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Rebalancing the assembly lines: exact solution approaches

INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH 2017年第20期55卷 5991-6010页

作者： Sanci, Ece Azizoglu, Meral Univ Michigan Dept Ind & Operat Engn Ann Arbor MI 48109 USA Middle East Tech Univ Dept Ind Engn Ankara Turkey

In this study, we consider an assembly line rebalancing problem with disruptions caused by workstation breakdowns or shutdowns. After the disruption, we aim to find a rebalance so as to catch the trade-off between the efficiency measure of cycle time and stability measure of number of tasks assigned to different workstations in the original and new balances. Our aim is to generate all nondominated objective vectors with respect to the efficiency and stability measures. We develop two optimisation algorithms: a Mixed Integer Linear Programming-based algorithm and a branch and bound algorithm. The results of our experiments have shown the favourable performances of both algorithms and the superiority of the branch and bound algorithm.

关键词： assembly lines rebalancing mixed integer linear programming branch and bound algorithm nondominated objective vectors

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Signed Clique Search in Signed Networks: Concepts and algorithms

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IEEE TRANSACTIONS ON KNOWLEDGE AND DATA ENGINEERING 2021年第2期33卷 710-727页

作者： Li, Ronghua Dai, Qiangqiang Qin, Lu Wang, Guoren Xiao, Xiaokui Yu, Jeffrey Xu Qiao, Shaojie Beijing Inst Technol Beijing 100081 Peoples R China Univ Technol Sydney Ultimo NSW 2007 Australia Natl Univ Singapore Singapore 119077 Singapore Chinese Univ Hong Kong Shatin Hong Kong Peoples R China Chengdu Univ Informat Technol Chengdu 610225 Sichuan Peoples R China

Mining cohesive subgraphs from a network is a fundamental problem in network analysis. Most existing cohesive subgraph models are mainly tailored to unsigned networks. In this paper, we study the problem of seeking cohesive subgraphs in a signed network, in which each edge can be positive or negative, denoting friendship or conflict, respectively. We propose a novel model, called maximal (alpha, k)-clique, that represents a cohesive subgraph in signed networks. Specifically, a maximal (alpha, k)-clique is a clique in which every node has at most k negative neighbors and at least inverted right perpendicular alpha kinverted left perpendicular positive neighbors (alpha >= 1). We show that the problem of enumerating all maximal (alpha, k)-cliques in a signed network is NP-hard. To enumerate all maximal (alpha, k)-cliques efficiently, we first develop an elegant signed network reduction technique to significantly prune the signed network. Then, we present an efficient branch and bound enumeration algorithm with several carefully-designed pruning rules to enumerate all maximal (alpha, k)-cliques in the reduced signed network. In addition, we also propose an efficient algorithm with three novel upper-bounding techniques to find the maximum (alpha, k)-clique in a signed network. The results of extensive experiments on five large real-life datasets demonstrate the efficiency, scalability, and effectiveness of our algorithms.

关键词： Signed clique signed network maximal clique enumeration branch and bound algorithm

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Optimal parallel machines scheduling with machine availability and eligibility constraints

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INTERNATIONAL JOURNAL OF ADVANCED MANUFACTURING TECHNOLOGY 2008年第1-2期36卷 132-139页

作者： Sheen, Gwo-Ji Liao, Lu-Wen Lin, Cheng-Feng Natl Cent Univ Inst Ind Management Tao Yuan 32001 Taiwan

In reality, the machine might become unavailable due to machine breakdowns or various inevitable reasons, and machine might have different capability to processing job. Motivated by this, we consider the problem of scheduling n non-preemptive and independent jobs on m identical machines incorporating machine availability and eligibility constraints while minimizing the maximum lateness. Each machine is capable of processing at specific availability intervals. We develop a branch and bound algorithm applying several immediate selection rules for solving this scheduling problem.

关键词： parallel machine scheduling availability constraint eligibility constraint maximum lateness branch and bound algorithm

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SOLUTION APPROACHES TO LINEAR FRACTIONAL PROGRAMMING AND ITS STOCHASTIC GENERALIZATIONS USING SECOND ORDER CONE APPROXIMATIONS

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SIAM JOURNAL ON OPTIMIZATION 2021年第1期31卷 945-971页

作者： Kim, Cheolmin Mehrotra, Sanjay Northwestern Univ Dept Ind Engn & Management Sci Evanston IL 60208 USA

We consider linear fractional programming problems in a form of which the linear fractional program and its stochastic and distributionally robust counterparts with finite support are special cases. We introduce a novel reformulation that involves differences of square terms in the constraint, subsequently using a piecewise linear approximation for the concave part. Using the resulting second order cone programs (SOCPs), we develop a solution algorithm in the branch and bound framework. Our method iteratively refines the piecewise linear approximations by dividing hyper-rectangles and solves SOCPs to obtain lower bounds for the sub-hyper-rectangles. We derive a bound on the optimality gap as a function of the approximation errors at the iterate and prove that the number of iterations to attain an epsilon-optimal solution is in the order of O(root epsilon). Numerical experiments show that the proposed algorithm scales better than state-of-the-art linear-programming-based algorithms and commercial solvers to solve linear fractional programs. Specifically, the proposed algorithm achieves two or more digits of accuracy in significantly less time than the time required by the known algorithms on medium to larger size problem instances. Experimental results with Wasserstein ambiguity sets reveal that our reformulation-based approach solves small size distributionally robust linear fractional programs, with the cardinality of support up to 25.

关键词： distributionally robust optimization linear fractional programming second order cone approximations branch and bound algorithm convergence analysis

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A simultaneous diagonalization based SOCP relaxation for portfolio optimization with an orthogonality constraint

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COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 2023年第1期85卷 247-261页

作者： Xu, Zhijun Zhou, Jing Zhejiang Univ Technol Coll Sci Hangzhou 310023 Peoples R China

The portfolio rebalancing with transaction costs plays an important role in both theoretical analyses and commercial applications. This paper studies a standard portfolio problem that is subject to an additional orthogonality constraint guaranteeing that buying and selling a same security do not occur at the same time point. Incorporating the orthogonality constraint into the portfolio problem leads to a quadratic programming problem with linear complementarity constraints. We derive an enhanced simultaneous diagonalization based second order cone programming (ESDSOCP) relaxation by taking advantage of the feature that the objective and constraint matrices are commutative. The ESDSOCP relaxation has lower computational complexity than the semi-definite programming (SDP) relaxation, and it is proved to be as tight as the SDP relaxation. It is worth noting that the original simultaneous diagonalization based second order cone programming relaxation (SDSOCP) is only guaranteed to be as tight as the SDP relaxation on condition that the objective matrix is positive definite. Note that the objective matrix in this paper is positive semidefinite (while not positive definite), thus the ESDSOCP relaxation outperforms the original SDSOCP relaxation. We further design a branch and bound algorithm based on the ESDSOCP relaxation to find the global optimal solution and computational results illustrate the effectiveness of the proposed algorithm.

关键词： Portfolio optimization Second order cone programming relaxation Semi-definite programming relaxation branch and bound algorithm Simultaneous diagonalization Orthogonality constraint

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Mean-variance portfolio optimal problem under concave transaction cost

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APPLIED MATHEMATICS AND COMPUTATION 2006年第1期174卷 1-12页

作者： Xue, HG Xu, CX Feng, ZX Xi An Jiao Tong Univ Fac Sci Sch Econ & Finance Xian 710049 Peoples R China Xi An Jiao Tong Univ Fac Sci Xian 710049 Peoples R China Xi An Jiao Tong Univ JinHe Ctr Econ Res Xian 710049 Peoples R China

In this paper, the classical mean-variance portfolio model is modified for calculating a globally optimal portfolio under concave transaction costs. A non-decreasing concave function is employed to approximate origin transaction cost function. The resulting model is a. D-C (difference of two convex functions) programming and a branch and bound algorithm is designed to solve the problem. A series Of numerical experiments on the model is presented. The history data of nine stocks in Shan Xi province is used in experiments, and efficient frontiers generated from the resulting model with different limitations on investments are presented to show the effect of the model and the efficiency of the algorithm solving the model. (c) 2005 Elsevier Inc. All rights reserved.

关键词： mean-variance concave transaction cost globally optimal portfolio branch and bound algorithm efficient frontier

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Optimization of a long-short portfolio under nonconvex transaction cost

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COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 2005年第1-2期32卷 115-132页

作者： Konno, H Akishino, K Yamamoto, R Chuo Univ Dept Ind & Syst Engn Hachioji Tokyo Japan

The purpose of this paper is to propose a practical branch and bound algorithm for solving a class of long-short portfolio optimization problem with concave and d.c. transaction cost and complementarity conditions on the variables. We will show that this algorithm can solve a problem of practical size and that the long-short strategy leads to a portfolio with significantly better risk-return structure compared with standard purchase only portfolio both in terms of ex-ante and ex-post performance.

关键词： portfolio theory long-short portfolio concave cost d.c. cost branch and bound algorithm global optimization

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Single machine scheduling to minimize maximum lateness subject to release dates and precedence constraints

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COMPUTERS & OPERATIONS RESEARCH 2010年第9期37卷 1537-1543页

作者： Liu, Zhixin Univ Michigan Dept Management Studies Coll Business Dearborn MI 48126 USA

This paper considers the problem of finding a nonpreemptive schedule for a single machine to minimize the maximum lateness with release dates and precedence constraints. A branch and bound algorithm is developed. The algorithm uses four different heuristics to find upper bounds at the initial branch node: early release date heuristic, modified Schrage's heuristic, heuristic BLOCK, and a variable neighborhood descent procedure. At each branch node, two branches evolve from a schedule found by heuristic BLOCK using a binary branching rule based on bottleneck and critical jobs, and a lower bound is obtained by optimally solving the relaxed problem with preemption. The algorithm solves 14,984 out of the 15,000 systematically generated instances with up to 1,000 jobs within I minute of CPU time. (C) 2009 Elsevier Ltd. All rights reserved.

关键词： Deterministic scheduling Maximum lateness Release date Precedence constraint branch and bound algorithm

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OPTIMAL PLACEMENT OF ACTIVE ELEMENTS IN CONTROL AUGMENTED STRUCTURAL SYNTHESIS

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AIAA JOURNAL 1993年第10期31卷 1906-1915页

作者： SEPULVEDA, AE JIN, IM SCHMIT, LA University of California Los Angeles Los Angeles California 90024

A methodology for structural/control synthesis is presented in which the optimal location of active members is treated in terms of (0,1) variables. Structural member sizes, control gains, and (0,1) placement variables are treated simultaneously as design variables. Optimization is carried out by generating and solving a sequence of explicit approximate problems using a branch and bound strategy. Intermediate design variable and intermediate response quantity concepts are used to enhance the quality of the approximate design problems. Numerical results for example problems are presented to illustrate the efficacy of the design procedure set forth.

关键词： Structural Members Trusses Damping Coefficient Closed Loop System Dynamic Displacements Piezoelectric Materials Feedback Control Young's Modulus branch and bound algorithm Nonlinear Programming

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Application of mathematical programming to the fixed channel assignment problem in mobile radio networks

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IEE PROCEEDINGS-COMMUNICATIONS 1997年第4期144卷 257-264页

作者： Giortzis, AI Turner, LF Univ London Imperial Coll Sci Technol & Med Dept Elect & Elect Engn London SW7 2BT England

The fixed channel assignment problem (CAP) is formulated as an integer linear programming problem with compatibility and requirement constraints. The proposed formulation is general and has been extended for the case of maximum packing fixed channel assignment problems. For the solution of the resulting formulation a special branch and bound algorithm has been used. The exploitation of the problem's special structure can improve the computational efficiency of the algorithm used. The model has been applied to a number of different benchmark problems that have appeared in the literature. The examples presented show that using the proposed formulation and a specially designed branch and bound algorithm, it is possible to solve optimally and efficiently fairly large channel assignment problems.

关键词： mobile radio network channel assignment integer linear programming branch and bound algorithm

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