优化题组设计 促进深度学习

教学实践表明,优化的题组有助于学生对知识的理解、掌握和运用,常能收到事半功倍、精彩纷呈的课堂教学效果。教师抓住教学重点、难点、易混易错点及知识拓展等关键节点,优化题组设计,能有效促进学生深度学习,提高教学实效。

利用学案制教学模式,探索数学高效课堂——以高考复习《数形结合在高考中的应用》为例

数与形的结合,使抽象思维与形象思维结合起来,实现概念与形象、表象与联系的转化,化难为易,是数学解题的重要思想方法之一.新高考之下,为了学生能够更加合理有效地学习数学,打破"低效沉闷"的复习模式,采用学案制教学模式,结合高三第一轮复习内容及学生认知水平现状,通过几组逐级提升的题目和变式问题的设计,将相关知识要点与相应配套练习融合,从而促进学生原有知识水平的新提升.以高考复习中的《数形结合在高考中的应用》为例,具体阐述如何运用学案制教学模式激活高三复习课堂,提高复习效率.

ADAPTIVE GENETIC ALGORITHM BASED ON SIX FUZZY LOGIC CONTROLLERS

The performance of genetic algorithm(GA) is determined by the capability of search and optimization for satisfactory solutions. The new adaptive genetic algorithm(AGA) is built for inducing suitable search and optimization relationship. The use of six fuzzy logic controllers(6FLCs) is proposed for dynamic control genetic operating parameters of a symbolic-coded GA. This paper uses AGA based on 6FLCs to deal with the travelling salesman problem (TSP). Experimental results show that AGA based on 6FLCs is more efficient than a standard GA in solving combinatorial optimization problems similar to TSP.

Hopfield neural network based on ant system

Hopfield neural network is a single layer feedforward neural network. Hopfield network requires some control parameters to be carefully selected, else the network is apt to converge to local minimum. An ant system is a nature inspired meta heuristic algorithm. It has been applied to several combinatorial optimization problems such as Traveling Salesman Problem, Scheduling Problems, etc. This paper will show an ant system may be used in tuning the network control parameters by a group of cooperated ants. The major advantage of this network is to adjust the network parameters automatically, avoiding a blind search for the set of control parameters. This network was tested on two TSP problems, 5 cities and 10 cities. The results have shown an obvious improvement.

A novel hybrid algorithm based on a harmony search and artificial bee colony for solving a portfolio optimization problem using a mean-semi variance approach

Portfolio selection is one of the major capital allocation and budgeting issues in financial management, and a variety of models have been presented for optimal selection. Semi-variance is usually considered as a risk factor in drawing up an efficient frontier and the optimal portfolio. Since semi-variance offers a better estimation of the actual risk portfolio, it was used as a measure to approximate the risk of investment in this work. The optimal portfolio selection is one of the non-deterministic polynomial(NP)-hard problems that have not been presented in an exact algorithm, which can solve this problem in a polynomial time. Meta-heuristic algorithms are usually used to solve such problems. A novel hybrid harmony search and artificial bee colony algorithm and its application were introduced in order to draw efficient frontier portfolios. Computational results show that this algorithm is more successful than the harmony search method and genetic algorithm. In addition, it is more accurate in finding optimal solutions at all levels of risk and return.

Joint Resource Allocation Using Evolutionary Algorithms in Heterogeneous Mobile Cloud Computing Networks

The problem of joint radio and cloud resources allocation is studied for heterogeneous mobile cloud computing networks. The objective of the proposed joint resource allocation schemes is to maximize the total utility of users as well as satisfy the required quality of service(QoS) such as the end-to-end response latency experienced by each user. We formulate the problem of joint resource allocation as a combinatorial optimization problem. Three evolutionary approaches are considered to solve the problem: genetic algorithm(GA), ant colony optimization with genetic algorithm(ACO-GA), and quantum genetic algorithm(QGA). To decrease the time complexity, we propose a mapping process between the resource allocation matrix and the chromosome of GA, ACO-GA, and QGA, search the available radio and cloud resource pairs based on the resource availability matrixes for ACOGA, and encode the difference value between the allocated resources and the minimum resource requirement for QGA. Extensive simulation results show that our proposed methods greatly outperform the existing algorithms in terms of running time, the accuracy of final results, the total utility, resource utilization and the end-to-end response latency guaranteeing.

Membrane-inspired quantum bee colony optimization and its applications for decision engine

In order to effectively solve combinatorial optimization problems,a membrane-inspired quantum bee colony optimization(MQBCO)is proposed for scientific computing and engineering applications.The proposed MQBCO algorithm applies the membrane computing theory to quantum bee colony optimization(QBCO),which is an effective discrete optimization algorithm.The global convergence performance of MQBCO is proved by Markov theory,and the validity of MQBCO is verified by testing the classical benchmark functions.Then the proposed MQBCO algorithm is used to solve decision engine problems of cognitive radio system.By hybridizing the QBCO and membrane computing theory,the quantum state and observation state of the quantum bees can be well evolved within the membrane structure.Simulation results for cognitive radio system show that the proposed decision engine method is superior to the traditional intelligent decision engine algorithms in terms of convergence,precision and stability.Simulation experiments under different communication scenarios illustrate that the balance between three objective functions and the adapted parameter configuration is consistent with the weights of three normalized objective functions.

Optimizing bus services with variable directional and temporal demand using genetic algorithm

As a major mode choice of commuters for daily travel, bus transit plays an important role in many urban and metropolitan areas. This work proposes a mathematical model to optimize bus service by minimizing total cost and considering a temporally and directionally variable demand. An integrated bus service, consisting of all-stop and stop-skipping services is proposed and optimized subject to directional frequency conservation, capacity and operable fleet size constraints. Since the research problem is a combinatorial optimization problem, a genetic algorithm is developed to search for the optimal result in a large solution space. The model was successfully implemented on a bus transit route in the City of Chengdu, China, and the optimal solution was proved to be better than the original operation in terms of total cost. The sensitivity of model parameters to some key attributes/variables is analyzed and discussed to explore further the potential of accruing additional benefits or avoiding some of the drawbacks of stop-skipping services.

Solving material distribution routing problem in mixed manufacturing systems with a hybrid multi-objective evolutionary algorithm

The material distribution routing problem in the manufacturing system is a complex combinatorial optimization problem and its main task is to deliver materials to the working stations with low cost and high efficiency. A multi-objective model was presented for the material distribution routing problem in mixed manufacturing systems, and it was solved by a hybrid multi-objective evolutionary algorithm (HMOEA). The characteristics of the HMOEA are as follows: 1) A route pool is employed to preserve the best routes for the population initiation; 2) A specialized best?worst route crossover (BWRC) mode is designed to perform the crossover operators for selecting the best route from Chromosomes 1 to exchange with the worst one in Chromosomes 2, so that the better genes are inherited to the offspring; 3) A route swap mode is used to perform the mutation for improving the convergence speed and preserving the better gene; 4) Local heuristics search methods are applied in this algorithm. Computational study of a practical case shows that the proposed algorithm can decrease the total travel distance by 51.66%, enhance the average vehicle load rate by 37.85%, cut down 15 routes and reduce a deliver vehicle. The convergence speed of HMOEA is faster than that of famous NSGA-II.

A novel hybrid estimation of distribution algorithm for solving hybrid flowshop scheduling problem with unrelated parallel machine

The hybrid flow shop scheduling problem with unrelated parallel machine is a typical NP-hard combinatorial optimization problem, and it exists widely in chemical, manufacturing and pharmaceutical industry. In this work, a novel mathematic model for the hybrid flow shop scheduling problem with unrelated parallel machine(HFSPUPM) was proposed. Additionally, an effective hybrid estimation of distribution algorithm was proposed to solve the HFSPUPM, taking advantage of the features in the mathematic model. In the optimization algorithm, a new individual representation method was adopted. The(EDA) structure was used for global search while the teaching learning based optimization(TLBO) strategy was used for local search. Based on the structure of the HFSPUPM, this work presents a series of discrete operations. Simulation results show the effectiveness of the proposed hybrid algorithm compared with other algorithms.

ANALYSIS OF AFFECTIVE ECG SIGNALS TOWARD EMOTION RECOGNITION

Recently,as recognizing emotion has been one of the hallmarks of affective computing,more attention has been paid to physiological signals for emotion recognition.This paper presented an approach to emotion recognition using ElectroCardioGraphy(ECG) signals from multiple subjects.To collect reliable affective ECG data,we applied an arousal method by movie clips to make subjects experience specific emotions without external interference.Through precise location of P-QRS-T wave by continuous wavelet transform,an amount of ECG features was extracted sufficiently.Since feature selection is a combination optimization problem,Improved Binary Particle Swarm Optimization(IBPSO) based on neighborhood search was applied to search out effective features to improve classification results of emotion states with the help of fisher or K-Nearest Neighbor(KNN) classifier.In the experiment,it is shown that the approach is successful and the effective features got from ECG signals can express emotion states excellently.

MODS： A Novel Metaheuristic of Deterministic Swapping for the Multi-Objective Optimization of Combinatorials Problems

This paper states a new metaheuristic based on Deterministic Finite Automata （DFA） for the multi - objective optimization of combinatorial problems. First, a new DFA named Multi - Objective Deterministic Finite Automata （MDFA） is defined. MDFA allows the representation of the feasible solutions space of combinatorial problems. Second, it is defined and implemented a metaheuritic based on MDFA theory. It is named Metaheuristic of Deterministic Swapping （MODS）. MODS is a local search strategy that works using a MDFA. Due to this, MODS never take into account unfeasible solutions. Hence, it is not necessary to verify the problem constraints for a new solution found. Lastly, MODS is tested using well know instances of the Bi-Objective Traveling Salesman Problem （TSP） from TSPLIB. Its results were compared with eight Ant Colony inspired algorithms and two Genetic algorithms taken from the specialized literature. The comparison was made using metrics such as Spacing, Generational Distance, Inverse Generational Distance and No-Dominated Generation Vectors. In every case, the MODS results on the metrics were always better and in some of those cases, the superiority was 100%.

A Water Line Network Failure Application of Network Design Problems

This study investigated a water supply recovery problem involving municipal water service piping. The problem consisted in recovering full service after network failure, in order to rapidly satisfy all urgent citywide demands. The optimal recovery solution was achieved through the application of so-called network design problems （NDPs）, which are a form of combinatorial optimization problem. However, a conventional NDP is not suitable for addressing urgent situations because （1） it does not utilize the non-failure arcs in the network, and （2） it is solely concerned with stable costs such as flow costs. Therefore, to adapt the technique to such urgent situations, the conventional NDP is here modified to deal with the specified water supply problem. In addition, a numerical illustration using the Sendai water network is presented.

Genetic approach for Cell-by-Cell dynamic spectrum allocation in the heterogeneous scenario

In this paper,a genetic algorithm (GA) is investigated to deal with cell-by-cell dynamic spectrumallocation (DSA) in the heterogeneous scenario with temporal and spatial traffic demand changes,whichis also known as a difficult combinatorial optimization problem.A new two-dimensional chromosome encodingscheme is defined according to characteristics of the heterogeneous scenario,which prevents forminginvalid solutions during the genetic operation and enables much faster convergence.A novel randomcoloring gene generation function is presented which is the basic operation for initialization and mutationin the genetic algorithm.Simulative comparison demonstrates that the proposed GA-based cell-by-cellDSA outperforms the conventional contiguous DSA scheme both in terms of spectral efficiency gain andquality of service (QoS) satisfaction.

The P-Median Problem： A Tabu Search Approximation Proposal Applied to Districts

P-median is one of the most important Location-Allocation problems. This problem determines the location of facilities and assigns demand points to them. The p-median problem can be established as a discrete problem in graph terms as： Let G = （V, E） be an undirected graph where V is the set of n vertices and E is the set of edges with an associated weight that can be the distance between the vertices dij= d（vi, Vj） for every i, j =1,...,n in accordance to the determined metric, with the distances a symmetric matrix is formed, finding Vp∈ V such that ｜ Vp｜∈ = p, where p can be either variable or fixed, and the sum of the shortest distances from the vertices in {V-Vp} to their closet vertex in Vp is reduced to the minimum. Under these conditions the P-median problem is a combinatory optimization problem that belongs to the NP-hard class and the approximation methods have been of great aid in recent years because of this. In this point, we have chosen data from OR-Library [1] and we have tested three algorithms that have given good results for geographical data （Simulated Annealing, Variable Neighborhood Search, Bioinspired Variable Neighborhood Search and a Tabu Search-VNS Hybrid （TS-VNS）. However, the partitioning method PAM （Partitioning Around Medoids）, that is modeled like the P-median, attained similar results along with TS-VNS but better results than the other metaheuristics for the OR-Library instances, in a favorable computing time, however for bigger instances that represent real states in Mexico, TS-VNS has surpassed PAM in time and quality in all instances. In this work we expose the behavior of these five different algorithms for the test matrices from OR-Library and real geographical data from Mexico. Furthermore, we made an analysis with the goal of explaining the quality of the results obtained to conclude that PAM behaves with efficiency for the OR-Library instances but is overcome by the hybrid when applied to real instances. On the other hand we have tested the 2 best algorithms （PAM and TS-VNS） with geographic data geographic from Jalisco, Queretaro and Nuevo Leon. In this point, as we said before, their performance was different than the OR-Library tests. The algorithm that attains the best results is TS-VNS.

A Decision Support System for Energy Trading and Portfolio Optimization

In the new competitive environment of the electricity market, risk analysis is a powerful tool to guide investors under both contract uncertainties and energy prices of the spot market. Moreover, simulation of spot price scenarios and evaluation of energy contracts performance, are also necessary to the decision maker, and in particular to the trader to foresee opportunities and possible threats in the trading activity. In this context, computational systems that allow what-if analysis, involving simulation of spot price, contract portfolio optimization and risk evaluation are rather important. This paper proposes a decision support system not only for solving the problem of contracts portfolio optimization, by using linear programming, but also to execute risks analysis of the contracts portfolio performance, with VaR and CVaR metrics. Realistic tests have demonstrated the efficiency of this system.

Approach for earth observation satellite real-time and playback data transmission scheduling

The scheduling of earth observation satellites(EOSs)data transmission is a complex combinatorial optimization problem. Current researches mainly deal with this problem on the assumption that the data transmission mode is fixed, either playback or real-time transmission. Considering the characteristic of the problem, a multi-satellite real-time and playback data transmission scheduling model is established and a novel algorithm based on quantum discrete particle swarm optimization(QDPSO)is proposed. Furthermore, we design the longest compatible transmission chain mutation operator to enhance the performance of the algorithm. Finally, some experiments are implemented to validate correctness and practicability of the proposed algorithm.

An SDP randomized approximation algorithm for max hypergraph cut with limited unbalance

We consider the design of semidefinite programming （SDP） based approximation algorithm for the problem Max Hypergraph Cut with Limited Unbalance （MHC-LU）： Find a partition of the vertices of a weighted hypergraph H = （V, E） into two subsets V1, V2 with ｜｜V2｜ - ｜1/1 ｜｜ ≤ u for some given u and maximizing the total weight of the edges meeting both V1 and V2. The problem MHC-LU generalizes several other combinatorial optimization problems including Max Cut, Max Cut with Limited Unbalance （MC-LU）, Max Set Splitting, Max Ek-Set Splitting and Max Hypergraph Bisection. By generalizing several earlier ideas, we present an SDP randomized approximation algorithm for MHC-LU with guaranteed worst-case performance ratios for various unbalance parameters τ = u/｜V｜. We also give the worst-case performance ratio of the SDP-algorithm for approximating MHC-LU regardless of the value of τ. Our strengthened SDP relaxation and rounding method improve a result of Ageev and Sviridenko （2000） on Max Hypergraph Bisection （MHC-LU with u = 0）, and results of Andersson and Engebretsen （1999）, Gaur and Krishnamurti （2001） and Zhang et al. （2004） on Max Set Splitting （MHC-LU with u = ｜V｜）. Furthermore, our new formula for the performance ratio by a tighter analysis compared with that in Galbiati and Maffioli （2007） is responsible for the improvement of a result of Galbiati and Maffioli （2007） on MC-LU for some range of τ.

DYNAMIC CVAR WITH MULTI-PERIOD RISK PROBLEMS

This paper studies multi-period risk management problems by presenting a dynamic risk measure. This risk measure is the sum of conditional value-at-risk of each period. The authors model it by Markov decision processes and derive its optimality equation. This equation is further transformed equivalently to an analytically tractable one. The authors then use the model and its results to a multi-period portfolio optimization when the return rate vectors at each period form a Markov chain.

A smoothing Newton method for mathematical programs constrained by parameterized quasi-variational inequalities

We consider a class of mathematical programs governed by parameterized quasi-variational inequalities(QVI).The necessary optimality conditions for the optimization problem with QVI constraints are reformulated as a system of nonsmooth equations under the linear independence constraint qualification and the strict slackness condition.A set of second order sufficient conditions for the mathematical program with parameterized QVI constraints are proposed,which are demonstrated to be sufficient for the second order growth condition.The strongly BD-regularity for the nonsmooth system of equations at a solution point is demonstrated under the second order sufficient conditions.The smoothing Newton method in Qi-Sun-Zhou [2000] is employed to solve this nonsmooth system and the quadratic convergence is guaranteed by the strongly BD-regularity.Numerical experiments are reported to show that the smoothing Newton method is very effective for solving this class of optimization problems.