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

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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MULTIPLE algorithm SOLUTION TO THE ARTIFICIAL-INTELLIGENCE DESIGN CHALLENGE

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 1988年第5期11卷 397-402页

作者： DOTY, KW The Aerospace Corporation El Segundo California

This paper responds to the Artificial Intelligence Design Challenge at the 1987 AIAA Guidance, Navigation, and Control Conference. It describes a computer program that solves a variation of the classical traveling salesman problem that is representative of problems encountered in complex guidance and control systems. The problem is to find a tour connecting some or all of 11 cities that maximizes the total value of the cities visited while meeting a travel budget constraint. The solution procedure used was to construct several candidate tours using a variety of approaches, then adjust the highest-value tour found by solving the traveling salesman problem to find the optimal city ordering. An efficient bounding procedure was used to reduce the number of computations required to evaluate the stochastic budget constraint. The program consistently produced in a small amount of time the best answers known on 25 data sets designed to test the program's robustness.

关键词： Artificial Intelligence Computer Programs Control Systems Perturbation Method Computing Probability Distribution 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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An algorithm for the capacitated, multi-commodity multi-period facility location problem

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COMPUTERS & OPERATIONS RESEARCH 2001年第5期28卷 411-427页

作者： Canel, C Khumawala, BM Law, J Loh, A Univ N Carolina Dept Prod & Decis Sci Wilmington NC 28403 USA Univ Houston Dept Informat & Decis Sci Houston TX 77204 USA Chinese Univ Hong Kong Dept Decis Sci & Managerial Econ Shatin Hong Kong Peoples R China Univ Houston Dept Ind Engn Houston TX 77204 USA

There are substantial number of exact and heuristic solution methods proposed for solving the facilities location problems. This paper develops an algorithm to solve the capacitated, multi-commodity, multiperiod (dynamic), multi-stage facility location problem. The literature on such composite facility location problem is still sparse, The proposed algorithm consists of two parts: in the first part branch and bound is used to generate a list of candidate solutions for each period and then dynamic programming is used to find the optimal sequence of configurations over the multi-period planning horizon. bounds commonly known in the location literature as delta and omega are used extensively to effectively reduce the total number of transshipment subproblems needed to be solved. The proposed algorithm is particularly effective when the facility reopening and closing costs are relatively significant in the multi-period problem. An example problem is included to illustrate the proposed solution procedure.

关键词： facility location branch and bound algorithm

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Constraint reformulation and a Lagrangian relaxation-based solution algorithm for a least expected time path problem

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TRANSPORTATION RESEARCH PART B-METHODOLOGICAL 2014年 59卷 22-44页

作者： Yang, Lixing Zhou, Xuesong Beijing Jiaotong Univ State Key Lab Rail Traff Control & Safety Beijing 100044 Peoples R China Arizona State Univ Sch Sustainable Engn & Built Environm Tempe AZ 85287 USA

Using a sample-based representation scheme to capture spatial and temporal travel time correlations, this article constructs an integer programming model for finding the a priori least expected time paths. We explicitly consider the non-anticipativity constraint associated with the a priori path in a time-dependent and stochastic network, and propose a number of reformulations to establish linear inequalities that can be easily dualized by a Lagrangian relaxation solution approach. The relaxed model is further decomposed into two sub-problems, which can be solved directly by using a modified label-correcting algorithm and a simple single-value linear programming method. Several solution algorithms, including a sub-gradient method, a branch and bound method, and heuristics with additional constraints on Lagrangian multipliers, are proposed to improve solution quality and find approximate optimal solutions. The numerical experiments investigate the quality and computational efficiency of the proposed solution approach. (C) 2013 Elsevier Ltd. All rights reserved.

关键词： A priori least expected time path Time-dependent traffic network Lagrangian relaxation branch and bound algorithm

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Worst-case analysis of the X-38 crew return vehicle flight control system

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 2001年第2期24卷 261-269页

作者： Shin, JY Balas, GJ Packard, AK Univ Minnesota Dept Aerosp Engn & Mech Minneapolis MN 55455 USA Univ Calif Berkeley Dept Mech Engn Berkeley CA 94704 USA

A linear fractional transformation (LFT model of the linearized equation of the lateral-directional axes of the X-38 crew return vehicle is developed to facilitate the analysis of flight control systems. The LFT model represents uncertainty in nine aerodynamic stability derivatives at a given flight condition with frequency-domain performance specifications. The X-38 LFT model combined with a controller at specific Right conditions is used to determine the aerodynamic coefficients that result in the worst-case performance and gain/phase margin of the closed-loop system. The,objective is to verify that a given controller remains stable and achieves desired performance objectives for all predefined aerodynamic variations at select operating conditions along its flight trajectory.

关键词： Crew Return Vehicle Flight Control System Aerodynamic Stability Closed Loop System Digital to Analog Converters Control Systems Ailerons International Space Station branch and bound algorithm Johnson Space Center

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Bilevel integer programming on a Boolean network for discovering critical genetic alterations in cancer development and therapy

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2022年第2期300卷 743-754页

作者： Moon, Kyungduk Lee, Kangbok Chopra, Sunil Kwon, Steve Pohang Univ Sci & Technol Dept Ind & Management Engn Pohang 37673 South Korea Northwestern Univ Kellogg Sch Management Evanston IL 60208 USA Holy Name Med Ctr Teaneck NJ 07666 USA

Boolean network is a modeling tool that describes a dynamic system with binary variables and their logical transition formulas. Recent studies in precision medicine use a Boolean network to discover critical genetic alterations that may lead to cancer or target genes for effective therapies to individuals. In this paper, we study a logical inference problem in a Boolean network to find all such critical genetic alterations in a minimal (parsimonious) way. We propose a bilevel integer programming model to find a single minimal genetic alteration. Using the bilevel integer programming model, we develop a branch and bound algorithm that effectively finds all of the minimal alterations. Through a computational study with eleven Boolean networks from the literature, we show that the proposed algorithm finds solutions much faster than the state-of-the-art algorithms in large data sets. (C) 2021 Elsevier B.V. All rights reserved.

关键词： Bioinformatics Boolean network Bilevel programming branch and bound algorithm

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The design of capacitated facility networks for long term care service

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COMPUTERS & INDUSTRIAL ENGINEERING 2015年 89卷 177-185页

作者： Song, Byung Duk Ko, Young Dae Hwang, Hark Korea Adv Inst Sci & Technol Dept Ind & Syst Engn Daejeon 305701 South Korea Deloitte Touche Tohmatsu Ltd Deloitte Consulting Data Analyt Grp Seoul 150945 South Korea

Life expectancy is going up and the demand of long term care facilities is increasing in most countries. This study deals with designing problem of facility networks for long-term care services in a city consisting of a number of regions. Assuming that in each region a candidate site for long-term care facility exists, we seek to identify regions where opening of a long-term care facility is desirable and also determine the type of new facility. For the problem, an integer programming model is formulated with the objective of minimizing the total construction cost. The closest assignment rule is adopted to reflect the preference of patient in choosing long term care facility by assigning patient to an open facility closest from his home. To solve the model, we develop a branch and bound algorithm for exact solution and a genetic algorithm to solve large sized problem. The validity of the mathematical model and the proposed algorithms are illustrated through a number of problem instances. (C) 2015 Elsevier Ltd. All rights reserved.

关键词： Long term care services Closest assignment rule branch and bound algorithm Genetic algorithm

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Improved generation of minimal addition chains

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COMPUTING 2006年第2期78卷 161-172页

作者： Bahig, Hatem M. Ain Shams Univ Fac Sci Dept Math Comp Sci Cairo Egypt

An addition chain for a natural number n is a sequence 1 = a(0) < a(1) <. . . a(r) = n of numbers such that for each 0 < i <= r, a(i) = a(j) + a(k) for some 0 <= k <= j < i. An improvement by a fa... 详细信息

An addition chain for a natural number n is a sequence 1 = a(0) < a(1) <. . . a(r) = n of numbers such that for each 0 < i <= r, a(i) = a(j) + a(k) for some 0 <= k <= j < i. An improvement by a factor of 2 in the generation of all minimal (or one) addition chains is achieved by finding sufficient conditions for star steps, computing what we will call nonstar lower bound in a minimal addition chain and omitting the sorting step.

关键词： addition chain branch and bound algorithm nonstar lower bound sorting

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