用概率统计方法预测洪水水位

河流的水位变化从局部时间看是偶然的，但从长远看，这些偶然的数据常常是必然的结果。在自然条件下取得的水位数据，从本质上看都是随机的，正因为其随机性，统计方法尤为重要。本文试用统计方法分析预测河水的最高洪水水位，这对建筑桥梁、修建堤坝具有一定的参考价值。     

Constraint Handling in Genetic Algorithms: The Set Partitioning Problem

In this paper we present a genetic algorithm-based heuristic for solving the set partitioning problem (SPP). The SPP is an important combinatorial optimisation problem used by many airlines as a mathematical model for flight crew scheduling.A key feature of the SPP is that it is a highly constrained problem, all constraints being equalities. New genetic algorithm (GA) components: separate fitness and unfitness scores, adaptive mutation, matching selection and ranking replacement, are introduced to enable a GA to effectively handle such constraints. These components are generalisable to any GA for constrained problems.We present a steady-state GA in conjunction with a specialised heuristic improvement operator for solving the SPP. The performance of our algorithm is evaluated on a large set of real-world problems. Computational results show that the genetic algorithm-based heuristic is capable of producing high-quality solutions.     

A genetic algorithm for the two-dimensional strip packing problem with rectangular pieces

Given a set of rectangular pieces and a container of fixed width and variable length, the two-dimensional strip packing problem (2D-SPP) consists of orthogonally placing all the pieces within the container, without overlapping, such that the overall length of the layout is minimised. Until now mainly heuristics, for example genetic algorithms (GA), were proposed for the 2D-SPP which use encoded solutions that are manipulated by standard operators. In this paper a GA for the 2D-SPP is suggested that works without any encoding of solutions. Rather fully defined layouts are manipulated as such by means of specific genetic operators. Two additional constraints, namely the orientation constraint and the guillotine constraint, can be taken into account. The GA is subjected to a comprehensive test using benchmark instances with up to 5000 pieces. Compared to eleven competing methods from the literature the GA performs best.     

Spectral scale of self-adjoint operators and trace inequalities

Two mathematical models are presented which yield some mechanical aspects of this elastoplastic plate bending. The frist model proves insufficient if the classical Sobolev space framework is kept up. With the second model, an existence result for the transverse displacement problem formulation is obtained when the load does not exceed a specific critical value. The study of the stability problem leads to differentiation of a projector on a closed convex set, which is a difficult question; nevertheless, a hypothesis of regularity of the solution of some plasticity problem is introduced, and the existence of a critical load under which there is stability in Some sense is shown.     

ARMA model order and parameter estimation using genetic algorithms

A new method for simultaneously determining the order and the parameters of autoregressive moving average (ARMA) models is presented in this article. Given an ARMA (p, q) model in the absence of any information for the order, the correct order of the model (p, q) as well as the correct parameters will be simultaneously determined using genetic algorithms (GAs). These algorithms simply search the order and the parameter spaces to detect their correct values using the GA operators. The proposed method works on the principle of maximizing the GA fitness value relying on the deviation between the actual plant output, with or without an additive noise, and the estimated plant output. Simulation results show in detail the efficiency of the proposed approach. In addition to that, a practical model identification and parameter estimation is conducted in this article with results obtained as desired. The new method is compared with other well-known methods for ARMA model order and parameter estimation.     

The Container Transshipment Problem: Searching Representation Landscapes with Metaheuristic Algorithms

The container transshipment problem involves scheduling a fleet of lorries to collect and deliver containers of various sizes while minimizing the total distance travelled. The problem originates in the need for logistics companies to solve the problem on a regular basis as part of their daily operations. In this paper, we compare two genetic algorithms tailored to solve this problem based on permutation and bin-packing inspired encodings. Results are presented and analysed in order to evaluate the validity and robustness of the two approaches. As part of the analysis, bounds were calculated to determine how well both GAs perform in absolute terms as well as relative to each other. Of the two GA there is one clear winner, although it is not the one that would have been indicated by previous research. Whilst the winning GA is able to generate significant savings in practice, compared to the optimum there remains room for further improvement.     

Crossing Over Genetic Algorithms: The Sugal Generalised GA

Sugal is a major new public-domain software package designed to support experimentation with, and implementation of, Genetic Algorithms. Sugal includes a generalised Genetic Algorithm, which supports the major popular versions of the GA as special cases. Sugal also has integrated support for various datatypes, including real numbers, and features to make hybridisation simple. This paper discusses the Sugal GA, showing how recombining the features of the popular algorithms results in the creation of a number of useful hybrid algorithms.     

垂直与水平渗透作用下潜水非稳定渗流运动规律

对河渠边界控制的半无限含水层,建立垂向入渗与河渠水平渗透共同作用下的潜水非稳定渗流模型;利用Boussinesq第一线性化方法,通过Laplace变换,给出模型的解析解. 证明相关经典公式与模型特定解之间的转换关系,分析经典公式适用范围．根据模型解,逐一定量研究下述变量,如垂向入渗强度、河渠水位变动幅度、含水层结构参数如给水度和导压系数、计算点与边界之间的距离,对渗流过程的影响．这些变量的变化,对潜水位获最大上升速度的时间产生延迟效应;论证一些变量间产生等效延迟效应的条件．根据解的数学特征,讨论其对应的物理意义和潜水位变动规律．     

Selecting informative rules with parallel genetic algorithm in classification problem

The classification system is very important for making decision and it has been attracted much attention of many researchers. Usually, the traditional classifiers are either domain specific or produce unsatisfactory results over classification problems with larger size and imbalanced data. Hence, genetic algorithms (GA) are recently being combined with traditional classifiers to find useful knowledge for making decision. Although, the main concerns of such GA-based system are the coverage of less search space and increase of computational cost with the growth of population. In this paper, a rule-based knowledge discovery model, combining C4.5 (a Decision Tree based rule inductive algorithm) and a new parallel genetic algorithm based on the idea of massive parallelism, is introduced. The prime goal of the model is to produce a compact set of informative rules from any kind of classification problem. More specifically, the proposed model receives a base method C4.5 to generate rules which are then refined by our proposed parallel GA. The strength of the developed system has been compared with pure C4.5 as well as the hybrid system (C4.5 + sequential genetic algorithm) on six real world benchmark data sets collected from UCI (University of California at Irvine) machine learning repository. Experiments on data sets validate the effectiveness of the new model. The presented results especially indicate that the model is powerful for volumetric data set.     

Extensive Testing of a Hybrid Genetic Algorithm for Solving Quadratic Assignment Problems

A robust search algorithm should ideally exhibit reasonable performance on a diverse and varied set of problems. In an earlier paper Lim et al. (Computational Optimization and Applications, vol. 15, no. 3, 2000), we outlined a class of hybrid genetic algorithms based on the k-gene exchange local search for solving the quadratic assignment problem (QAP). We follow up on our development of the algorithms by reporting in this paper the results of comprehensive testing of the hybrid genetic algorithms (GA) in solving QAP. Over a hundred instances of QAP benchmarks were tested using a standard set of parameters setting and the results are presented along with the results obtained using simple GA for comparisons. Results of our testing on all the benchmarks show that the hybrid GA can obtain good quality solutions of within 2.5% above the best-known solution for 98% of the instances of QAP benchmarks tested. The computation time is also reasonable. For all the instances tested, all except for one require computation time not exceeding one hour. The results will serve as a useful baseline for performance comparison against other algorithms using the QAP benchmarks as a basis for testing.     

Helper-objectives: Using multi-objective evolutionary algorithms for single-objective optimisation

This paper investigates the use of multi-objective methods to guide the search when solving single-objective optimisation problems with genetic algorithms. Using the job shop scheduling and travelling salesman problems as examples, experiments demonstrate that the use of helper-objectives (additional objectives guiding the search) significantly improves the average performance of a standard GA. The helper-objectives guide the search towards solutions containing good building blocks and help the algorithm escape local optima. The experiments reveal that the approach works if the number of simultaneously used helper-objectives is low. However, a high number of helper-objectives can be used in the same run by changing the helper-objectives dynamically. The experiments reveal that for the majority of problem instances studied, the proposed approach significantly outperforms a traditional GA.The experiments also demonstrate that controlling the proportion of non-dominated solutions in the population is very important when using helper-objectives, since the presence of too many non-dominated solutions removes the selection pressure in the algorithm.     

Promoting cooperation in selfish computational grids

In distributed computing, the recent paradigm shift from centrally-owned clusters to organizationally distributed computational grids introduces a number of new challenges in resource management and scheduling. In this work, we study the problem of Selfish Load Balancing which extends the well-known load balancing (LB) problem to scenarios in which each processor is concerned only with the performance of its local jobs. We propose a simple mathematical model for such systems and a novel function for computing the cost of the execution of foreign jobs. Then, we use the game-theoretic framework to analyze the model in order to compute the expected result of LB performed in a grid formed by two clusters. We show that, firstly, LB is a socially-optimal strategy, and secondly, for similarly loaded clusters, it is sufficient to collaborate during longer time periods in order to make LB the dominant strategy for each cluster. However, we show that if we allow clusters to make decisions depending on their current queue length, LB will never be performed. Then, we propose a LB algorithm which balances the load more equitably, even in the presence of overloaded clusters. Our algorithms do not use any external forms of compensation (such as money). The load is balanced only by considering the parameters of execution of jobs. This analysis is assessed experimentally by simulation, involving scenarios with multiple clusters and heterogeneous load.     

阶梯状黄土边坡稳定性分析的改进遗传算法及应用

阶梯状黄土边坡稳定性分析的关键是估算其稳定系数的最小值.稳定系数的求解涉及诸多因素且计算过程繁杂,传统优化算法往往不能有效地搜索到其全局最小解.为此,提出一种改进的自适应遗传算法.算法对基因变量空间进行网格状划分,采用迭代选优法建立均匀分布的初始种群,运用优质个体保留遗传策略,并按照特定的准则自适应地调整交叉概率和变异概率,提高算法的全局搜索能力和收敛速度.实例应用表明算法能够快速有效地收敛于土坡稳定系数的全局最小解,且计算结果与实际情况更加吻合.     

Rapid dynamic programming algorithms for RNA secondary structure

Prediction of RNA secondary structure from the linear RNA sequence is an important mathematical problem in molecular biology. Dynamic programming methods are currently the most useful computer technique but are frequently very expensive in running time. In this paper new dynamic programming algorithms are presented which reduce the required computation. The first polynomial time algorithm is given for predicting general secondary structure.     

CABRI AS A COGNITIVE TOOL FOR THE EVOLUTION OF A SENSE OF PROVING

Cognitive technologies have been described in the literature as reorganisers of thinking processes, especially where problem solving is concerned. This paper aims to analyse the possible use of Cabri-Géomètre as a cognitive tool in the elaboration of mathematical justifications in the context of problem-based mathematics. Some empirical examples are given to illustrate the significance of the specific learning situation. The complexity of learning environments incorporating computer-based activities is stressed as a condition for them to be effective in the introduction of the idea of mathematical justification and its evolution towards a sense of proving.     

Optimizing multi-item multi-period inventory control system with discounted cash flow and inflation: Two calibrated meta-heuristic algorithms

A mixed binary integer mathematical programming model is developed in this paper for ordering items in multi-item multi-period inventory control systems, in which unit and incremental quantity discounts as well as interest and inflation factors are considered. Although the demand rates are assumed deterministic, they may vary in different periods. The situation considered for the problem at hand is similar to a seasonal inventory control model in which orders and sales happen in a given season. To make the model more realistic, three types of constraints including storage space, budget, and order quantity are simultaneously considered. The goal is to find optimal order quantities of the products so that the net present value of total system cost over a finite planning horizon is minimized. Since the model is NP-hard, a genetic algorithm (GA) is presented to solve the proposed mathematical problem. Further, since no benchmarks can be found in the literature to assess the performance of the proposed algorithm, a branch and bound and a simulated annealing (SA) algorithm are employed to solve the problem as well. In addition, to make the algorithms more effective, the Taguchi method is utilized to tune different parameters of GA and SA algorithms. At the end, some numerical examples are generated to analyze and to statistically and graphically compare the performances of the proposed solving algorithms.     

基于遗传算法的对规避目标搜索模型

分析了在应召条件下对规避目标搜索行动的特点,然后采用遗传算法建立了可用于辅助搜索决策者制定协同搜索方案的模型,为分析应召搜索提供了新的方法,该方法克服了传统的运筹学搜索论在协同行动等复杂条件下寻求最优搜索方案的不足     

An optimal solution to a three echelon supply chain network with multi-product and multi-period

Recently, Kadadevaramath et al. (2012) [1] presented a mathematical model for optimizing a three echelon supply chain network. Their model is an integer linear programming (ILP) model. In order to solve it, they developed five algorithms; four of them are based on a particle swarm optimization (PSO) method and the other is a genetic algorithm (GA). In this paper, we develop a more general mathematical model that contains the model developed by Kadadevaramath et al. (2012) [1]. Furthermore, we show that all instances proved in Kadadevaramath et al. (2012) [1] can easily be solved optimally by any integer linear programming solver.     

A new hybrid algorithm based on optimal fuzzy controller in multimachine power system

In this article, a new methodology based on fuzzy proportional‐integral‐derivative (PID) controller is proposed to damp low frequency oscillation in multimachine power system where the parameters of proposed controller are optimized offline automatically by hybrid genetic algorithm (GA) and particle swarm optimization (PSO) techniques. This newly proposed method is more efficient because it cope with oscillations and different operating points. In this strategy, the controller is tuned online from the knowledge base and fuzzy interference. In the proposed method, for achieving the desired level of robust performance exact tuning of rule base and membership functions (MF) are very important. The motivation for using the GA and PSO as a hybrid method are to reduce fuzzy effort and take large parametric uncertainties in to account. This newly developed control strategy mixed the advantage of GA and PSO techniques to optimally tune the rule base and MF parameters of fuzzy controller that leads to a flexible controller with simple structure while is easy to implement. The proposed method is tested on three machine nine buses and 16 machine power systems with different operating conditions in present of disturbance and nonlinearity. The effectiveness of proposed controller is compared with robust PSS that tune using PSO and the fuzzy controller which is optimized rule base by GA through figure of demerit and integral of the time multiplied absolute value of the error performance indices. The results evaluation shows that the proposed method achieves good robust performance for a wide range of load change in the presents of disturbance and system nonlinearities and is superior to the other controllers. © 2014 Wiley Periodicals, Inc. Complexity 21: 78–93, 2015     

The water resources assessment based on resource exergy for the mainstream Yellow River

Based on the resource exergy theory, a unified exergetic index is proposed to assess both the quantity and quality of the water of the mainstream Yellow River, thus verifying the real available quantity of the river water in an ecological thermodynamics view. The chemical exergy, thermal exergy, potential exergy and sediment exergy of the river water as partial exergies are, respectively, calculated with the field river water intake data of the mainstream Yellow River. Exergetic potential is also defined to describe different working capacities of the river water along the mainstream. Finally, the temporal and spatial variation of the water resources of the mainstream Yellow River is illuminated with the proposed exergetic measure.