FracSym: Automated symbolic computation of Lie symmetries of fractional differential equations

In this paper, we present an algorithm for the systematic calculation of Lie point symmetries for fractional order differential equations (FDEs) using the method as described by Buckwar & Luchko (1998) and Gazizov, Kasatkin & Lukashchuk (2007, 2009, 2011). The method has been generalised here to allow for the determination of symmetries for FDEs with n$n$ independent variables and for systems of partial FDEs. The algorithm has been implemented in the new MAPLE package FracSym (Jefferson and Carminati 2013) which uses routines from the MAPLE symmetry packages DESOLVII (Vu, Jefferson and Carminati, 2012) and ASP (Jefferson and Carminati, 2013). We introduce FracSym by investigating the symmetries of a number of FDEs; specific forms of any arbitrary functions, which may extend the symmetry algebras, are also determined. For each of the FDEs discussed, selected invariant solutions are then presented.     

A multi-objective hyper-heuristic based on choice function

Hyper-heuristics are emerging methodologies that perform a search over the space of heuristics in an attempt to solve difficult computational optimization problems. We present a learning selection choice function based hyper-heuristic to solve multi-objective optimization problems. This high level approach controls and combines the strengths of three well-known multi-objective evolutionary algorithms (i.e. NSGAII, SPEA2 and MOGA), utilizing them as the low level heuristics. The performance of the proposed learning hyper-heuristic is investigated on the Walking Fish Group test suite which is a common benchmark for multi-objective optimization. Additionally, the proposed hyper-heuristic is applied to the vehicle crashworthiness design problem as a real-world multi-objective problem. The experimental results demonstrate the effectiveness of the hyper-heuristic approach when compared to the performance of each low level heuristic run on its own, as well as being compared to other approaches including an adaptive multi-method search, namely AMALGAM.     

CO2泡沫压裂液的流变性及井筒摩阻计算方法研究

进行了CO2泡沫压裂液的室内配制、流变性测定以及摩阻计算方法研究。室内实验中观测了CO2泡沫压裂液的形成、动态变化、泡沫结构,测定了CO2泡沫压裂液的流变性,发现其属于假塑性非牛顿流体。推导了CO2泡沫压裂液在油管内流动的摩阻计算公式,计算了不同管径、不同排量、不同泡沫质量时的摩阻曲线,进行了井筒内CO2泡沫压裂液摩阻压降实测,与计算方法相比误差在工程应用允许范围内。该研究所得到的CO2泡沫压裂液流动特性、摩阻压降计算方法、经验图版等,可供工程应用中参考。     

A new Probe Guided Mutation operator and its application for solving the cardinality constrained portfolio optimization problem

This paper revisits the classical Polynomial Mutation (PLM) operator and proposes a new probe guided version of the PLM operator designed to be used in conjunction with Multiobjective Evolutionary Algorithms (MOEAs). The proposed Probe Guided Mutation (PGM) operator is validated by using data sets from six different stock markets. The performance of the proposed PGM operator is assessed in comparison with the one of the classical PLM with the assistance of the Non-dominated Sorting Genetic Algorithm II (NSGAII) and the Strength Pareto Evolutionary Algorithm 2 (SPEA2). The evaluation of the performance is based on three performance metrics, namely Hypervolume, Spread and Epsilon indicator. The experimental results reveal that the proposed PGM operator outperforms with confidence the performance of the classical PLM operator for all performance metrics when applied to the solution of the cardinality constrained portfolio optimization problem (CCPOP). We also calculate the True Efficient Frontier (TEF) of the CCPOP by formulating the CCPOP as a Mixed Integer Quadratic Program (MIQP) and we compare the relevant results with the approximate efficient frontiers that are generated by the proposed PGM operator. The results confirm that the PGM operator generates near optimal solutions that lie very close or in certain cases overlap with the TEF.     

化学反应蚁群优化算法

针对化学反应优化对反馈信息利用不足导致后期求解效率低的问题,提出化学反应蚁群优化算法.该算法利用化学反应优化生成较优解,通过信息素转换策略将较优解转换为蚁群算法的初始信息素,最后由蚁群算法累积更新信息素得到最优解.以TSP为例进行仿真,结果表明,与化学反应优化、蚁群算法、模拟退火算法相比,所提算法具有更高的寻优能力、收敛效率和计算效率.     

基于显式计算的单播链路时延估计

为提高基于单播测量的网络链路时延分布估计速度,提出了一种基于显式计算的单播链路时延快速估计方法.由于网络设备多样化导致链路时延特征存在差异,首先根据端到端测量数据为各链路分配不同的离散间隔;然后利用背靠背探测包在网络中引入的二层二叉树结构,通过显式计算推断各链路的时延分布,能明显提高估计速度.仿真结果表明,该方法将链路时延分布的估计时间降低至数百毫秒,同时更准确地捕获链路时延特征.该方法基于显式计算,计算复杂度非常低,因此能够满足实际应用的实时性要求.     

Computer Algebra Derivation of the Bias of Linear Estimators of Autoregressive Models

Abstract. A symbolic method which can be used to obtain the asymptotic bias and variance coefficients to order O(1/n) for estimators in stationary time series is discussed. Using this method, the large‐sample bias of the Burg estimator in the AR(p) for p = 1, 2, 3 is shown to be equal to that of the least squares estimators in both the known and unknown mean cases. Previous researchers have only been able to obtain simulation results for the Burg estimator's bias because this problem is too intractable without using computer algebra. The asymptotic bias coefficient to O(1/n) of Yule–Walker as well as least squares estimates is also derived in AR(3) models. Our asymptotic results show that for the AR(3), just as in the AR(2), the Yule–Walker estimates have a large bias when the parameters are near the nonstationary boundary. The least squares and Burg estimates are much better in this situation. Simulation results confirm our findings.     

基于PBIL算法的物流中心选址问题研究

介绍了基于种群竞争式学习的PBIL算法的基本原理和实现方法。比较了PBIL算法和遗传算法求解过程的异同点。分析了PBIL算法在物流中心选址问题中的应用,并且通过实例验证了算法的可行性和有效性,证明了PBIL算法比遗传算法具有更高的搜索效率。     

Holographic algorithms on bases of rank 2

An essential problem in the design of holographic algorithms is to decide whether the required signatures can be realized under a suitable basis transformation (SRP). For holographic algorithms with matchgates on domain size 2, , ,  and  have built a systematical theory. In this paper, we reduce SRP on domain size k≥3$k\ge 3$ to SRP on domain size 2 for holographic algorithms with matchgates on bases of rank 2. Furthermore, we generalize the collapse theorem of [3] to domain size k≥3$k\ge 3$.     

Undecidability of accordance for open systems with unbounded message queues

We study asynchronously communicating open systems modeled as Petri nets with an interface. An accordance preorder describes when one open system can be safely replaced by another open system without affecting some behavioral property of the overall system. Although accordance is decidable for several behavioral properties if we assume a previously known bound on the maximal number of pending messages, we show that it is not decidable without this assumption.