Genetic algorithm-based subproblem solution procedures for a modified shifting bottleneck heuristic for complex job shops

In this paper, we consider a modified shifting bottleneck heuristic for complex job shops. The considered job shop environment contains parallel batching machines, machines with sequence-dependent setup times and reentrant process flows. Semiconductor wafer fabrication facilities (Wafer Fabs) are typical examples for manufacturing systems with these characteristics. Our primary performance measure is total weighted tardiness (TWT). The shifting bottleneck heuristic uses a disjunctive graph to decompose the overall scheduling into scheduling problems for single tool groups. The scheduling algorithms for these scheduling problems are called subproblem solution procedures (SSPs). In previous research, only subproblem solution procedures based on dispatching rules have been considered. In this paper, we are interested in how much we can gain in terms of TWT if we apply more sophisticated subproblem solution procedures like genetic algorithms for parallel machine scheduling. We conduct simulation experiments in a dynamic job shop environment in order to assess the performance of the suggested subproblem solution procedures. It turns out that using near to optimal subproblem solution procedures leads in many situations to improved results compared to dispatching-based subproblem solution procedures.     

A note on mixed procedures for decomposing linear programming problems

This paper shows how to combine primal and dual decomposition procedures where both a vertical and a horizontal decomposition approach can be applied. The motivation for using a mixed procedure is that it improves the possibility of efficiently initializing the procedure, which has been shown to be crucial for the convergence of the procedures, Additionally mixed procedures have important interpretations as mixed price and budget planning procedures for decentralized organizations.     

New labeling procedures for the basis graph in generalized networks

Labeling procedures for the basis graph of a generalized network are introduced which build on procedures designed for pure networks. Computational results are presented which show that a primal simplex code which uses these procedures is about 60 times faster than a general purpose linear programming code.     

Parallel Galerkin domain decomposition procedures for wave equation

Parallel Galerkin domain decomposition procedures for wave equation are given. These procedures use implicit method in the sub-domains and simple explicit flux calculation on the inter-boundaries of sub-domains by integral mean method or extrapolation method. Thus, the parallelism can be achieved by these procedures. The explicit nature of the flux prediction induces a time step constraint that is necessary to preserve the stability. L²-norm error estimates are derived for these procedures. Experimental results are presented to confirm the theoretical results.     

Optimal rejection curves for exact false discovery rate control

Finner et al. (2012) provided multiple hypothesis testing procedures based on a nonlinear rejection curve for exact false discovery rate control. This paper constructs classes of such procedures and compares the most powerful procedure in each class to competing procedures.     

Extended procedures for extrapolation to the limit

In this paper, new procedures for the extrapolation to the limit of slowly convergent sequences and functions are proposed. They are based on the notions of error estimates and annihilation operators. We obtain generalizations of the discrete and confluent E-transformation, which are the most general sequence and function transformations known so far. It is shown that many transformations studied in the literature are included in our formalism. Particular cases of these procedures are discussed. Then, several extensions of the E-algorithm are given. Finally, the procedure Θ is applied to our procedures to produce new procedures for extrapolation to the limit.     

Two New Heuristic Procedures for the Joint Replenishment Problem

In this paper, we develop two new efficient heuristic procedures for the joint replenishment problem. Each of the two heuristic procedures generates iteratively a near-optimal replenishment policy starting with ordering frequencies that are derived from the solution to a relaxed version of the joint replenishment problem. Both heuristic procedures are illustrated with an example problem involving five jointly ordered items. Seven more illustrative problems, taken from the joint replenishment problem literature, are also solved to assess the cost performance of the two heuristic procedures. They both provide the global optimal replenishment policies for all the illustrative problems.     

Dual Decomposition Schemes for Multicriteria Decision Making

This paper presents two interactive procedures for decisionproblems with multiple criteria and decentralized information.One is a resource-directive procedure and the other is a price-directiveprocedure. The procedures are completely general and make nopresumptions about linearity or convexity. Nevertheless, successivelyimproved upper and lower bounds on the optimal value are determinedin each iterative step. Consequently, the communication is progressive.The procedures are illustrated in an example from integer programming.     

On tests for selection of variables and independence under multivariate regression models

The authors consider various procedures for testing the hypotheses of independence of two sets of variables and certain regression coefficients are zero under multivariate regression model. Various properties of these procedures and the asymptotic distributions associated with these procedures are also considered.     

On iterative refinements for spectral sets and spectral subspaces

Stewart (1971) and Demmel (1987) have proposed iterative procedures for refining invariant subspaces of Hilbert space operators and matrices respectively. In this paper, modifications are proposed for these procedures which facilitates their application to bounded Banach space operators. Under regularity conditions (which could include densely defined closed operators) it is shown that the modifications perform as well as or better than the procedures of Stewart and Demmel.     

Smoothing iterative block methods for linear systems with multiple right-hand sides

In the present paper, we present smoothing procedures for iterative block methods for solving nonsymmetric linear systems of equations with multiple right-hand sides. These procedures generalize those known when solving one right-hand linear systems. We give some properties of these new methods and then, using these procedures we show connections between some known iterative block methods. Finally we give some numerical examples.     

Monotone iterative methods for nonlinear operator equations ∗)

We give general affine invariant conditions for the monotone convergence of a class of iterative procedures for solving nonlinear operator equations. The theorems obtained in the paper generalize and unify many known results and provide a convenient framework for studying new iterative procedures     

Truncated selection procedures for the most probable event and the least probable event

This paper proposes two sequential procedures for selecting respectively the multinomial cell with the largest cell probability and the multinomial cell with the smallest cell probability. The stopping rule for both procedures uses truncation of the procedure studied by Ramey and Alam (1979, Biometrika, 66, 171–173). A property of the least favorable configuration of the proposed procedures is proved, which partially solves a conjecture given in Ramey and Alam (1979). The proposed procedures are compared with other procedures which have been considered in the literature and are found to be better in certain respects.     

Method for optimum cutting of rectangular sheets

This paper describes a method to divide a large rectangle into smaller ones of given size which gives minimum wastage if one is restricted to a certain class of technologically convenient cutting procedures. The method should be useful for obtaining cutting procedures for sheet metal, presspan, mica, etc.     

Bandwidth choice for differentiation

We propose a class of procedures for choosing the bandwidth, or smoothing parameter, for linear nonparametric estimates of the rth derivative of a smooth function observed with error on a discrete set of points. These procedures are based on minimizing a nearly unbiased estimate of the integrated mean square error. Theoretical justification is provided in the special case of a tapered Fourier series estimate.     

Approximation Algorithms for MAX 4-SAT and Rounding Procedures for Semidefinite Programs

Karloff and Zwick obtained recently an optimal 7/8-approximation algorithm for MAX 3-SAT. In an attempt to see whether similar methods can be used to obtain a 7/8-approximation algorithm for MAX SAT, we consider the most natural generalization of MAX 3-SAT, namely MAX 4-SAT. We present a semidefinite programming relaxation of MAX 4-SAT and a new family of rounding procedures that try to cope well with clauses of various sizes. We study the potential, and the limitations, of the relaxation and of the proposed family of rounding procedures using a combination of theoretical and experimental means. We select two rounding procedures from the proposed family of rounding procedures. Using the first rounding procedure we seem to obtain an almost optimal 0.8721-approximation algorithm for MAX 4-SAT. Using the second rounding procedure we seem to obtain an optimal 7/8-approximation algorithm for satisfiable instances of MAX 4-SAT. On the other hand, we show that no rounding procedure from the family considered can be shown, using the current techniques, to yield an approximation algorithm for MAX 4-SAT whose performance guarantee for all instances of the problem is greater than 0.8724. We also show that the integrality ratio of the proposed relaxation, as a relaxation of MAX {1, 4}-SAT, is at most 0.8754.The 0.8721-approximation for MAX 4-SAT that we seem to obtain substantially improves the performance guarantees of all previous algorithms suggested for the problem. It is extremely close to being optimal as a (7/8 + ε)-approximation algorithm for MAX 4-SAT, for any fixed ε > 0, would imply that P = NP. Our investigation also indicates, however, that additional ideas are required in order to obtain optimal 7/8-approximation algorithms for MAX 4-SAT and MAX SAT.Although most of this paper deals specifically with the MAX 4-SAT problem, we believe that the new family of rounding procedures introduced and the methodology used in the design and in the analysis of the various rounding procedures considered have a much wider range of applicability.     

Facet identification for the symmetric traveling salesman polytope

Several procedures for the identification of facet inducing inequalities for the symmetric traveling salesman polytope are given. An identification procedure accepts as input the support graph of a point which does not belong to the polytope, and returns as output some of the facet inducing inequalities violated by the point. A procedure which always accomplishes this task is calledexact, otherwise it is calledheuristic. We give exact procedures for the subtour elimination and the 2-matching constraints, based on the Gomory—Hu and Padberg—Rao algorithms respectively. Efficient reduction procedures for the input graph are proposed which accelerate these two algorithms substantially. Exact and heuristic shrinking conditions for the input graph are also given that yield efficient procedures for the identification of simple and general comb inequalities and of some elementary clique tree inequalities. These procedures constitute the core of a polytopal cutting plane algorithm that we have devised and programmed to solve a substantial number of large-scale problem instances with sizes up to 2392 nodes to optimality.Partial financial support by NSF grant DMS8508955 and ONR grant R&T4116663.Work done while visiting New York University. Partial financial support by a New York University Research Challenge Fund grant and ONR grant R&T4116663.     

删失回归模型中的变量选择

在一个删失回归模型("Tobit"模型)中,我们常常要研究如何选择重要的预报变量.本文提出了基于信息理论准则的两种变量选择程序,并建立了它们的相合性.     

具有随机效应的Wiener加速退化模型的可靠性研究

研究了有随机效应的Wiener退化模型基于加速退化数据的统计推断问题.利用广义枢轴量方法得到了模型参数和感兴趣可靠性指标的广义置信区间.说明了不含随机效应的Wiener退化模型的统计推断问题是有随机效应的Wiener退化模型的特殊情况.蒙特卡罗模拟结果显示文中提出的区间估计有较好的覆盖比例.最后利用LED加速退化数据说明文中提供的方法的有效性.