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Star reduction among minimal length addition chains

COMPUTING 2011年第4期91卷 335-352页

作者： Bahig, Hatem M. Ain Shams Univ Fac Sci Dept Math Div Comp Sci Cairo 11566 Egypt

An addition chain for a natural number n is a sequence 1 = a(0) < a(1) < ....< a(r) = n of minimal length of an addition chain for n is denoted by l(n). If j=i-1, then step is called a star step. We show that there is a minimal length addition chain for n such that the last four steps are stars. Then we conjecture that there is a minimal length addition chain for n such that the last [l(n)/2]-steps are stars. We verify that the conjecture is true for all numbers up to 2(18). An application of the result and the conjecture to generate a minimal length addition chain reduce the average CPU time by 23-29% and 38-58% respectively, and memory storage by 16-18% and 26-45% respectively for m-bit numbers with 14 <= m <= 22.

关键词： Addition chain branch and bound algorithm Minimal length addition chain Star chain

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An algorithm for Optimal Cyclic Scheduling in a Robotic Cell with Flexible Processing Times

An Algorithm for Optimal Cyclic Scheduling in a Robotic Cell...

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International Conference on Industrial Engineering and Engineering Management

作者： Yan, Pengyu Chu, Chengbin Che, Ada Yang, Naiding Northwestern Polytech Univ Sch Management Xian 710072 Peoples R China Univ Technol Troyes CNRS LOSI Inst Charles Delaunay FRE 2848 Troyes France

ISBN: (纸本)9781424426294

This paper describes an exact algorithm for the optimal cyclic scheduling in a robotic cell with flexible processing times and a material handling robot. The problem is formulated with the prohibited intervals of the cycle time based on the capacity constraints of the machines and the robot. After the analysis of the developed mathematic model, the problem is transformed to enumerate the non-prohibited intervals for the cycle time. An efficient branch and bound algorithm is proposed to complete this enumeration procedure. Computational results on randomly generated test instances indicate that the algorithm is effective.

关键词： branch and bound algorithm cyclic scheduling flexible processing times robotic cell

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A Solution of a Mathematical Model Which Simulates Football Game as a Logistics Network 7

A Solution of a Mathematical Model Which Simulates Football ...

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7th International Conference on Sport Sciences Research and Technology Support (icSPORTS)

作者： Menguc, Kenan Beykent Univ Appl Sch Logist TR-34522 Istanbul Turkey

ISBN: (纸本)9789897583834

Routing is very important in team sports as well as in many parts of daily life. On 01.07.2018, in the World Cup tournament organized in Russia, Spain lost the match with a penalty shootout although it performed a higher number of passes. As a result of the elimination of Spain despite its very high ball possession, the nature of modern football doesn't necessarily require the multiplicity of passes. It is important to know where the passes are done, rather than high amounts of them. This study has simulated a mathematical model by bringing a different interpretation to the categorization of pass throws.

关键词： Transshipment Problem Optimization Spatio-temporal Data branch and bound algorithm Football Logistic

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On the Minimization of the Width of the Control Memory of Microprogrammed Processors

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IEEE Transactions on Computers 1979年第4期C-28卷 310-316页

作者： Baer, Jean-Loup Koyama, Barbara Department of Computer Science University of Washington Seattle WA 98195 United States Lawrence Livermore Laboratory Livermore CA United States

A branch and bound method to minimize the width of the control memory of microprogrammed processors is given. Although it is exponential in the worst case, it appears much more effective than previous enumerative solutions. Furthermore, it can lead quickly to near-optimal solutions representing “good engineering” reductions. Copyright © 1979 by the Institute of Electrical and Electronics Engineers, Inc.

关键词： bin packing branch and bound algorithm control store width microprogramming near-optimal solutions NP-complete

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An Improved algorithm of Integer Programming to Solve the Cournot Model

An Improved Algorithm of Integer Programming to Solve the Co...

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International Seminar on Business and Information Management (ISBIM 2008)

作者： Wang Zhu-fang Liu Ying-jie Shenyang Univ Technol Sch Management Shenyang Peoples R China

ISBN: (纸本)9780769535609

Nash Equilibrium is the solution of the Cournot Model considering the reaction functions provided that outputs are successive. However in practice, the outputs of some products are not successive. An improved branch and bound algorithm is proposed combining the Nash Equilibrium, considering the discontinuous output. The proposed algorithm is different from the traditional algorithm where the respond functions would be converted into constrains. While the improved algorithm is used to calculate the output of each manufacturer, the worst solution arising in the mid-process of calculation will be removed firstly, and then the final common integer solution of all manufactures will be the optimal solution. The procedure of the proposed algorithm is explicated in this paper. An example where two manufactures exist is studied, and the results validate the effectiveness of the method.

关键词： quantitative economics cournot model branch and bound algorithm integer program game

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Scheduling on Identical Machines with Batch Arrivals in Semiconductor Testing House

Scheduling on Identical Machines with Batch Arrivals in Semi...

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International Conference on Industrial Engineering and Engineering Management

作者： Chung, T. P. Liao, C. J. Su, L. H. Natl Taiwan Univ Sci & Technol Dept Ind Management Taipei Taiwan Chung Yuan Christian Univ Dept Ind Engn Chungli Taiwan

ISBN: (纸本)9781424426294

In the scheduling literature, it is often assumed that jobs arrive either simultaneously or individually. However, this assumption is invalid in most practical situations because jobs usually arrive in batches, e.g., the final testing house in the manufacturing of semiconductor. The concept of batch arrivals has been mentioned in some studies, but it has not been explored from an operational viewpoint. This paper first addresses an identical parallel machine problem with batch arrivals to minimize the total completion time. Since the problem is NP-hard, a heuristic based on binary integer program Is proposed. Computational results show that the proposed heuristic can efficiently obtain good solutions with an average percentage error of 0.41.

关键词： Batch arrivals identical parallel machines semiconductor scheduling branch and bound algorithm total completion time

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Mining scheduling knowledge for job shop scheduling problem 15

Mining scheduling knowledge for job shop scheduling problem

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15th IFAC Symposium on Information Control Problems in Manufacturing

作者： Wang, C. L. Rong, G. Weng, W. Feng, Y. P. Zhejiang Univ Inst Cyber Syst & Control State Key Lab Ind Control Technol Hangzhou 310003 Zhejiang Peoples R China Waseda Univ Grad Sch Informat Prod & Syst Wakamatsu Ku Kitakyushu Fukuoka 8080135 Japan

The optimal or near-optimal schedules generated by traditional optimization or approximation methods for job shop scheduling problems (JSSP) contain valuable scheduling patterns about this kind of scheduling problems. These patterns could be used to improve the dispatching performance and provide insights into the corresponding scheduling problems. This paper uses timed Petri nets to describe the dispatching processes of the job shop scheduling scenarios. On this basis, a data mining based scheduling knowledge extraction framework is developed to mine the expected scheduling knowledge from the solutions generated by traditional optimization or approximation method for JSSP. Based on this, we show how to use the extracted knowledge as a new dispatching rule to generate complete schedules. A novel method is further developed to combine the extracted knowledge with traditional heuristics to construct new composite dispatching rules which could gain better performance. Besides, we propose a novel approach to utilize the extracted knowledge to improve a Petri net based branch and bound algorithm used in this paper. A series of experiments is carried out to evaluate the performance of the proposed methods. (C) 2015, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.

关键词： Job shop scheduling Data mining Dispatching rule Petri net branch and bound algorithm

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algorithm and Application of a Kind of Quadratic Integer Programming Model

Algorithm and Application of a Kind of Quadratic Integer Pro...

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2nd International Conference on Business Intelligence and Financial Engineering

作者： Wang, Zhufang Liu, Yingjie Shenyang Univ Technol Sch Management Shenyang 110178 Peoples R China

ISBN: (纸本)9780769537054

In order to solve a kind of quadratic integer programming problem with unrestrained conditions and multi-objective function, improvements on the traditional branch and bound algorithm are carried out in this paper. By introducing response function, a practical branch and bound algorithm to solve the quadratic integer programming model is derived. The procedure of the proposed algorithm is explicated in this paper and an example with two manufactures is studied. Numerical results show that the proposed algorithm is more effective than the traditional branch and bound algorithm, and fit for more complex problems.

关键词： branch and bound algorithm quadratic integer programming response function cournot model

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Optimal EV Charging Network Design: When Users Have Choices 11

Optimal EV Charging Network Design: When Users Have Choices

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11th IEEE International Conference on Wireless Communications and Signal Processing (WCSP)

作者： Chen, Yuchen Qin, Zhida Gan, Xiaoying Shanghai Jiao Tong Univ Dept Elect Engn Shanghai 200240 Peoples R China Southeast Univ Natl Mobile Commun Res Lab Nanjing 210096 Jiangsu Peoples R China

ISBN: (纸本)9781728135557

The penetration rate of Electric Vehicles is increasing as expected. To meet the charging needs, numerous charging stations are built, which are small because of space and grid limitation in city. Such a high density distribution of charging stations offers EV users more choices when seeking for charging service. In order to offer users better choices with global knowledge, recommendation systems are developed. However, the cost generated from recommendation system is not considered when designing the charging network, which result in an increase of overall system cost. Therefore, this paper mainly focuses on the charging network design problem under generalized recommendation systems to find a better co-working solution. We first formulate the EV charging network design as a cost minimization problem, considering construction cost, incentive cost for users' to transfer in the charging network, and cost for the loss of users leaving the system, which is a nonlinear mixed-integer optimization problem. In order to solve such problem, we propose a branch and bound algorithm. By combining local search heuristic and cutting plane process, the exact optimal solution can be obtained efficiently. To demonstrate the superiority of the scheme proposed by us, simulation are conducted.

关键词： Electric Vehicles Charging Network Nonlinear Mixed-Integer Programming branch and bound algorithm

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Computational Approaches for Efficient Scheduling of Steel Plants as Demand Response Resource 19

Computational Approaches for Efficient Scheduling of Steel P...

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19th Power Systems Computation Conference (PSCC)

作者： Zhang, Xiao Hug, Gabriela Kolter, Zico Harjunkoski, Iiro Carnegie Mellon Univ Elect & Comp Engn Pittsburgh PA 15213 USA Swiss Fed Inst Technol Informat Technol & Elect Engn Zurich Switzerland Carnegie Mellon Univ Comp Sci Pittsburgh PA 15213 USA ABB Corp Res Ladenburg Germany

ISBN: (纸本)9788894105124

Demand response is seeing increased popularity worldwide and industrial loads are actively taking part in this trend. As a host of energy-intensive industrial processes, steel plants have both the motivation and potential to provide demand response. However, the scheduling of steel plants is very complex and the involved computations are intense. In this paper, we focus on these difficulties and propose methods such as adding cuts and implementing an application-specific branch and bound algorithm to make the computations more tractable.

关键词： branch and bound algorithm mixed integer programming demand response steel plant scheduling resource task network

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