Table of Content

30 June 2016, Volume 4 Issue 2

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Management Science

An Examination of Some Factory Physics Principles

Hong Chen,Heng-Qing Ye

2016, 4(2):  131.  doi:10.1007/s40305-015-0115-x

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In this paper, we examine some principles in managing manufacturing systems. These principles are concerned with the variability, the utilization, the rework, the lead time, and the constant work-in-process efficiency. While these principles are developed through analyzing some simpler disconnected flow line manufacturing systems, we examine whether they can have broad applications. For some of these principles, we provide sufficient conditions, while for others, we provide counterexamples. Our analysis suggests that we should be very cautious about these laws when applied to non-Markov and non-tandem systems.

Discrete Optimization

A New Infeasible-Interior-Point Algorithm Based on Wide Neighborhoods for Symmetric Cone Programming

Chang-He Liu,Dan Wu,You-Lin Shang

2016, 4(2):  147.  doi:DOI10.1007/s40305-016-0118-2

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In this paper, we present an infeasible-interior-point algorithm, based on a new wide neighborhood for symmetric cone programming. We treat the classical Newton direction as the sum of two other directions, and equip them with different step sizes.We prove the complexity bound of the new algorithm for the Nesterov-Todd (NT) direction, and the xs and sx directions. The complexity bounds obtained here are the same as small neighborhood infeasible-interior-point algorithms over symmetric cones.

Continuous Optimization

An Efficient Inexact Newton-CG Algorithm for the Smallest Enclosing Ball Problem of Large Dimensions

Ya-Feng Liu, Rui Diao,Feng Ye,Hong-Wei Liu

2016, 4(2):  167.  doi:DOI10.1007/s40305-015-0097-8

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In this paper, we consider the problem of computing the smallest enclosing ball (SEB) of a set of m balls in Rⁿ ,where the product mn is large. We first approximate the non-differentiable SEB problem by its log-exponential aggregation function and then propose a computationally efficient inexact Newton-CG algorithm for the smoothing approximation problem by exploiting its special (approximate) sparsity structure. The key difference between the proposed inexact Newton-CG algorithm and the classical Newton-CG algorithm is that the gradient and the Hessian-vector product are inexactly computed in the proposed algorithm, which makes it capable of solving the large-scale SEB problem. We give an adaptive criterion of inexactly computing the gradient/Hessian and establish global convergence of the proposed algorithm.We illustrate the efficiency of the proposed algorithm by using the classical Newton-CG algorithm as well as the algorithm from Zhou et al. (Comput Optim Appl 30:147–160, 2005) as benchmarks.

Discrete Optimization

Transportation Problem with Multi-choice Cost and Demand and Stochastic Supply

Sankar Kumar Roy

2016, 4(2):  193.  doi:DOI10.1007/s40305-016-0125-3

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This paper analyzes the multi-choice stochastic transportation problem where the cost coefficients of the objective function and the demand parameters of the constraints follow multi-choice parameters. Assume that the supply parameters of the constraints in a transportation problem (TP) follow logistic distribution. The main objective of this paper is to select an appropriate choice from the multi-choices for the cost coefficients of the objective function and the demand of the constraints in the TP by introducing Lagrange’s interpolating polynomial in such a way that the total cost is minimized and satisfies the required demand. Using stochastic programming, the stochastic supply constraints of the TP are transformed into deterministic constraints. Finally, a non-linear deterministic model is formulated. Using Lingo software, the optimal solution of the proposed problem is derived. To illustrate the methodology, a real-life problem on the TP is considered.

Continuous Optimization

Semidefinite Relaxation for Two Mixed Binary Quadratically Constrained Quadratic Programs: Algorithms and Approximation Bounds

Zi Xu, Ming-Yi Hong

2016, 4(2):  205.  doi:DOI10.1007/s40305-015-0082-2

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This paper develops new semidefinite programming (SDP) relaxation techniques for two classes of mixed binary quadratically constrained quadratic programs and analyzes their approximation performance. The first class of problems finds two minimum norm vectors in N-dimensional real or complex Euclidean space, such that M out of 2M concave quadratic constraints are satisfied. By employing a special randomized rounding procedure, we show that the ratio between the norm of the optimal
solution of this model and its SDP relaxation is upper bounded by 54M²/ π in the real case and by 2√4M/π in the complex case. The second class of problems finds a series of minimum norm vectors subject to a set of quadratic constraints and cardinality constraints with both binary and continuous variables. We show that in this case the approximation ratio is also bounded and independent of problem dimension for both the real and the complex cases.

Discrete Optimization

General Schemes of Iterative Optimization with Applications to Optimal Control Problems

Oles Vladimirovich Fesko,Vladimir Iosifovich Gurman

2016, 4(2):  223.  doi:DOI10.1007/s40305-015-0102-2

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A general (abstract) scheme of iterative improvement and optimization on the base of extension, localization principles which would help to generate new concrete methods and algorithms for new problems is proposed. Application to optimal control problems for continuous systems is considered. Visual example is given.

The Optimal Tenement Allocation for Reducing Traffic Burden

Ke-Lin Luo,Yin-Feng Xu,Yong-Feng Cao

2016, 4(2):  233.  doi:DOI10.1007/s40305-015-0100-4

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For reducing traffic jams without widening streets, we come up with a tenement rearrangement problem. In this paper, we study a tenement allocation model which includes two types of tenants, i.e., typical tenants and special tenants who owned houses by themselves. The optimal allocation is that total transportation cost is minimized without undermining tenants’ individual housing preference or increasing individual cost. Besides, we present a Modified Hungarian Algorithm for the above tenement allocation problem and prove that it can be solved in polynomial time. Furthermore, computational tests show that this algorithm has a good performance.

Continuous Optimization

Alternating Direction Method of Multipliers for 1₁-1₂-Regularized Logistic Regression Model

Yan-Qin Bai| Kai-Ji Shen

2016, 4(2):  243.  doi:DOI10.1007/s40305-015-0090-2

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Logistic regression has been proved as a promising method for machine learning, which focuses on the problem of classification. In this paper, we present an  1₁-1₂-regularized logistic regression model, where the 1₁-norm is responsible for yielding a sparse logistic regression classifier and the  1₂-norm for keeping better classification accuracy. To solve the 1₁1₂-regularized logistic regression model, we develop an alternating direction method of multipliers with embedding limited-Broyden-Fletcher Goldfarb-Shanno (L-BFGS) method. Furthermore, we implement our model for binary classification problems by using real data examples selected from the University of California, Irvine Machines Learning Repository (UCI Repository).We compare our numerical results with those obtained by the well-known LIBSVM and SVM-Light software. The numerical results showthat our 1₁-1₂-regularized logistic regression model achieves better classification and less CPU Time.

Discrete Optimization

On the Stability of the Solution Set Mappings to Parametric Set Optimization Problems

Yang-Dong Xu|Ping-Ping Zhang

2016, 4(2):  255.  doi:10.1007/s40305-015-0110-2

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In this paper, under some suitable assumptions without any involving information on the solution set, we give some sufficient conditions for the upper semicontinuity, lower semicontinuity, and closedness of the solution set mapping to a parametric set optimization problem with possible less order relation.