一种求解作业车间调度问题的混和遗传算法

作业车间调度问题(JSSP)是组合优化问题中的NP难问题。本文提出了以适用于JSSP问题的二进制编码遗传算法为基础,在算法中增加了两种启发式算子:激活算子和瓶颈修复算子,并相应调整算法结构,形成混和遗传算法解决JSSP问题。激活算子以GT算法为依据,将种群中部分个体转化为活动调度个体,是一种较有独创性的新算子;瓶颈修复算子对所得结果进一步优化。算例运行结果表明与其它算法相比,该算法在全局搜索能力和运行效率上都有突出的表现。     

Functional coefficient autoregressive conditional root model

This paper proposes an extended model based on ACR model:Functional coefficient autoregressive conditional root model（FCACR）.Under some assumptions,the authors show that the process is geometrically ergodic,stationary and all moments of the process exist.The authors use the polynomial spline function to approximate the functional coefficient,and show that the estimate is consistent with the rate of convergence O_p(h^v+1+n^-1/3).By simulation study,the authors discover the proposed method can approximate well the real model.Furthermore,the authors apply the model to real exchange rate data analysis.     

Polynomial dynamic programming algorithms for lot sizing models with bounded inventory and stockout and/or backlogging

This paper addresses a dynamic lot sizing problem with bounded inventory and stockout where both no backlogging and backlogging allowed cases are considered. The stockout option means that there is outsourcing in a period only when the inventory level at that period is non-positive. The production capacity is unlimited and production cost functions are linear but with fixed charges. The problem is that of satisfying all demands in the planning horizon at minimal total cost. We show that the no backlogging case can be solved in ) O(T ²) time with general concave inventory holding and outsourcing cost functions where T is the length of the planning horizon. The complexity can be reduced to O(T) when the inventory holding cost functions are also linear and have some realistic properties, even if the outsourcing cost functions remain general concave functions. When the inventory holding and outsourcing cost functions are linear, the backlogging case can be solved in O(T ³logT) time whether the outsourcing level at each period is bounded by the sum of the demand of that period and backlogging level from previous periods, or only by the demand of that period.     

NNMDS codes

C is an[n,k,d]_q linear code over F₉.And s（C）=n+1-k-d is the Singleton defect of C.An MDS code C with s（C）=0 has been studied extensively.Recently,a near-MDS code C with s（C）=s（C^⊥）=1 is studied by many scholars,where C^⊥denotes the dual code of C.This paper concentrates on the linear code C with s（C）=s（C^⊥）=2,and the author calls it an NNMDS code.A series of iff conditions of NNMDS codes are presented.And the author gives an upper bound on length of NNMDS codes.In the last,some examples of NNMDS are given.     

An Adjusted Gray Map Technique for Constructing Large Four-Level Uniform Designs

A uniform experimental design (UED) is an extremely used powerful and efficient methodology for designing experiments with high-dimensional inputs, limited resources and unknown underlying models. A UED enjoys the following two significant advantages: (i) It is a robust design, since it does not require to specify a model before experimenters conduct their experiments; and (ii) it provides uniformly scatter design points in the experimental domain, thus it gives a good representation of this domain with fewer experimental trials (runs). Many real-life experiments involve hundreds or thousands of active factors and thus large UEDs are needed. Constructing large UEDs using the existing techniques is an NP-hard problem, an extremely time-consuming heuristic search process and a satisfactory result is not guaranteed. This paper presents a new effective and easy technique, adjusted Gray map technique (AGMT), for constructing (nearly) UEDs with large numbers of four-level factors and runs by converting designs with s two-level factors and n runs to (nearly) UEDs with 2^t?1s four-level factors and 2^tn runs for any t ≥ 0 using two simple transformation functions. Theoretical justifications for the uniformity of the resulting four-level designs are given, which provide some necessary and/or sufficient conditions for obtaining (nearly) uniform four-level designs. The results show that the AGMT is much easier and better than the existing widely used techniques and it can be effectively used to simply generate new recommended large (nearly) UEDs with four-level factors.

     

Weighted <Emphasis Type="Italic">L</Emphasis><Superscript>2</Superscript>-estimates of solutions for damped wave equations with variable coefficients

The authors establish weighted L²-estimates of solutions for the damped wave equations with variable coefficients u _tt ? divA(x)?u+au _t = 0 in ? ⁿ under the assumption a(x) ≥ a₀[1+ρ(x)]^?l, where a₀ > 0, l < 1, ρ(x) is the distance function of the metric g = A^?1(x) on ? ⁿ . The authors show that these weighted L²-estimates are closely related to the geometrical properties of the metric g = A^?1(x).     

ANALYSIS AND COMPUTATIONAL ALGORITHM FOR QUEUES WITH STATE-DEPENDENT VACATIONS II： M（n）/G/1/K

We study a single-server queueing system with state-dependent arrivals and general service distribution, or simply M（n）/G/1/K, where the server follows an N policy and takes multiple vacations when the system is empty. We provide a recursive algorithm using the supplementary variable technique to numerically compute the stationary queue length distribution of the system. The only input requirements are the Laplace-Stieltjes transforms of the service time distribution and the vacation time distribution, and the state-dependent arrival rate. The computational complexity of the algorithm is O（K^3）.     

THE PERIODIC CAPACITATED ARC ROUTING PROBLEM LINEAR PROGRAMMING MODEL, METAHEURISTIC AND LOWER BOUNDS

1. Introduction The Capacitated Arc Routing Problem(CARP) is defined on an undirected network inwhich a fleet of identical vehicles with limitedcapacity is based at a depot node. Each edge hasa non-negative traversal cost and can betraversed any number…     

ACCURACY ANALYSIS FOR QUASI-CAREY ELEMENT*

In this paper, a new triangular element （Quasi-Carey element） is constructed by the idea of Specht element. It is shown that this Quasi-Carey element possesses a very special property, i.e., the consistency error is of order O（h^2）, one order higher than its interpolation error when the exact solution belongs to H^3（Ω）. However, the interpolation error and consistency error of Carey element are of order O（h）. It seems that the above special property has never been seen for other triangular elements for the second order problems.     

求解随机需求库存-路径问题的一种算法

库存-路径问题是研究在供应商管理用户库存策略下，供应商如何合理安排长期库存及配送计划的一类问题，属于NP—hard类问题，也是运筹学领域中研究最活跃的方向之一。本文以零售商系统下随机需求的IRP为研究对象，提出了一种基于马尔科夫决策过程与修正的C—W节约算法的启发式分解算法，并给出了相应的数值算例。     

Linear chaos in the quantum harmonic oscillator

In this note,it is proved that for the annihilation operator B of the unforced quantum harmonic oscillator,B~n is mixing and generically 5-chaotic with any 0 δ 2 for each positive integer n.Besides,by using the result in[Wu X and Zhu P,J.Phys.A：Math.Theor.,2011,44：505101],the authors obtain that the principal measure of B~n is equal to 1 for each positive integer n.     

A unified approach to construct generalized B-splines for isogeometric applications

Generalized B-splines have been employed as geometric modeling and numerical simulation tools for isogeometric analysis(IGA for short). However, the previous models used in IGA,such as trigonometric generalized B-splines or hyperbolic generalized B-splines, are not the unified mathematical representation of conics and polynomial parametric curves/surfaces. In this paper,a unified approach to construct the generalized non-uniform B-splines over the space spanned by{α(t), β(t), ξ(t), η(t), 1, t, ···, t~(n-4)} is proposed, and the corresponding isogeometric analysis framework for PDE solving is also studied. Compared with the NURBS-IGA method, the proposed frameworks have several advantages such as high accuracy, easy-to-compute derivatives and integrals due to the non-rational form. Furthermore, with the proposed spline models, isogeometric analysis can be performed on the computational domain bounded by transcendental curves/surfaces, such as the involute of circle, the helix/helicoid, the catenary/catenoid and the cycloid. Several numerical examples for isogeometric heat conduction problems are presented to show the effectiveness of the proposed methods.     

A Quantum Computing Based Numerical Method for Solving Mixed-Integer Optimal Control Problems

Mixed-integer optimal control problems (MIOCPs) usually play important roles in many real-world engineering applications. However, the MIOCP is a typical NP-hard problem with considerable computational complexity, resulting in slow convergence or premature convergence by most current heuristic optimization algorithms. Accordingly, this study proposes a new and effective hybrid algorithm based on quantum computing theory to solve the MIOCP. The algorithm consists of two parts: (i) Quantum Annealing (QA) specializes in solving integer optimization with high efficiency owing to the unique annealing process based on quantum tunneling, and (ii) Double-Elite Quantum Ant Colony Algorithm (DEQACA) which adopts double-elite coevolutionary mechanism to enhance global searching is developed for the optimization of continuous decisions. The hybrid QA/DEQACA algorithm integrates the strengths of such algorithms to better balance the exploration and exploitation abilities. The overall evolution performs to seek out the optimal mixed-integer decisions by interactive parallel computing of the QA and the DEQACA. Simulation results on benchmark functions and practical engineering optimization problems verify that the proposed numerical method is more excel at achieving promising results than other two state-of-the-art heuristics.

     

Conditional Congruence Closure over Uninterpreted and Interpreted Symbols

A framework for generating congruence closure and conditional congruence closure of ground terms over uninterpreted as well as interpreted symbols satisfying various properties is proposed. It is based on some of the key concepts from Kapur’s congruence closure algorithm (RTA97) for ground equations based on introducing new symbols for all nonconstant subterms appearing in the equation set and using ground completion on uninterpreted constants and purified equalities over interpreted symbols belonging to different theories. In the original signature, the resulting rewrite systems may be nonterminating but they still generate canonical forms. A byproduct of this framework is a constant Horn completion algorithm using which ground canonical Horn rewrite systems can be generated for conditional ground theories.

New efficient algorithms for generating congruence closure of conditional and unconditional equations on ground terms over uninterpreted symbols are presented. The complexity of the conditional congruence closure is shown to be O(n*log(n)), which is the same as for unconditional ground equations. The proposed algorithm is motivated by our attempts to generate efficient and succinct interpolants for the quantifier-free theory of equality over uninterpreted function symbols which are often a conjunction of conditional equations and need additional simplification. A completion algorithm to generate a canonical conditional rewrite system from ground conditional equations is also presented. The framework is general and flexible and is used later to develop congruence closure algorithms for cases when function symbols satisfy simple properties such as commutativity, nilpotency, idempotency and identity as well as their combinations. Interesting outcomes include algorithms for canonical rewrite systems for ground equational and conditional theories on uninterpreted and interpreted symbols leading to generation of canonical forms for ground terms, constrained terms and Horn equations.

     

含作业到达时间的同类机调度问题启发式算法

研究了目标函数是最小化完成时间和的同类机调度问题,其中作业到达时间可能不同.此问题被证明是强NP-hard问题.由于同类机调度是一种重要的平行机调度问题,而最小完成时间和目标是最常见的正则目标之一,因此完成时间和的同类机调度问题在相关研究领域具有非常重要的地位.为此问题建立数学模型,通过对单机和同型机的相应问题研究成果的推广,提出6个启发式算法,给出算例及其计算结果,并通过实验对算法的性能及算法适应的情形进行了分析.     

Reliability indices of discrete-time Geox/G/1 queueing system with unreliable service station and multiple adaptive delayed vacations

This paper considers the discrete-time Geo~x/G/1 queueing model with unreliable service station and multiple adaptive delayed vacations from the perspective of reliability research.Following problems will be discussed:1) The probability that the server is in a "generalized busy period" at time n;2) The probability that the service station is in failure at time n,i.e.,the transient unavailability of the service station,and the steady state unavailability of the service station;3) The expected number of service station failures during the time interval(0,n],and the steady state failure frequency of the service station;4) The expected number of service station breakdowns in a server’s "generalized busy period".Finally,the authors demonstrate that some common discrete-time queueing models with unreliable service station are special cases of the model discussed in this paper.     

Scheduling problems with rejection to minimize the maximum flow time

This paper considers the scheduling problem with rejection on m identical parallel machines to minimize the maximum flow time. The authors show that this problem is NP-hard even when there is a single machine and all jobs have two distinct release dates. Furthermore, the authors present a dynamic programming algorithm and two approximation algorithms to solve them.     

Construction of one-Lee weight and two-Lee weight codes over F<Subscript><Emphasis Type="Italic">p</Emphasis></Subscript> + <Emphasis Type="Italic">v</Emphasis>F<Subscript><Emphasis Type="Italic">p</Emphasis></Subscript>

This paper is devoted to the construction of one-Lee weight codes and two-Lee weight codes over F _p + vF _p (v ² = v) with type \({p^{2{k_1}}}{p^{{k_2}}}{p^{{k_3}}}\) based on two different distance-preserving Gray maps from ((F _p + vF _p ) ⁿ , Lee weight) to (F _p ²ⁿ , Hamming weight), where p is a prime. Moreover, the authors prove that the obtained two-Lee weight codes are projective only when p = 2.     

A New Algorithm for Computing the Extended Hensel Construction of Multivariate Polynomials

This paper presents a new algorithm for computing the extended Hensel construction(EHC) of multivariate polynomials in main variable x and sub-variables u_1, u_2, ···, u_m over a number field K. This algorithm first constructs a set by using the resultant of two initial coprime factors w.r.t. x, and then obtains the Hensel factors by comparing the coefficients of x~i on both sides of an equation. Since the Hensel factors are polynomials of the main variable with coefficients in fraction field K(u_1, u_2, ···, u_m), the computation cost of handling rational functions can be high. Therefore,the authors use a method which multiplies resultant and removes the denominators of the rational functions. Unlike previously-developed algorithms that use interpolation functions or Gr?bner basis, the algorithm relies little on polynomial division, and avoids multiplying by different factors when removing the denominators of Hensel factors. All algorithms are implemented using Magma, a computational algebra system and experiments indicate that our algorithm is more efficient.     

Construction of one-gray weight codes and two-Gray weight codes over ℤ<Subscript>4</Subscript> + <Emphasis Type="Italic">u</Emphasis>ℤ<Subscript>4</Subscript>

This paper firstly gives some necessary conditions on one-Gray weight linear codes. And then we use these results to construct several classes of one-Gray weight linear codes over ?₄+u?₄(u ² = u) with type \({16^{{k_1}}}{8^{{k_2}}}{8^{{k_3}}}{4^{{k_4}}}{4^{{k_5}}}{4^{{k_6}}}{2^{{k_7}}}{2^{{k_8}}}\) based on a distance-preserving Gray map from (?₄ + u?₄) ⁿ to ? ₄ ²ⁿ . Secondly, the authors use the similar approach to do works on two-Gray (projective) weight linear codes. Finally, some examples are given to illustrate the construction methods.