基于时间窗延迟的资源约束项目调度双层优化研究

本研究从业主—承包商交互的视角构建了一种RCPSP(resource-constrained project scheduling problem)双层优化模型,即在可更新资源约束条件下,项目双方如何进行交互决策达到双方NPV(Net present value)最大化的目标。首先对研究问题进行界定,构建资源约束下的max-NPV项目调度双层优化模型;然后利用延迟优先规则设计了一种基于时间窗延迟的嵌套式自适应遗传算法来求解该模型,以达到双方NPV最大化;最后用一个算例验证算法的有效性,同时通过PSPLIB数值实验说明算法的稳定性,并分析关键参数对项目双方收益的影响。研究结果为项目进程的安排以及奖励机制的设计提供依据,以提高双方利益。     

Inverse optimization for linearly constrained convex separable programming problems

In this paper, we study inverse optimization for linearly constrained convex separable programming problems that have wide applications in industrial and managerial areas. For a given feasible point of a convex separable program, the inverse optimization is to determine whether the feasible point can be made optimal by adjusting the parameter values in the problem, and when the answer is positive, find the parameter values that have the smallest adjustments. A sufficient and necessary condition is given for a feasible point to be able to become optimal by adjusting parameter values. Inverse optimization formulations are presented with ℓ₁ and ℓ₂ norms. These inverse optimization problems are either linear programming when ℓ₁ norm is used in the formulation, or convex quadratic separable programming when ℓ₂ norm is used.     

求解半定乘性规划的外部逼近算法

定义了半定乘性规划问题,提出一种求解它的外部逼近算法,并通过具体的实例说明算法的可行性.     

On an open problem of Sankaranarayanan

Let λ(n) be the n-th normalized Fourier coeficient of a holomorphic Hecke eigenform f(z) ∈ Sk(Γ) for the full modular group.In one of his papers,Sankaranarayanan mentioned that it is an open problem to give a non-trivial estimate for the sum of λ(n) over cubes,i.e.n x λ(n3).In this paper,we are able to use the analytic properties of symmetric power L-functions to solve his problem.More precisely,we prove that Σn≤zλ(n3) x(3/4 +ε),Σn≤zλ(n4) x(97+ε).     

An explanation for deviations from the quark number scaling of elliptic flows in low pT region

We carry out a systematic study of the different contributions to the deviations of the elliptic flows from the quark number scaling in high energy heavy ion collision in a quark combination model.The effects that we considered are:the resonance decay,the flavor dependence of the quark elliptic flow and the combination of quarks/antiquarks with slightly different transverse momenta.Our results show that the deviations observed in experiments can be well reproduced within the combination framework if all the three effects are considered. We make a detailed analysis of the different contributions using a Monte-Carlo program and suggest measuring the quark number scaling in intermediate pT range more precisely.     

QPECgen, a MATLAB Generator for Mathematical Programs with Quadratic Objectives and Affine Variational Inequality Constraints

We describe a technique for generating a special class, called QPEC, of mathematical programs with equilibrium constraints, MPEC. A QPEC is a quadratic MPEC, that is an optimization problem whose objective function is quadratic, first-level constraints are linear, and second-level (equilibrium) constraints are given by a parametric affine variational inequality or one of its specialisations. The generator, written in MATLAB, allows the user to control different properties of the QPEC and its solution. Options include the proportion of degenerate constraints in both the first and second level, ill-conditioning, convexity of the objective, monotonicity and symmetry of the second-level problem, and so on. We believe these properties may substantially effect efficiency of existing methods for MPEC, and illustrate this numerically by applying several methods to generator test problems. Documentation and relevant codes can be found by visiting http://www.ms.unimelb.edu.au/danny/qpecgendoc.html.     

Conversion of a head-mounted microphone signal intocalibrated SPL units

A method is reviewed for conversion of a microphone signal into calibrated Sound Pressure Level (SPL) units. The method follows American National Standards Institute (ANSI) standard for S1.4 SPL meters and requires an accurate SPL meter and an accurate calibration sound source for conversion. Accuracy and validation data from test signals and human phonation are provided. The results indicate that under typical speech conditions, an absolute accuracy of plus or minus 1.6 dB (type I SPL meter) can be obtained with a miniature head-mounted microphone.     

Correctness proof of an in-place permutation

The correctness of an in-place permutation algorithm is proved. The algorithm exchanges elements belonging to a permutation cycle. A suitable assertion is constructed from which the correctness can be deduced after completion of the algorithm.An in-place rectangular matrix transposition algorithm is given as an example.     

Correspondence between spin-dynamic phases and pulse program phases of NMR spectrometers

Spin state selective experiments have become very useful tools in solution NMR spectroscopy, particularly in the context of TROSY line narrowing. However, the practical implementation of such pulse sequences is frequently complicated by unexpected instrument behavior. Furthermore, a literal theoretical analysis of sequences published with specific phase settings can fail to rationalize such experiments and can seemingly contradict experimental findings. In this communication, we develop a practical approach to this ostensible paradox. Spin-dynamic design, rationalization, and simulation of NMR pulse sequences, as well as their confident and reliable implementation across current spectrometer hardware platforms, require precise understanding of the underlying nutation axis conventions. While currently often approached empirically, we demonstrate with a simple but general pulse program how to uncover these correspondences a priori in the general case. From this, we deduce a correspondence table between the spin-dynamic phases used in NMR theory and simulation on the one hand and pulse program phases of current commercial spectrometers on the other. As a practical application of these results, we analyze implementations of the original (1)H-(15)N TROSY experiment and illustrate how steady-state magnetization can be predictably, rather than empirically, added to a desired component. We show why and under which circumstances a literal adoption of phases from published sequences can lead to incorrect results. We suggest that pulse sequences should be consistently given with spin-dynamically correct (physical) phases, rather than in spectrometer-specific (software) syntax.     

Local branching

The availability of effective exact or heuristic solution methods for general Mixed-Integer Programs (MIPs) is of paramount importance for practical applications. In the present paper we investigate the use of a generic MIP solver as a black-box ``tactical' tool to explore effectively suitable solution subspaces defined and controlled at a ``strategic' level by a simple external branching framework. The procedure is in the spirit of well-known local search metaheuristics, but the neighborhoods are obtained through the introduction in the MIP model of completely general linear inequalities called local branching cuts. The new solution strategy is exact in nature, though it is designed to improve the heuristic behavior of the MIP solver at hand. It alternates high-level strategic branchings to define the solution neighborhoods, and low-level tactical branchings to explore them. The result is a completely general scheme aimed at favoring early updatings of the incumbent solution, hence producing high-quality solutions at early stages of the computation. The method is analyzed computationally on a large class of very difficult MIP problems by using the state-of-the-art commercial software ILOG-Cplex 7.0 as the black-box tactical MIP solver. For these instances, most of which cannot be solved to proven optimality in a reasonable time, the new method exhibits consistently an improved heuristic performance: in 23 out of 29 cases, the MIP solver produced significantly better incumbent solutions when driven by the local branching paradigm. Mathematics Subject Classification (2000):90C06, 90C10, 90C11, 90C27, 90C59