也是NP-hard•理论上, 启发式和优化难度是一样的•许多实际问题经常被解到最优•我的优化问题很难解•所以我只开发了自己的启发式算法•那么你就是这次演讲的最佳听众•启发式算法和优化算法并不对立, 可以融合•我们将展示•Gurobi启发式的想法(ideas), 或许可以帮助您开发和改进您的启发式算法•如何融合Gurobi优化算法和您的启发式算法为您找到更好的解决方案GUROBI Heuristics GUROBI启发式算法Gurobi Heuristics 启发式算法•Gurobi has more than 30 heuristics有30多种启发式算法•Different types 不同种类•Non-LP based基于非LP•Enumerate, search, greedy, …•LP based基于LP•Rounding, fixing & diving, …•Reformulation模型改建•Zero-objective, min relaxation, …•Improvement改进型•RINS..•SubMIP and recursive子MIP和递归•Target heuristic, RINS, …•Problem specific针对具体问题的启发式•Fixed charge network heuristic•Features helping heuristics有助于启发式的功能•Pump reduceNon-LP Based Heuristics: Greedy基于非LP启发式算法:贪婪算法•Famous algorithms 着名算法•Optimal 最优的: shortest path最短的路径, min spanning tree最小生成树•Not optimal非最优的: 0-1 Knapsack 背包Max 10 u + 8 v + 11 x + 7 y + 5 zs.t. 3 u + 4 v + 6 x + 4 y + 3 z ≤ 14u, v, x, y, z are binary variablesSorting variables based on the ratio of the obj. coefficient and constraint coefficient, already sortedSetting variables to one based on the order until it become infeasible. Here setting y to one become infeasibleSo the solution is (u, v, x, y, z) = (1, 1, 1, 0, 0) with obj. value 29Optimal solution (u, v, x, y, z) = (1, 1, 0, 1, 1) with obj. value 30•Gurobi blind heuristics 盲目启发式(blind means not using LP relaxation solution)•Sort binary/integer variables based on some measure 用某种度量对二进制/整数变量进行排序•Fixing them in the greedy order 按贪婪顺序固定它们•Propagate fixing and bound changes for each fix 传播变量固定和收紧界值•Without it, it is almost impossible to find a feasible solution•Solve the remaining LP model, if there are continuous variables•LP based greedy heuristics 基于LP的贪婪算法•It is often more effective to use relaxation solution to sort variables 用松弛解对变量排序通常更有效Non-LP Based Heuristics 基于非LP启发式算法•They can find integer solutions quickly 有可能可以快速找到整数解•The quality of the solutions is often very poor 解的质量通常很差•One poor solution is good enough, poor solutions often won’t help overall optimization 一个差的解就足够了,差的解往往无法帮助整体优化•Multi cores and difficulty to parallelize the root node are the reasons to pay some attention to non-LP based heuristics 多核电脑和难以对根节点并行化是关注基于非LP的启发式算法的原因LP Based Heuristics 基于LP启发式算法•Rounding 取整法•Solve LP relaxation, round the solution values to nearest integer values 解LP松弛问题，将解值四舍五入到最接近的整数值•0-1 knapsack example (same example) 0-1背包例子(相同例子)Max 10 u + 8 v + 11 x + 7 y + 5 zs.t. 3 u + 4 v + 6 x + 4 y + 3 z ≤ 14u, v, x, y, z are binary variablesOptimal LP relaxation solution (u, v, x, y, z) = (1, 1, 1, ¼, 0)Rounded solution (u, v, x, y, z) = (1, 1, 1, 0, 0) is integer feasible with obj. value 29•Simple rounding won’t work well, especially for models with equalities简单的取整不会很好，特别是具有等式约束的模型•Consider integer values on both sides 考虑两边的整数值•Rounding with propagating, fixing variables and tightening bounds取整时需传播变量固定和收紧界值•Gurobi has several different versions of rounding heuristics Gurobi有多种不同版本的取整启发式算法•Most Gurobi heuristics are LP based or need LP relaxation solutions 大多数Gurobi启发式算法都是基于LP或需要LP松弛解•LP relaxation solution is very important for heuristics to get high quality solutions!LP松弛解对于启发式算法获取高质量解非常重要！•Example 例子Min 3 u + 8 v + 3 w + 2 x + 7 y + 5 zs.t. 3 u + 4 v -4 w + 8 x + 4 y + 3 z ≤ 95 u + 2 v + 4 x + 7 y + 9 z = 15u, v, x, y, z are non negative integer variables, w is a binary variable•Zero-objective heuristic 去目标启发式•Remove the objective and solve it as a feasible problem 删除目标并将其为可行问题去解•Hope that presolve can have more reductions and the resulting presolved model is easier to solve 希望预预优化可以使模型变的更小，并且最终的预优化模型更容易解•For this example, the reformulated model is 对于这个例子，重新改建的模型是Min 0s.t. 3 u + 4 v -4 w + 8 x + 4 y + 3 z ≤ 95 u + 2 v + 4 x + 7 y + 9 z = 15u, v, x, y, z are non negative integer variables, w is a binary variable•Variables x and v are parallel, x can be fixed to 0•Variable w can be fixed to 1, which will only help the feasibility of the first constraint•Minimum relaxation heuristic 最小松弛启发式•For each inequality, add one penalty variable for the constraint violation 对于每个不等式，加一个违反约束的惩罚变量•For each equality, add two penalty variables for the two directions of the violation对于每个等式，加两个违反约束的惩罚变量, 两个方向各一个•Then minimize the sum of violations 然后对违约总和求最小化•If the optimal solution has the sum = 0, then we find a feasible solution; otherwise the original model is infeasible 如果最优总和为0, 那我们找到一个可行解; 否则原始模型是不可行的•For this example, the reformulated model is 对于这个例子，重新改建的模型是Min r + s + ts.t. 3 u + 4 v -4 w + 8 x + 4 y + 3 z -r ≤ 95 u + 2 v + 4 x + 7 y + 9 z + s -t = 15u, v, x, y, z are non negative integer variablesw is a binary variabler, s, t are non negative continuous variablesRINS•Relaxation induced neighborhood search(RINS) 松弛诱导邻域搜索•Given the incumbent (the best integer solution found so far) and the current fractional solution of the node relaxation 给定现任整数解和节点松弛的当前分数解•Fix a variable if its incumbent value and its relaxation value agrees 如果变量的整数解值和松弛解值一致，则固定变量•Solve the partially fixed model as a subMIP将部分固定的模型作为子MIP去解•It is an improvement heuristics 这是一种改进型的启发式算法•It is the our most effective heuristic 这是我们最有效的启发式算法SubMIP and Recursive Solve 子MIP和递归•Many Gurobi heuristics will 许多Gurobi启发式算法会•Have a target to fix some percentage of variables, say 80% 设一个目标来固定一定比例的变量，比如80％•Fix one variable and then propagate 固定一个变量然后传播•Repeat fixing and propagating until the target is reached or it becomes infeasible 重复固定和传播，直到达到目标或它变得不可行•Solve it as a subMIP将其为子MIP去解•In the subMIP, it will call the same heuristics, so recursively 在子MIP中,它将以递归方式调用相同的启发式算法•It often works well and finds feasible solutions quickly 它通常非常有效,可迅速找到可行解Feasibility Pump Heuristic泵式缩减启发式•Fischetti, Glover and Lodi, 2004•Solve the relaxation and round the solution解松弛问题并舍入到整数解•Replace the objective to minimize the distance to the rounded solution (quadratic)目标换成到舍入整数解距离最小(二次）•Use L1 norm (sum |xj –xj*|), where x* is the rounded solution (linear)使用L1范数(sum | xj-xj* |)，其中x *是取整解（线性）•If a binary variable xj = 0.3, then xj* = 0, then the objective part for xjis | xj–0| = xj, i.e. obj. coefficient is 1•If a binary variable xj= 0.7, then obj. coefficient will be -1•Solve the modified LP and repeat 解修改后的LP并重复•Until it hits some limit or the relaxation solution is integer feasible直到它达到一定限值或松弛解是整数可行的•Setting the limit to e.g. 10, i.e. solving the LP 10 times is expensive and it usually won’t be lucky例如将限值设为10,则需解LP10次, 很化时,通常很难运气好Pump Reduce泵式缩减•Motivated by feasibility pump heuristic 受泵式缩减启发式算法的启发•Observation 观察•Most models are dual degenerate, i.e. relaxation has alternative optimal solutions大多数模型对偶退化,即松弛问题有多个的最优解•Goal 目标• A relaxation solution with less fractional integer variables 有较少整数变量取分数值的松弛解•Possible zero fractional integer variables, but not the goal, so it isn’t heuristic 可能没有分数整数变量，但不是目标，所以它不是启发式的•Such relaxation solution helps heuristics and b&b significantly to find integer feasible solutions这样的松弛解很显著地帮助启发式和b＆b找到可行的整数解•Steps步骤•Solve the relaxation and fix all variables with nonzero reduced costs, making sure to stay in the optimal space 解松弛问题,固定非零递减成本的所有变量, 确保保持在最优空间•Round the relaxation solution, replace the objective with L1 norm distance to the rounded solution舍入松弛解,目标换成到舍入整数解距离最小(L1 范数)•Solve the modified LP, round and repeat解修改后的LP并重复•Until it hits some limit or the number of fractional integer variables doesn’t go down直到它达到一定限值或取分数值的整数变量的数量不下降GUROBI Heuristic Parameters Gurobi 启发式参数Heuristic Parameters 启发式参数•Main MIP parameter 主要MIP参数, MIPFocus•Main heuristic parameter 主要启发式参数, Heuristics•Individual heuristic parameters 个别启发式参数•Other parameters affecting feasible solutions 影响可行解的其他参数MIPFocus•Define high-level solution strategy 定义解高层策略•Default默认, balance between finding new feasible solutions and proving that the current solution is optimal. 在找新的可行解和证明最优性之间取得平衡•= 1, more interested in finding feasible solutions quickly 更注重找到可行解•= 2, more attention on proving optimality 更注重证明最优性•= 3, focus on the objective bound 更注重目标界值Heuristics•Main heuristic parameter主要启发式参数•The parameter value is roughly the fraction of time that we will spend on heuristics 参数值大致是我们在启发式上花费时间的部分值•Default value默认值= 0.05•> 0.05, more aggressive, 1 most aggressive•< 0.05, less aggressive, 0 no heuristicsIndividual heuristic parameters个别启发式参数•Pump reduce 泵式缩减(or degenerate simplex moves), Degenmoves •Feasibility pump heuristic泵式缩减启发式, PumpPasses•Improvement heuristic parameters改进型的启发式参数•ImproveStartGap•ImproveStartNodes•ImproveStartTime(warning: not deterministic)•Minimum relaxation heuristic最小松弛启发式, MinRelNodes•RINS heuristic RINS启发式, RINS•Zero objective heuristic去目标启发式, ZeroObjNodesOther Parameters Affecting Heuristics影响启发式的其他参数•Nodes explored by sub-MIP heuristics, SubMIPNodes•Branch direction preference, BranchDir•Setting the value to 1 may help MIP diving to find a feasible solution more quickly•Tuning criterion, TuneCriterion•= 2 objective value, i.e. focusing more on finding good feasible solutionsUser Input for GUROBI Heuristics 启发式的用户输入功能MIP Start / Multiple MIP Starts MIP起始值/多个MIP起始值•User can provide a MIP start or multiple MIP starts (new in 8.0) 用户可以提供一个或多个MIP起始值(多个为8.0的新功能）• A good MIP start, even a partial solution often can produce a good feasible solution instantly 良好的MIP起始值，即使是部分解，也可以立即产生好的可行解•Useful when you have multiple partial solutions 有多个部分解可能会很有用•MIP solver will try to complete them, and will store the ones it finds•For distributed MIP, MIP starts will be evaluated on different machines 对于分布式MIP，将在不同的机器上评估MIP起始值Variable Hints MIP提示•Provide hints to the solver about which variable should take which value 向优化器提示哪个变量应采用哪个值•Guides heuristics and branching 指导启发式和分支•VarHintVal attribute 属性•Specifies a value for a variable 指定变量的值•VarHintPri attribute 属性•Specifies a level of confidence in this particular variable value 指定此特定变量值的置信度•Comparison to MIP start 与MIP起始值比较•MIP start is used to provide an initial feasible solution to the solver MIP起始值用于为优化器提供初始可行解•Is evaluated prior to starting the solution process•Provides incumbent if feasible•Does not influence solution process if it is not feasible•Variable Hints guide the search 变量提示指导搜索•High quality hints should lead to a high quality solution quickly•Either through heuristics or through branching•Affects the whole solution processPartition Heuristic分区启发式算法•User-specified local improvement heuristic 用户指定的局部改进型启发式算法•RINS is our most effective heuristic RINS是我们最有效的启发式算法•It is a sub-MIP heuristic 这是一个子MIP启发式算法•Fix a subset of the variables to incumbent values 将变量的子集固定为现任整数解的值•Solve the resulting MIP (recursively) 解生成的MIP(递归）•Reoptimizes over just that portion of the problem•Sub-MIP heuristics extremely effective in general 子MIP启发式算法一般非常有效•How to choose the sub-problem to reoptimize? 如何选择子问题进行重新优化？•RINS chooses automatically RINS自动选择•This feature allows user to make the choice 此功能允许用户做出选择•Example sub-problems:•All decisions related to a single time period•All decisions related to a single machine•All decisions related to physical sub-regions (e.g., Western US, Eastern US, etc.)MIP Heuristic Callback 启发式回调•Motivations•Our MIP solver is mostly a black box solver 我们的MIP求解器主要是黑盒求解器•We try to recognize some common structures, but very limited•Users know the structure of their model 用户知道他们模型的结构•Relaxation solutions help heuristics a lot 松弛解对启发式算法很有帮助•Knowledge of problem structure and the relaxation solutions often mean fast good feasible solutions 对问题结构和松弛解的了解通常意味着快速找到可行解•Heuristic callback•At each node, Gurobi will call back 在每个节点，Gurobi都会回调•Users can query the relaxation solution and use it to guide their heuristics 用户可以查询松弛解并使用它来指导他们的启发式算法•Users can provide a full or partial solution vector to Gurobi through callback 用户可以通过回调向Gurobi 提供完整或部分解•If it is partial, Gurobi will try to complete it 如果它是部分的，Gurobi将尝试完成它What to do with too big/hard models 如何处理太大/太难的模型Too Big/Hard Models, Really?太大/太难的模型,真的吗？•“My model is too big or too hard, I have no choice but heuristic”, really? “我的模型太大或太难，我别无选择,只有启发式算法”,真的吗？•Old MIP experiences don’t count 旧的MIP经验不算数•At the end of 80’s and earlier 90’s, people in electrical power industry concluded that MIP was a nicetool, which couldn’t solve real unit commitment model•Close to 2000, people revisited MIP technology and people now solve the unit commitment modelroutinely•The similar stories happened more and more•I tried open source solvers, they are hopeless 我试过开源优化器，没有希望解我的问题•We have a lot of users, who send us their models, since the open solver they used couldn’t find afeasible solution in hours. Gurobi often solved the models in less than one second•All open source solvers are way behind the state of art commercial solvers•Gurobi users often solve their MIP models with millions of variables/constraints Gurobi用户经常解有数百万个变量/约束的MIP模型•Our customer model sets have a lot of such models, many of them we can solve or find good solutions within 10% MIPGap.Gurobi MIP Library 模型集(4538 models)1101001000100001000001000000100000001000000001E+09C o l u m n sMIP 速度不断提高, 主要版本每次提高几乎两倍0.000.501.001.502.002.503.00V e r s i o n -t o -V e r s i o n S p e e d u p•Have you tried to solve the relaxation? 你试过解松弛问题吗？•LP relaxation is polynomial-time solvable LP松弛问题是多项式时间可解的•Gurobi has solved LP models with 100M+ variables/constraints Gurobi解过许多超过几亿个变量/约束的LP模型•Relaxation solution is often very useful for heuristics松弛解对启发式算法很有帮助•The objective value of the relaxation solution provides the bound, without it, it is hard to know how gooda heuristic solution is 松弛解提供目标界值，没有它，很难知道启发式解有多好•Have you tried to reduce the models?你试过减小模型吗?•Aggregate汇总•Daily schedule -> weekly schedule日计划->周计划•Decompose big model into smaller pieces 将大模型分解为较小的部分•World -> America, Europe and Asia 世界->美洲,欧洲和亚洲•Local improvement 局部改进•Use heuristic to generate an initial solution 使用启发式算法生成初始解•Use MIP to reoptimize over a portion of the model, like RINS 使用MIP重新优化模型的一部分，如RINS •No lower bound, but often produces very high quality global solutions 没有下限，但通常会产生非常高质量的整体解•Successful stories to combine optimization and heuristics融合优化和启发式的成功案例•MIP based heuristics 基于MIP的启发式算法•Rolling horizon heuristics 滚动时段启发式算法•Relax integrality of future periods•May aggregate future time periods•Solve smaller LP/MIP•Air taxi and mining•Local search heuristics 局部搜索启发式算法•In group of periods, machines etc, solve smaller LP/MIP•Lenstra et al., local search in combinatorial optimization•Lin-Kernighan heuristic for TSP 货郎担问题的启发式算法•Solve relaxation and use reduced costs to guide•Etc.Always Try MIP总是试试MIPConclusion结论•Always try Gurobi, it should be better than pure heuristics 试试Gurobi，它应该比纯启发式更好!。

LINGO简介

LINGO简介（LINGO v11.0 Demo）美国芝加哥(Chicago)大学的Linus Schrage教授于1980年前后开发, 后来成立LINDO系统公司（LINDOSystems Inc. 公司网址：）.这套软件现在包括4种：1. What's Best!What's Best! lets you build linear, nonlinear, and integer models in Excel. Models are easy to build and understanding standard spreadsheet equations. Excel users can often begin building models within minutes of installing the What's Best! program, and the problem capacities of the larger What's Best! versions allow large scale, real world problems to be solved.2.LINGOLINGO is a comprehensive tool designed to help you build and solve linear, nonlinear, and integer optimization models quickly, easily, and efficiently. LINGO includes a powerful modeling language, a full-featured environment for building and editing problems, the ability to read and write to Excel and databases, and a set of fast built-in solvers.3.LINDO APIWith the LINDO API, you can easily create your own optimization applications. It allows you to plug the power of the LINDO solver right into customized applications that you have written.4.Classic LINDOClassic LINDO's simple interface and straightforward model expression style make it easy to learn and use. Classic LINDO is appropriate for building and solving moderately sized linear and integer models.这套软件取得了非常巨大的成功，据网站提供的信息：全球《财富》杂志500强企业中，一半以上使用上述产品，其中前25强企业中有23家使用上述产品。

精益生产LPPPT教学讲义

Shanghai ·Tianjin ·Shenzhen ·Guangzhou ·Hangzhou ·Suzhou ·Wuxi ·Changzhou ·Nantong ·Jinan ·Qingdao
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培训目标
能区别增值和非增值工作;
能描述七种浪费;
了解每个精益生产工具的好处与收益;
Shanghai ·Tianjin ·Shenzhen ·Guangzhou ·Hangzhou ·Suzhou ·Wuxi ·Changzhou ·Nantong ·Jinan ·Qingdao
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第二天内容
上午9:00~12:00 ▪ 招数8：看板 Kanban 下午2:00~6:00 ▪ 招数9：快速换型 SMED/Quick Changeover ▪ 招数10：制约管理 TOC-Theory of Constraints ▪ 精益生产总结篇Summary
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ＴＰＭ的定义1989
1. 以建立出追求生产系统效率化极限的企业体质为目标 2. 在现场现物所构筑的生产系统中,以全体生命周期为对象,追
求「零故障」、「零不良」、「零灾害」,防止所有损失于未然 3. 由生产部门开始,而后跨越开发、营业、管理等所有部门 4. 从高阶主管到第一线全员参加 5. 以重复小集团活动来达成零损失
Basis of Lean Production
Shanghai ·Tianjin ·Shenzhen ·Guangzhou ·Hangzhou ·Suzhou ·Wuxi ·Changzhou ·Nantong ·Jinan ·Qingdao
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生产的历史

造飞机模型的英语作文

造飞机模型的英语作文Title: Building an Airplane Model。

Building an airplane model is not merely a hobby; it's an intricate craft that demands patience, precision, and creativity. From selecting the right materials to mastering the art of assembly, constructing an airplane model is a journey that enthusiasts embark on with passion and dedication.To begin with, selecting the appropriate materials is crucial. The choice of materials can significantly impact the outcome of the model. Typically, balsa wood, plastic, and metal are the primary materials used in airplane model construction. Each material offers unique properties and challenges, thus requiring careful consideration. Balsa wood, for instance, is lightweight and easy to carve, making it ideal for crafting delicate components such as wings and fuselage. Plastic, on the other hand, offers versatility and durability, making it suitable forproducing intricate details and structural components. Lastly, metal components provide strength and stability, essential for supporting the model's overall structure.Once the materials are chosen, the construction process can commence. It often begins with meticulously studying the blueprints or reference images of the chosen aircraft model. Understanding the intricacies of the real aircraftis vital for accurately replicating its features in the model. From the curvature of the wings to the placement of the engines, attention to detail is paramount.Next comes the assembly phase, where precision is key. Every component must be cut, shaped, and assembled with utmost accuracy to ensure the model's integrity. This phase requires patience and steady hands as even the slightest error can affect the model's appearance and performance. Techniques such as sanding, gluing, and painting are employed to refine the model's finish and enhance its realism.As the model takes shape, creativity comes into play.Enthusiasts often personalize their models by adding custom details such as decals, insignias, and weathering effects. These touches not only enhance the model's aesthetic appeal but also imbue it with character and authenticity.Beyond the construction phase, displaying the finished model is a source of pride for enthusiasts. Whether showcased in a display case or suspended from the ceiling, the completed model serves as a testament to the builder's skill and passion for aviation.In conclusion, building an airplane model is a labor of love that requires a combination of technical expertise and artistic flair. From selecting the right materials to mastering intricate assembly techniques, every step of the process contributes to the creation of a masterpiece that celebrates the beauty of flight. So, if you're looking for a rewarding hobby that challenges your creativity and attention to detail, consider building an airplane model—it's an experience like no other.。

Problem description

This paper describes an analysis and visualization tool for assessing the insertability of cementless custom orthopaedic hip implants. The tool enables designers to determine if an implant can be inserted without interferences into a canal carved in the bone and simulate the interference-free insertion path before surgery. It allows designers to position and visualize complex, three-dimensional implant and canal shapes, compute interference-free insertion paths, and identify implant stuck con gurations and interfering surfaces. The tool validates implant designs and supports shape modi cation and redesign.
Preoperative Insertability Analysis and Visualization of Custom Hip Implant Designs
IBM T.J. Watson Research Center P.O. Box 704, Yorktown Heights, NY 10598, USA

天文台如何建造的英语作文

天文台如何建造的英语作文Building an observatory is no easy task. It requires careful planning, precise engineering, and a lot of hard work. First, a suitable location must be chosen, away from light pollution and with clear, unobstructed views of the sky. Once the location is secured, the foundation must be laid, ensuring stability and durability. Then comes the construction of the dome, which must be able to open and close smoothly to allow for observation. Finally, the telescope and other equipment must be installed, calibrated, and tested to ensure they function properly.The materials used in building an observatory arecrucial to its success. The dome, for example, must be made of a durable, weather-resistant material that can withstand the elements while providing a clear view of the sky. The telescope itself must be made of high-quality materials to ensure precision and accuracy in its observations. Additionally, the building materials used for the structure must be strong and reliable to ensure the observatory'slongevity.The construction of an observatory requires a team of skilled workers, including engineers, architects, and astronomers. Each member of the team plays a crucial rolein the design, construction, and operation of the observatory. Engineers are responsible for ensuring the structural integrity of the building, architects for the design and aesthetics, and astronomers for the placement and operation of the telescope and other equipment.The cost of building an observatory can vary greatly depending on the size, location, and complexity of the project. In addition to the initial construction costs, there are ongoing expenses for maintenance, equipment upgrades, and staffing. Securing funding for an observatory can be a challenge, but many observatories are funded through a combination of government grants, private donations, and educational institutions.In conclusion, building an observatory is a complex and challenging endeavor that requires careful planning,skilled labor, and adequate funding. However, the rewards of having a dedicated space for astronomical observation and research are well worth the effort. Observatories play a crucial role in advancing our understanding of the universe and inspiring future generations of astronomers.。

搭建塔台模型作文英语

搭建塔台模型作文英语Building a Tower Model。

Building a tower model can be an exciting and rewarding project, whether you're doing it for a school assignment, a hobby, or simply for the joy of creating something. In this essay, I'll guide you through the process of constructing a tower model step by step.1. Choose Your Design: The first step in building a tower model is deciding what type of tower you want to build. Towers come in various shapes and sizes, from medieval castles to modern skyscrapers. Consider your interests and the materials you have available when selecting a design.2. Gather Materials: Once you've chosen a design, gather all the materials you'll need for the project. This may include cardboard, wood, paper, glue, paint, and any other decorations or embellishments you want to add to yourmodel.3. Plan Your Construction: Before you start building,it's essential to plan out your construction process.Create a blueprint or sketch of your tower, including its dimensions and any intricate details you want to include. This will help you stay organized and ensure that yourmodel turns out the way you envision it.4. Start Building: With your materials and plan in hand, it's time to start building your tower model. Begin by constructing the base of the tower, using sturdy materials like cardboard or wood to provide stability. As you work your way up, remember to take your time and pay attentionto detail to ensure a high-quality finished product.5. Add Details: Once the basic structure of your toweris complete, it's time to add details and embellishments to bring your model to life. This could include windows, doors, battlements, and any other architectural features that are characteristic of your chosen design. Get creative anddon't be afraid to experiment with different materials andtechniques to achieve the desired effect.6. Paint and Decorate: After you've added all the necessary details, it's time to paint and decorate your tower model. Choose colors that complement your design and use paintbrushes or spray paint to apply an even coat to the entire structure. You can also add additional decorations like flags, banners, or landscaping around the base of the tower to enhance its visual appeal.7. Final Touches: Once the paint is dry, step back and admire your handiwork. Take this opportunity to make any final adjustments or touch-ups to your tower model to ensure that it meets your standards of perfection. This could include fixing any loose parts, smoothing out rough edges, or adding extra details to enhance its overall appearance.8. Display Your Model: Finally, find a prominent place to display your tower model where it can be admired by others. Whether it's on a shelf in your room, at a school exhibition, or as part of a larger diorama, showcasing yourcreation will allow you to share your creativity and hard work with the world.In conclusion, building a tower model is a fun and fulfilling project that allows you to unleash your creativity and attention to detail. By following these steps and putting in the time and effort, you can create a stunning replica of your chosen tower design that will impress and inspire others. So gather your materials, roll up your sleeves, and get ready to embark on a journey of construction and discovery!。

两个建筑的对比英语作文

两个建筑的对比英语作文Building A is modern and sleek, with clean lines and a minimalist design. It stands out in the city skyline, a symbol of progress and innovation.Building B, on the other hand, is old and traditional, with intricate details and a sense of history. It blends in with the surrounding architecture, a reminder of the past.The interior of Building A is spacious and bright, with high ceilings and large windows that let in plenty of natural light. It feels open and airy, perfect for a contemporary lifestyle.In contrast, the interior of Building B is cozy and intimate, with warm wood paneling and ornate decorations.It has a sense of charm and character that is hard to find in newer buildings.The materials used in Building A are cutting-edge andeco-friendly, reflecting a commitment to sustainability and efficiency. It is a showcase of modern technology and design.Building B, on the other hand, is built withtraditional materials like brick and stone, giving it a timeless quality that will never go out of style. It is a testament to the craftsmanship of the past.Overall, Building A represents the future, with its innovative design and sustainable features. It is a bold statement of progress and modernity.In contrast, Building B is a nod to the past, with its historic charm and traditional architecture. It is a reminder of where we come from and the values that have shaped us.。

高考英语二轮复习阅读理解生态环保类限时检测

语鹅市安置阳光实验学校阅读理解之生态环保类(共3篇，限时23分钟)A(2013·福建名校第一次质检)The “Give It Up for Earth Day” encourages people to commit themselves to giving up actions that are harmful to the environment, such as using poisonous cleaners.Throughout the month of April, Canadians are being asked to “Give It Up for Earth Day！” Earth Day has been celebrated every year on April 22 since 1970. Earth Day Canada's president Jed Goldberg says that as people become more environmentally aware, they want to find ways to reduce their environmental influence, not just celebrate one special event.“Earth Day is a great launching_pad for thinking about environmental action every day，” said Goldberg. “Choosing healthier options, even for the short term, can lead to thinking about the influence of our decisions for a lifetime.”That's the reason behind the “Give It Up for Earth Day” campaign. It's designed to encourage healthy habits that benefit people and the planet. It challenges everyone to help create a healthier world by making changes in their daily routine.“We wanted to plan an actiontargeted campaign that will give people a chance to act on their concern for the environment in a positive way，” said Goldberg.The campaign has identified four daily actions that can add up to huge environmental savings. They include pledging (保证) to turn off the TV, giving up the use of poisonous cleaners, reducing consumption of consumer products and cutting out meat.At the end of April, all of the pledges will be recorded and converted (转化)into the number of TV hours not watched, dollars not spent on unnecessary items, electricity saved, greenhouse gas emissions (排放) avoided by cutting out meat, and poisonous chemicals produced from homes and landfills.“What we're trying to achieve this year for Earth Day is to give people a chance to do something that is meaningful and measurable，” said Goldberg.语篇解读：4月22日是地球日，我们要在日常生活中进行改变，养成真正有益于地球、有益于人类的好习惯。

做模型飞船英语作文

做模型飞船英语作文Title: Building a Model Spaceship。

Building a model spaceship is not only a fascinating project but also an excellent opportunity to delve into the realms of creativity and imagination. From sketching out the design to assembling intricate components, every stepin the process contributes to a rewarding experience. In this essay, we will explore the steps involved in creating a model spaceship and the skills and knowledge gained along the way.To begin with, designing the model spaceship requires careful planning and attention to detail. It's essential to consider the shape, size, and functionality of the spaceship. Whether it's a sleek, futuristic design or a rugged, utilitarian vessel, the possibilities are endless. Sketching out rough drafts and brainstorming ideas can help in visualizing the final product.Once the design is finalized, the next step is gathering the necessary materials and components. This may include various types of plastic or metal sheets for the body, miniature engines and thrusters, LED lights for illumination, and other decorative elements. It's crucial to select high-quality materials that are easy to work with and durable enough to withstand the rigors of construction.With all the materials in hand, it's time to start assembling the model spaceship. This involves cutting and shaping the body components according to the design specifications, using tools such as hobby knives, scissors, and glue. Attention to detail is key during this phase to ensure that each part fits together seamlessly and accurately reflects the intended design.As the construction progresses, incorporatingelectronic components adds an extra layer of complexity and excitement to the project. Wiring the LED lights to simulate engine glow, installing miniature control panels, and adding sound effects can bring the model spaceship to life and enhance its realism. This phase requires patienceand precision to ensure that all the electronic systems function correctly.Throughout the construction process, problem-solving skills are continuously put to the test. From overcoming design flaws to troubleshooting technical issues, every challenge presents an opportunity to learn and grow. Collaborating with fellow enthusiasts and seeking advice from experienced model builders can provide invaluable insights and solutions.Finally, as the last pieces are put in place and the finishing touches applied, the sense of accomplishment is palpable. Seeing the model spaceship come together, reflecting hours of hard work and dedication, is truly rewarding. Whether displayed proudly on a shelf or used for imaginative play, the model spaceship serves as a testament to the power of creativity and ingenuity.In conclusion, building a model spaceship is afulfilling endeavor that offers countless opportunities for creativity, learning, and personal growth. From designingthe initial concept to assembling the final product, each step in the process contributes to a rich and rewarding experience. Whether undertaken as a solo project or as part of a group effort, the journey of building a model spaceship is sure to inspire wonder and excitement for enthusiasts of all ages.。

塔台模型制作作文英语

塔台模型制作作文英语Title: Construction of a Tower Model。

Building a tower model is an engaging and educational task that involves various steps and considerations. Inthis essay, we will delve into the process of constructing a tower model, discussing the materials required, the steps involved, and the educational benefits it offers.To begin with, let's outline the materials needed for constructing a tower model. Firstly, a sturdy base is essential to provide stability to the structure. This base can be made of materials like cardboard, wood, or foam board. Additionally, you will need materials for constructing the tower itself, such as popsicle sticks, toothpicks, or even spaghetti noodles, depending on the desired level of detail and complexity. Glue or adhesive is necessary for joining the components together securely. Finally, decorations such as paint, markers, or small embellishments can be used to enhance the aesthetic appealof the model.Now, let's move on to the steps involved in constructing the tower model. The first step is to plan the design and dimensions of the tower. Consider factors such as the height, width, and shape of the tower, as well as any architectural features you wish to incorporate. Once the design is finalized, proceed to assemble the base and attach any additional structural supports if needed.Next, begin constructing the tower itself by assembling the individual components. This may involve cutting, shaping, and gluing the materials together according to the chosen design. Pay close attention to detail and ensurethat each component fits together securely to form a stable structure. Depending on the complexity of the design, this step may require patience and precision to achieve the desired outcome.After the tower is assembled, allow sufficient time for the glue to dry and the structure to set firmly. Once the tower is stable, you can proceed to decorate it accordingto your preferences. This is where you can unleash your creativity and add personalized touches to the model. Whether it's painting intricate designs, adding texture with different materials, or incorporating miniature figurines, the possibilities are endless.Now that the tower model is complete, let's explore the educational benefits it offers. Building a tower model provides hands-on experience in various aspects of STEM (Science, Technology, Engineering, and Mathematics) education. It encourages problem-solving skills, spatial reasoning, and creativity as students navigate the challenges of design and construction. Additionally, constructing a tower model allows students to explore concepts such as structural stability, load-bearing capacity, and architectural principles in a tangible and engaging way.In conclusion, constructing a tower model is a rewarding and educational activity that offers valuable insights into the world of engineering and design. By following the steps outlined above and unleashing yourcreativity, you can build a tower model that is both visually impressive and intellectually stimulating. So, gather your materials, roll up your sleeves, and embark on the journey of building your very own tower model!。

做塔台模型作文英文

做塔台模型作文英文英文：Tower model is one of the most fascinating models that I have ever built. It requires precision and patience, but the result is always worth it. Building a tower model is like building a real tower, you have to make sure every piece is in the right place and everything is balanced.First, I started by researching tower models online and watching tutorial videos. Then I gathered all the necessary materials, including glue, scissors, and cardboard. I carefully cut out each piece and followed the instructions step by step. The most challenging part was assembling the tower's base, which required me to be very precise with the measurements.Once the base was complete, I moved on to the tower's body. I had to be very careful not to damage any of the pieces while assembling them. It was a bit like puttingtogether a puzzle, but with the added challenge of making sure everything was straight and secure.Finally, I added the finishing touches, such as painting and decorating the tower. I was very proud of the final result, and it looked great on my desk.Tower model building is not only a fun hobby, but it also teaches you valuable skills such as patience, precision, and attention to detail. It's a great way to challenge yourself and create something beautiful.中文：塔台模型是我曾经制作过的最迷人的模型之一。

我生活在这座城市作文英语

Living in a city can be a vibrant and enriching experience,offering a myriad of opportunities and conveniences that are often not found in rural areas.Heres an essay on the topic:Living in the City:A Symphony of LifeThe city,with its towering skyscrapers,bustling streets,and the constant hum of activity, is a place where millions call home.Its a place of contrasts,where the old and the new coexist,and where the quiet and the loud find their own rhythm.As a resident of this urban jungle,I have come to appreciate the unique charm and challenges that city living presents.The Pulse of ProgressOne of the most striking aspects of city life is the relentless pace of progress.The city is a hub of innovation,where new ideas and technologies are constantly being developed and implemented.This forward momentum is palpable,from the rapid construction of new buildings to the introduction of new public transportation systems.The city never sleeps, and neither do its inhabitants.The early morning rush hour,the latenight office lights, and the weekend hustle all contribute to the citys dynamic energy.Cultural MosaicThe city is a melting pot of cultures,where people from all walks of life come together. This diversity is one of the citys greatest strengths,offering a rich tapestry of experiences. From the ethnic neighborhoods with their unique cuisines and festivals to the art galleries and museums that showcase the work of local and international artists,the city is a treasure trove of cultural experiences.The citys cultural scene is everevolving,with new trends and movements emerging all the time.The Challenge of SpaceLiving in a city also means grappling with the challenge of limited space.Highrise apartments and condominiums are the norm,and personal space can sometimes feel like a luxury.However,this constraint also fosters a sense of community,as neighbors are often in close proximity.The citys parks and green spaces become essential oases,providing a muchneeded respite from the concrete jungle.The Hustle and BustleThe city is synonymous with the hustle and bustle of daily life.The streets are a constant stream of people,cars,and bicycles,each with their own destination.The citys public transportation system is a marvel of efficiency,connecting different parts of the city and allowing for easy movement.However,the citys congestion can also be a source of frustration,with traffic jams and crowded trains being a common sight.The Nightlife and EntertainmentThe city truly comes alive at night,with a vibrant nightlife scene that caters to all tastes. From the trendy bars and clubs to the intimate live music venues,the city offers a plethora of options for those looking to unwind after a long day.The citys entertainment options are just as diverse,with worldclass theaters,concert halls,and sports arenas hosting a range of events throughout the year.The Struggle and ResilienceDespite the many advantages of city living,there are also challenges that residents must face.The cost of living can be high,and the competition for jobs and resources can be fierce.However,the citys residents are a resilient lot,adapting to the everchanging urban landscape and finding ways to thrive in this fastpaced environment.ConclusionLiving in the city is a unique experience,one that is filled with both challenges and opportunities.It is a place where the past and the future collide,where dreams are made and broken,and where life is lived at a pace that is both exhilarating and exhausting.For me,the city is more than just a place to live it is a state of mind,a testament to the human spirits ability to adapt,innovate,and persevere.In conclusion,the city is a living,breathing entity that continues to evolve and grow.It is a place that demands much from its residents but also offers much in return.As a city dweller,I am constantly reminded of the importance of community,resilience,and the pursuit of progress.The city is a testament to the human spirits ability to create,adapt, and thrive in the most challenging of environments.。

高考试题解析第一部分选修七Module6

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2.“文化与传统”家族 ①tradition n. 传统 ②cultural adj. 文化的 ③custom n. 习惯；习俗 ④culture n. 文化；文明 ⑤civilization n. 文明；文化
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3.前缀en-动词面面观 ①enlarge 扩大，放大 ②encounter 遭遇 ③enchant 使着迷 ④enforce 实行，实施 ⑤entitle 给……定名 ⑥enclose 围绕
password of your email account. 3.Mankind has been trying every means to ___m__a_in_t_a_in___ (维持) the balance of nature. 4.We’ll go through the test of vocabulary while studying English.Try to ____e_n_la_r_g_e___ (扩
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3.recommend a good hotel 推荐一家好的旅馆 4.the evolution of the human species 人类的进化 5.the oldest inhabitant of the village 这个村最早的居民 6.a thorough knowledge of the subject 对这一学科的彻底了解 7.racial discrimination 种族歧视 8.primitive tribes 原始部落 9.undertake to finish the job 许诺完成这一工作 10.an endangered species 濒临绝种的生物 11.enlarge the vocabulary 扩大词汇量 12.waste precious time 浪费宝贵的时间

装配式建筑英语作文

装配式建筑英语作文1. Assembling buildings is like playing with giant Lego blocks, except these blocks are made of steel, glass, and concrete.2. The beauty of modular construction lies in its efficiency and speed. It's like watching a puzzle come together right before your eyes.3. Each piece is carefully crafted off-site, then brought together on-site to create a seamless and sturdy structure.4. The precision and accuracy required in assembling these buildings is truly impressive. It's like watching a well-choreographed dance of construction workers and machinery.5. The end result is a modern marvel of architecture, with clean lines and innovative design that stands out inany city skyline.6. Assembling buildings in this way not only saves time and money, but also reduces waste and environmental impact. It's a win-win for everyone involved.7. Witnessing the transformation from a pile of pieces to a fully functional building is a testament to human ingenuity and creativity. It's a reminder of what we can achieve when we work together towards a common goal.8. In the end, assembling buildings is not just about putting together physical structures, but also about building communities and shaping the future of our cities. It's a process that embodies progress and innovation in every sense of the word.。

制作太空船模型英语作文

制作太空船模型英语作文Building a Spaceship ModelBuilding a spaceship model can be an engaging and rewarding experience for both kids and adults alike. Whether you are a space enthusiast, a scifi lover, or simply enjoy working with your hands, creating a miniature version of a spacecraft can be a fun and exciting project.To start off, you will need some basic materials such as modeling clay, cardboard, paint, glue, and any other decorations you may want to add to your spaceship. It's also helpful to have reference images or drawings of different spaceship designs to inspire your creation.The first step is to decide on the size and design of your spaceship model. You can choose to recreate a famous spaceship from a movie or TV show, or you can let your imagination run wild and come up with your own unique design. Once you have a clear idea of what you want to build, you can start shaping the body of the spaceship using modeling clay or cardboard.Next, you can add details to your spaceship model such as wings, engines, windows, and other features that will make it look more realistic. Make sure to take your time and pay attention to small details to make your spaceship model as accurate as possible.Once the basic structure of your spaceship model is complete, you can start painting and decorating it to bring it to life. Choose colors that complement each other and add decals or stickers to give your spaceship that final touch of authenticity.Building a spaceship model is not only a fun and creative activity, but it can also help improve your fine motor skills and attention to detail. So, gather your materials, let your imagination soar, and start building your very own spaceship model today!。

Building excitement

Building excitementCan China avoid a bubble?THE property m arket illustrates the growing divergence between rich-world andem erging economies. In most developed countries (with a few exceptions, such as Australia and Canada) governments are trying to breathe life into property. In developing ones they are trying to cool things down. In the West the question is when prices will stop falling. In the East it is whether they will stop rising.For m any institutional investors, em erging markets, however buoyant, are not worth taking big bets on. Thanks to the bust, the rich world offers high-quality properties in liquid markets at lowish prices. The developing countries are a riskier development prospect, with new hom es, offices and m alls being built at speed to cope with fast-rising demand.That dem and is undoubtedly enormous. Brazil is thought to be short of som e 8m hom es; the whole of India has fewer hotel rooms than Las Vegas; in Saudi Arabia a long-awaited m ortgage law is expected to kickstart a residential boom. Yet the pitfalls are also cavernous. Legal issues are one source of uncertainty. Investors com plain that China’s system is capricious, for instance. “China will be one of the biggest property m arkets in the world in five years’ time,” says one big fund manager. “But if you put millions into a building in China and sell it, it is not clear that you will be able to take your money out.” Retail lenders express similar misgivings about the process for repossessing homes in developing m arkets.The biggest worry of all is the rush of new supply. The pace of developm ent is often frantic, nowhere m ore so than in China. According to Barclays Capital, m ore than 40% of the skyscrapers due for completion in the next six years will be in China, increasing the number of tall buildings in Chinese cities by m ore than half. Landscapes are changing in a m atter of days. One of the more hypnotic item s on YouTube is a tim e-lapse video of a 15-storey prefabricated hotel in Changsha being put up in just six days. “The rang e of outcom es in London and New York is pretty limited,” says one investor. “In Shenzhen you can be building a block of apart m ents with four others going up alongside.”One way to m anage the risk of oversupply is to take capital out of em erging m arkets as quickly as possible. ING’s real-estate asset-m anagem ent arm (soon to be part of CBRE) works with local firms to build flats and homes for sale in markets such as China, enabling it to realise profits in two or three years. Another is to go for the less crowded parts of the m arket. Mr White of CBRE thinks that the logistics sector is one of the m ore promising avenues for foreign investors, in part because the m arket is dominated by a handful of global firms based in America. Shopping centres are another area where foreigners still have an edge over locals.But m any investors who have raised funds for deployment in emerging m arkets will have trouble finding a hom e for their money. One reason is that these m arkets are thin: there is very little buying and selling of existing properties. Another iscom petition from locals. Mainland Chinese developers are wildly optimistic because they have seen values rise, says David Ellis of Mayer Brown JSM, a law firm. “They are using a different spreadsheet.”All this helps explain why many people are nervous about the state of the Chinese property m arket in general, and the residential part of it in particular. High-profile hedge-fund managers such as Jim Chanos give warning (self-servingly) of a property crash even worse than Dubai’s. In January three of the ten biggest short positions in Hong Kong-listed m ainland companies were held in property firms. Nationally, incom es in China have largely kept pace with rising prices (see chart 7), but an IMF report in Decem ber said that in som e big cities prices “appear to be increasingly disconnected from fundamentals”.Rationing the air supplyThe Chinese government has unveiled a series of m easures since April 2010 to mute house-price inflation. They include raising the minimum downpayment for first-tim e buyers to 30% of a home’s value, up from 20% before, and a stop on m ortgages for people buying a third or subsequent home. These m easures have had som e success. The year-on-year price rise has slowed down: in Decem ber it was 6.4%, not that much higher than the overall inflation rate.Even so, the m arket continues to look extremely buoyant on many measures. Total property loans outstanding last year rose by 27.5%, which at least was slower than in 2009. Policym akers lean towards further tightening. A property tax was announced in Shanghai and Chongqing at the start of this year, causing a rush to seal deals before it takes effect. Transactions in Shanghai in the first half of January reportedly jumped by more than a third year-on-year, according to local estate agents. Wen Jiabao, China’s prime minister, has said he wants to see the residential market return to a “reasonable level” before his term of office ends in 2013.As well as dampening down demand, the Chinese have been trying to increase supply. That m ay seem counterintuitive in a country with a home-ownership rate of about 80%. But that startlingly high rate was the result of a huge, one-off transfer of government housing to private ownership in the late 1990s. Much of it is dilapidated and most people want to m ove out and up. “There is pent-up dem and that has been building for 50 years,” says Michael Klibaner of JLL in Shanghai.The problem for the average buyer is that prices have been driven higher not just by other would-be hom eowners but by a com plex chain of speculative activities that reaches right back to another arm of China’s government, the local authorities. Land sales are a big source of revenue for local governments, and by draftingdevelopment plans for the land the government can hike its value several times over.Until recently, local governments would sell this land to developers for very little upfront. A firm could buy land worth 5 billion yuan with just 500m yuan ($75.9m) in working capital, says Jinsong Du of Credit Suisse. Even better, the developer could then offer that land as collateral for a loan of, say, 2.5 billion yuan from a bank. And instead of ploughing those borrowed billions into developing the site, they could use it to buy m ore land. Developers were not too worried about generating cash flow, because in a pinch they assum ed they could always sell the land at a profit or flog as-yet-unbuilt flats to eager buyers on the back of blueprints alone.The viability of this model depends on ever-growing demand, which often com es from speculative investors looking for a chance of quick capital gains. Some are wealthy private individuals; many are enterprises that have been diverting money from capital invest m ent, hoping for juicier returns from property.All of this is a big headache for the central government, which is aiming to keep property affordable for the m asses. A huge social-housing programme will eventually bring lots of cheaper housing on stream. In t he m eantime the government is trying to draw the air out of the speculative part of the m arket (by restricting mortgages taken out for invest m ent purposes, and by banning many state-owned enterprises from buying land) and to put developers under pressure t o build and release properties quickly. Banks now have to put m oney into an escrow account instead of lending directly to developers. The cash is paid out when construction reaches certain milestones. Downpayments from developers to local governments have shot up, too, and now total 60-70% of the land’s value. That stretches developers’ balance-sheets, encouraging them to drop prices.Carpeted landingThe slowdown in property-price rises suggests that these policies are having some effect. But the upward pressure is still immense. To get round the new rules, som e mainland developers are reportedly borrowing m oney offshore and dressing it up as equity when it com es onshore. The restrictions are not always properlyimplem ented, particularly in smaller cities. A 2009 law allowed mainland insurers to invest another wall of m oney in property for the first tim e. Individual savers keep an enormous am ount of cash in low-yielding bank deposits and have relatively few invest m ent options, which increases the appeal of property—as does rising inflation.Nonetheless, in two critical respects, com parisons between China and places such as Dubai are misplaced. One is underlying growth in demand. Some places in China may well be getting ahead of them selves: for example, it is not clear whether so many industrial cities really need a brand new central business district. If prices were to turn, the am ount of vacant property being held as invest m ent would m ake a wave of forced selling more likely. But China, with urbanisation and incom e growthon a m assive scale, is clearly different from Dubai’s model of “build it and they will com e.”There are better parallels in the Middle East. Emile Habib of GulfRelated, a property-developm ent joint venture in the region, says Dubai is saturated and the best prospects are plac es with lots of internal demand like Saudi Arabia.The second difference is the am ount of leverage in the system. The IMF reckons that loans to developers and mortgages accounted for under 20% of total outstanding loans in late 2009, com pared with 52% in Hong Kong and 57% in America. Again, nobody should draw too m uch com fort from this. In a cash-driven m arket, liquidity can flow out of the sector quickly; mortgage debt is rising fast from a low base; and a property bust could spill over into other fields t o which banks have lots of exposure. But as Western policym akers would now wearily agree, less debt m eans less systemic risk for the banks if and when the property cycle turns.。

高三练习题制作潜艇模型英语作文

高三练习题制作潜艇模型英语作文Creating a Submarine Model: A High School Senior Practice ExerciseAs high school seniors, we are often tasked with engaging in diverse activities that not only enhance our academic knowledge but also develop our practical skills. Among the many projects that we have undertaken, one that stands out is the construction of a submarine model. This exercise not only tested our understanding of engineering principles but also required precision, attention to detail, and creativity.The process of building a submarine model started with research. We delved into the history of submarines, their designs, and the science behind their functionality. Understanding the intricacies of how submarines operate was crucial in ensuring the accuracy of our model. We learned about ballast tanks, propulsion systems, and the structural components that make up a submarine.Once we had a solid foundation of knowledge, we began the handson aspect of the project. This involved planning the design of our model, selecting appropriate materials, and meticulously crafting each component. From the outer hull to the propeller, every detail had to be carefully considered and accurately represented. This process not only honed our technical skills but also fostered teamwork and collaboration among classmates.The construction phase was both challenging and rewarding. We encountered setbacks and obstacles along the way, but overcoming them through perseverance and creative problemsolving was a valuable learning experience. Whether it was figuring out the best way to waterproof the hull or ensuring the stability of the model in water, each step required careful thought and precision.As we neared the completion of our submarine model, we focused on adding the finishing touches that would bring our creation to life. Painting, detailing, and finetuning the model were tasks that required patience and attention to detail. Seeing the culmination of our efforts take shape before our eyes was immensely satisfying and instilled in us a sense of accomplishment.Finally, the moment arrived when we were able to test our submarine model in water. Watching it glide gracefully beneath the surface, propelled by our own hands, was a moment of pride and joy. Not only had we successfully built a functional submarine model, but we had also developed a deeper appreciation for the science and engineering behind submarines.In conclusion, the experience of creating a submarine model as a high school senior practice exercise was both challenging and enriching. It tested our knowledge, skills, and creativity while fostering teamwork and problemsolving abilities. As we move forward in our academic and professional journeys, thelessons learned from this project will undoubtedly serve us well, equipping us with the skills and mindset needed to tackle future challenges.。