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Priority allocation rules for single machine total weighted linear and square tardiness problems

PRODUCTION ENGINEERING-RESEARCH AND DEVELOPMENT 2016年第4-5期10卷 471-476页

作者： Yin, Aihua Punnen, Abraham P. Hu, Dongping Jiangxi Univ Finance & Econ Sch Software & Commun Engn Nanchang 330032 Peoples R China Simon Fraser Univ Dept Math Surrey BC V3T 0A3 Canada

The single machine scheduling problems minimizing total weighted tardiness and square tardiness objectives have been studied in literature for many years. Applications of the model include sequencing problems in manufacture and logistics. This paper proposes two new priority allocation rules, PAR 1 and PAR 2, for solving these two problems. Unlike most known dispatch rules and constructive algorithms, our new rules take advantage of not only the jobs' static characters values such as the process time, the due date and the weight, but also their dynamic characters values, i.e., the slack and the values of the objective function for different choices of some jobs. At any time when a job is being selected to process, some of the unprocessed jobs are delayed while the others are not. It means that the characters of these two sorts of jobs are different from each other. So, combining these characters with the objective function's value can obtain effective dispatch rule. Experimental analysis based on the instances from the OR-Library discloses that our priority allocation rules, PAR 1 and PAR 2, are efficient and have significant advantages over traditional approaches.

关键词： Single machine scheduling Priority allocation rule Heuristic constructive algorithm

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An enhanced harmony search integrated with adaptive mutation strategy

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INTERNATIONAL JOURNAL OF COMPUTING SCIENCE AND MATHEMATICS 2022年第2期16卷 136-148页

作者： Deng, Ying Zhong, Yiwen Wang, Lijin Fujian Agr & Forestry Univ Coll Comp & Informat Sci Fuzhou Peoples R China Fujian Agr & Forestry Univ Fujian Prov Univ Key Lab Smart Agr & Forestry Fuzhou Peoples R China Wuyi Univ Digital Fujian Tourism Big Data Inst Wuyishan 354300 Peoples R China

Aiming at making improvements on solutions to function optimisation problems, an enhanced harmony search, called EHS, is proposed by hybridising differential mutation strategies. EHS employs differential mutation strategies after a solution generated by harmony search, then the solution is integrated into the differential mutation strategies as a target or current vector. Moreover, four differential mutation operators, including target-to-rand/1, target-to-rand/2, target-to-best/1 and target-to-best/2 are invoked adaptively in a random way. Extensive experiments on CEC2014 benchmark functions demonstrate EHS is effective and efficient with the combination of harmony search and the differential mutation strategies.

关键词： harmony search differential mutation adaptive strategy current vector constructive algorithm

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Two-loop superstrings VII. Cohomology of chiral amplitudes

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NUCLEAR PHYSICS B 2008年第3期804卷 421-506页

作者： D'Hoker, Eric Phong, D. H. Univ Calif Los Angeles Dept Phys & Astron Los Angeles CA 90095 USA Columbia Univ Dept Math New York NY 10027 USA

The relation between superholomorphicity and holomorphicity of chiral superstring N-point amplitudes for NS bosons on a genus 2 Riemann surface is shown to be encoded in a hybrid cohomology theory, incorporating elements of both de Rham and Dolbeault cohomologies. A constructive algorithm is provided which shows that, for arbitrary N and for each fixed even spin structure, the hybrid cohomology classes of the chiral amplitudes of the N-point function on a surface of genus 2 always admit a holomorphic representative. Three key ingredients in the derivation are a classification of all kinematic invariants for the N-point function, a new type of 3-point Green's function, and a recursive construction by monodromies of certain sections of vector bundles over the moduli space of Riemann surfaces, holomorphic in all but exactly one or two insertion points. (c) 2008 Elsevier B.V. All rights reserved.

关键词： STRING PERTURBATION-THEORY NON-RENORMALIZATION THEOREM SUPER RIEMANN SURFACES COSMOLOGICAL CONSTANT MODULAR-FORMS FERMIONIC STRINGS NONRENORMALIZATION THEOREMS 4-PARTICLE AMPLITUDE OPERATOR-FORMALISM SLICE INDEPENDENCE constructive algorithm Riemann surfaces Holomorphic Amplitude

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Characterization of Cheeger sets for convex subsets of the plane

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PACIFIC JOURNAL OF MATHEMATICS 2006年第1期225卷 103-118页

作者： Kawohl, Bernd Lachand-Robert, Thomas Univ Cologne Inst Math D-50923 Cologne Germany Univ Savoie Lab Math F-73376 Le Bourget Du Lac France

Given a planar convex domain Omega, its Cheeger set l(Omega) is defined as the unique minimizer of vertical bar partial derivative X vertical bar/vertical bar X vertical bar among all nonempty open and simply connected subsets X of Omega. We prove an interesting geometric property of l(Omega), characterize domains Omega which coincide with l(Omega) and provide a constructive algorithm for the determination of l(Omega).

关键词： Cheeger constant Cheeger set convexity constructive algorithm connection-like coycle

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On application of generalised polynomials to constructing algorithms to recognise properties of k-valued functions defined by polynomials

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DISCRETE MATHEMATICS AND APPLICATIONS 2012年第4期22卷 409-420页

作者： Bukhman, A. V.

In this paper, we suggest an approach to constructing algorithms to recognise properties of k-valued functions defined by polynomials (for prime k). This approach is based on the concept of a generalised polynomial over a system of functions we introduce here. We establish a criterion for uniqueness of representation of a k-valued function by a generalised polynomial and prove a basic theorem which yields conditions for existence of polynomial recognising algorithms. We give examples of application of the basic theorem to recognition of the property of a k-valued function to preserve a predicate. This research was supported by the Russian Foundation for Basic Research, grant 1200706a.

关键词： algorithms constructive algorithm Polynomial Nutritive Value Theorem uniqueness

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Solving the inverse Sturm-Liouville problem with singular potential and with polynomials in the boundary conditions

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ANALYSIS AND MATHEMATICAL PHYSICS 2023年第5期13卷 1-35页

作者： Chitorkin, Egor E. Bondarenko, Natalia P. Samara Natl Res Univ Inst IT & Cybernet Moskovskoye Shosse 34 Samara 443086 Russia Saratov NG Chernyshevskii State Univ Dept Mech & Math Astrakhanskaya 83 Saratov 410012 Russia Samara Natl Res Univ Dept Appl Math & Phys Moskovskoye Shosse 34 Samara 443086 Russia Peoples Friendship Univ Russia RUDN Univ 6 Miklukho Maklaya St Moscow 117198 Russia

In this paper, we for the first time get constructive solution for the inverse Sturm-Liouville problem with complex-valued singular potential and with polynomials of the spectral parameter in the boundary conditions. The uniqueness of recovering the potential and the polynomials from the Weyl function is proved. An algorithm of solving the inverse problem is obtained and justified. More concretely, we reduce the nonlinear inverse problem to a linear equation in the Banach space of bounded infinite sequences and then derive reconstruction formulas for the problem coefficients, which are new even for the case of regular potential. Note that the spectral problem in this paper is investigated in the general non-self-adjoint form, and our method does not require the simplicity of the spectrum. In the future, our results can be applied to investigation of the inverse problem solvability and stability as well as to development of numerical methods for the reconstruction.

关键词： Inverse spectral problems Sturm-Liouville operator Polynomials in the boundary conditions Singular potential Uniqueness theorem constructive algorithm

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CRITICAL PATHS IN CIRCUITS WITH LEVEL-SENSITIVE LATCHES

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IEEE TRANSACTIONS ON VERY LARGE SCALE INTEGRATION (VLSI) SYSTEMS 1995年第2期3卷 273-291页

作者： BURKS, TM SAKALLAH, KA MUDGE, TN UNIV MICHIGAN DEPT ELECT ENGN & COMP SCIANN ARBORMI 48109

This paper extends the classical notion of critical paths in combinational circuits to the case of synchronous circuits that use level-sensitive latches. Critical paths in such circuits arise from setup, hold, and cyclic constraints on the data signals at the inputs of each latch and may extend through one or more latches. Two approaches are presented for identifying these critical paths and verifying their timing. The first implicitly checks all paths using a relaxation-based solution procedure. Results of this procedure are used to calculate slack values, which in turn identify satisfied and violated critical paths. The second approach is based on a constructive algorithm which generates all the critical paths in a circuit and then verifies that their timing constraints are satisfied. algorithms are evaluated and compared using circuits from the ISCAS89 sequential benchmark suite and the Michigan High Performance Microprocessor Project.

关键词： Logic Testing Sequential Circuits Flip Flops Graph Theory Circuit Analysis Computing Relaxation Theory Level Sensitive Latches Critical Paths Synchronous Circuits Relaxation Based Solution Procedure constructive algorithm Timing Constraints Verification Latches Timing Clocks Sequential Circuits Combinational Circuits Microprocessors Processor Scheduling Circuit Analysis Signal Analysis

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Neurofuzzy mixture of experts network parallel learning and model construction algorithms

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IEE PROCEEDINGS-CONTROL THEORY AND APPLICATIONS 2001年第6期148卷 456-465页

作者： Harris, CJ Hong, X Univ Southampton Image Speech & Intelligent Syst Grp Dept Elect & Comp Sci Southampton SO17 1BJ Hants England

A connection between a neurofuzzy network model with the Mixture of Experts Network (MEN) modelling approach is established. Based on this linkage, two new neurofuzzy MEN construction algorithms are proposed to overcome the curse of dimensionality that is inherent in the majority of associative memory networks and/or other rule based systems. The first construction algorithm employs a function selection manager module in an MEN system;a conventional latticed based neurofuzzy model is initially generated followed by parsimonious model selection at each iteration using a new simple MEN construction method using a cost criterion based on the MEN model Output sensitivity to each expert. This scheme uses an extension to the well established normalised least means squares as a model parametric learning algorithm. The second construction algorithm is based on a new parallel learning algorithm in which each model rule is trained independently, for which the parameter convergence property of the new learning method is established. As with the first approach, an expert selection criterion is utilised in this algorithm, where each rule is either trained or inhibited. These two construction methods are equivalent in their effectiveness in overcoming the Curse of dimensionality by reducing the dimensionality of the regression vector. but the latter has the additional computational advantage of parallel processing. The proposed algorithms are analysed for effectiveness followed by numerical examples to illustrate their efficacy for some difficult data based modelling problems.

关键词： Curse of Dimensionality algorithms iterative methods Clidemia hirta constructive algorithm model selection

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Parsimonious kernel extreme learning machine in primal via Cholesky factorization

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NEURAL NETWORKS 2016年 80卷 95-109页

作者： Zhao, Yong-Ping Nanjing Univ Aeronaut & Astronaut Coll Energy & Power Engn Jiangsu Prov Key Lab Aerosp Power Syst Nanjing 210016 Peoples R China

Recently, extreme learning machine (ELM) has become a popular topic in machine learning community. By replacing the so-called ELM feature mappings with the nonlinear mappings induced by kernel functions, two kernel ELMs, i.e., P-KELM and D-KELM, are obtained from primal and dual perspectives, respectively. Unfortunately, both P-KELM and D-KELM possess the dense solutions in direct proportion to the number of training data. To this end, a constructive algorithm for P-KELM (CCP-KELM) is first proposed by virtue of Cholesky factorization, in which the training data incurring the largest reductions on the objective function are recruited as significant vectors. To reduce its training cost further, PCCP-KELM is then obtained with the application of a probabilistic speedup scheme into CCP-KELM. Corresponding to CCP-KELM, a destructive P-KELM (CDP-KELM) is presented using a partial Cholesky factorization strategy, where the training data incurring the smallest reductions on the objective function after their removals are pruned from the current set of significant vectors. Finally, to verify the efficacy and feasibility of the proposed algorithms in this paper, experiments on both small and large benchmark data sets are investigated. (C) 2016 Elsevier Ltd. All rights reserved.

关键词： Extreme learning machine Kernel method Parsimoniousness constructive algorithm Destructive algorithm

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Stochastic configuration broad learning system and its approximation capability analysis

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INTERNATIONAL JOURNAL OF MACHINE LEARNING AND CYBERNETICS 2022年第3期13卷 797-810页

作者： Zhou, Wei Wang, Degang Li, Hongxing Bao, Menghong Dalian Univ Technol Minist Educ Key Lab Intelligent Control & Optimizat Ind Equip Dalian Peoples R China Dalian Univ Technol Sch Control Sci & Engn Dalian Peoples R China Beijing Normal Univ Sch Appl Math Zhuhai Peoples R China

In this paper, a kind of stochastic configuration broad learning system (SCBLS) is proposed for data modeling. The proposed SCBLS is established in the form of a flat network and its architecture is determined by a constructive learning approach. The input parameters of feature nodes and enhancement nodes of SCBLS are randomly assigned in the light of a supervisory mechanism. Inequality constraints are used to randomly assign the hidden parameters and adaptively select the scopes of random parameters. The output parameters of SCBLS are determined either by a constructive manner or by solving a global least squares problem. It is proved that the proposed SCBLS possesses universal approximation properties. The performances of the proposed SCBLS are evaluated by function approximation, benchmark datasets and time series prediction. Numerical examples show that SCBLS can achieve satisfactory approximation accuracy.

关键词： Stochastic configuration Broad learning system constructive algorithm Universal approximation

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