坐标系中三角形面积的求法模型例谈

为帮助初中学生有效地解决涉及＂已知三角形顶点坐标,求其面积＂的各种问题,构建解决此类问题的如下求法模型及其解题策略：奠基法、割补法、铅垂高法、矩形框法、梯形框法、坐标公式法等,以求提高此类问题的教学效益.

Perturbed Solving Method for Interdecadal Sea-air Oscillator Model

A coupled system of the interdecadal sea-air oscillator model is studied. The E1 Nifio-southem oscillation （ENSO） atmospheric physics oscillation is an abnormal phenomenon involved in the tropical Pacific ocean-atmosphere interactions. The oscillator model is involved with the variations of both the eastern and western Pacific anomaly pat- terns. This paper proposes an ENSO atmospheric physics model using a method of the perturbation theory. The aim is to create an asymptotic solving method for the ENSO model. Employing the perturbed method, the asymptotic solution of corresponding problem is obtained, and the asymptotic behaviour of the solution is studied. Thus we can obtain the prognoses of the sea surface temperature anomaly and related physical quantities.

A GA approach to vehicle routing problem with time windows considering loading constraints

As a new variant of vehicle routing problem( VRP),a finished vehicle routing problem with time windows in finished vehicle logistics( FVRPTW) is modeled and solved. An optimization model for FVRPTW is presented with the objective of scheduling multiple transport routes considering loading constraints along with time penalty function to minimize the total cost. Then a genetic algorithm( GA) is developed. The specific encoding and genetic operators for FVRPTW are devised.Especially,in order to accelerate its convergence,an improved termination condition is given. Finally,a case study is used to evaluate the effectiveness of the proposed algorithm and a series of experiments are conducted over a set of finished vehicle routing problems. The results demonstrate that the proposed approach has superior performance and satisfies users in practice. Contributions of the study are the modeling and solving of a complex FVRPTW in logistics industry.

Model and algorithm of optimizing alternate traffic restriction scheme in urban traffic network

An optimization model and its solution algorithm for alternate traffic restriction(ATR) schemes were introduced in terms of both the restriction districts and the proportion of restricted automobiles. A bi-level programming model was proposed to model the ATR scheme optimization problem by aiming at consumer surplus maximization and overload flow minimization at the upper-level model. At the lower-level model, elastic demand, mode choice and multi-class user equilibrium assignment were synthetically optimized. A genetic algorithm involving prolonging codes was constructed, demonstrating high computing efficiency in that it dynamically includes newly-appearing overload links in the codes so as to reduce the subsequent searching range. Moreover,practical processing approaches were suggested, which may improve the operability of the model-based solutions.

Performance Prediction of Structured Packing Column for Cryogenic Air Separation with Hybrid Model

A detailed investigation of a thermodynamic process in a structured packing distillation column is of great impor- tance in prediction of process efficiency. In order to keep the simplicity of an equilibrium stage model and the accu- racy of a non-equilibrium stage model, a hybrid model is developed to predict the structured packing column in cryogenic air separation. A general solution process for the equilibrium stage model is developed to solve the set of equations of the hybrid model, in which a separation efficiency function is introduced to obtain the resulting tri-diagonal matrix and its solution by the Thomas algorithm. As an example, the algorithm is applied to analyze an upper column of a cryogenic air separation plant with the capacity of 17000 m3·h-1. Rigorous simulations are conducted using Aspen RATEFRAC module to validate the approach. The temperature and composition distributions are in a good agreement with the two methods. The effects of inlet/outlet position and flow rate on the temperature and composition distributions in the column are analyzed. The results demonstrate that the hybrid model and the solution algorithms are effective in analvzin~ the distillation process for a a cryogenic structured packing column.

Parallel solving model for quantified boolean formula based on machine learning

A new parallel architecture for quantified boolean formula(QBF)solving was proposed,and the prediction model based on machine learning technology was proposed for how sharing knowledge affects the solving performance in QBF parallel solving system,and the experimental evaluation scheme was also designed.It shows that the characterization factor of clause and cube influence the solving performance markedly in our experiment.At the same time,the heuristic machine learning algorithm was applied,support vector machine was chosen to predict the performance of QBF parallel solving system based on clause sharing and cube sharing.The relative error of accuracy for prediction can be controlled in a reasonable range of 20%30%.The results show the important and complex role that knowledge sharing plays in any modern parallel solver.It shows that the parallel solver with machine learning reduces the quantity of knowledge sharing about 30%and saving computational resource but does not reduce the performance of solving system.

A scenario relaxation algorithm for finite scenario based robust assembly line balancing

A balancing problem for a mixed model assembly line with uncertain task processmg Ume anO daily model mixed changes is considered, and the objective is to minimize the work variances between stations in the line. For the balancing problem for the scenario-based robust assembly line with a finitely large number of potential scenarios, the direct solution methodology considering all potential scenarios is quite time-consuming. A scenario relaxation algorithm that embeds genetic al- gorithm is developed. This new algorithm guarantees termination at an optimal robust solution with relatively short running time, and makes it possible to solve robust problems with large quantities of potential scenarios. Extensive computational results are reported to show the efficiency and effectiveness of the proposed algorithm.

Reinforcement Learning Algorithm for Solving Load Commitment Problem Considering a General Load Model

Under the smart grid paradigm, in the near future all consumers will be exposed to variable pricing schemes introduced by utilities. Hence, there is a need to develop algorithms which could be used by the consumers to schedule their loads. In this paper, load scheduling problem is formulated as a LCP （load commitment problem）. The load model is general and can model atomic and non-atomic loads. Furthermore, it can also take into consideration the relative discomfort caused by delay in scheduling any load. For this purpose, a single parameter ＂uric＂ is introduced in the load model which captures the relative discomfort caused by delay in scheduling a particular load. Guidelines for choosing this parameter are given. All the other parameters of the proposed load model can be easily specified by the consumer. The paper shows that the general LCP can be viewed as multi-stage decision making problem or a MDP （Markov decision problem）. RL （reinforcement learning） based algorithm is developed to solve this problem. The efficacy of the algorithm is investigated when the price of electricity is available in advance as well as for the case when it is random. The scalability of the approach is also investigated.

Model and Algorithm of Transportation Problem on Network

Transportation problem on network needs to determine the freight quantity and the transportation route between supply point and demand point. Therefore, taken the uncertainty of freight supply and demand into account, a collaborative optimization model is formulated with transportation capacity constraint. In addition, a two-stage genetic algorithm （GA） is put forward. Herein, the first stage of this GA is adopted a priority-based encoding method for determining the supply and demand relationship between different points. Then supply and demand relationship which the supply and the demand are both greater than zero is a minimum cost flow （MCF） problem on network in the second stage. Aim at the purpose to solve MCF problem, a GA is employed. Moreover, this algorithm is suitable for balance and unbalance transportation on directed network or undirected network. At last, the model and algorithm are verified to be efficient by a numerical example.