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A greedy algorithm for maximizing a linear objective function

DISCRETE APPLIED MATHEMATICS 2004年第1-3期135卷 267-279页

作者： Shenmaier, VV Math Inst Novosibirsk 630090 Russia

It is well known that the problem of finding a maximum-weight base of matroid can be solved by a greedy algorithm. The aim of this paper is to extend this result for some more general problems. One of these problems is maximizing a linear objective function over a family 3 of integer nonnegative vectors. We establish a number of necessary and sufficient conditions for the greedy algorithm to find an optimal solution in the general and some special cases. For the Boolean case, Goecke et al. (in: Combinatorial Optimization, Lecture Notes in Mathematics, Vol. 1403, Springer, Berlin, 1986, p. 1986) proved that the algorithm works if and only if the so-called strong exchange property holds. We extend this result to a class of non-Boolean vector systems. (C) 2002 Elsevier B.V. All rights reserved.

关键词： matroid greedy algorithm linear objective function greedoid

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Fixed-Index-Set Based Approach for Solving a Bilevel Fuzzy Relation Programming With Addition-Min Composition

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IEEE TRANSACTIONS ON FUZZY SYSTEMS 2023年第12期31卷 4361-4373页

作者： Shu, Qianyu Yang, Xiaopeng Sichuan Normal Univ Sch Math Sci Chengdu 610066 Peoples R China Hanshan Normal Univ Sch Math Sci Chaozhou 521041 Peoples R China

In recent years, the addition-min fuzzy relation inequalities have been adopted to describe the flow constraint in a P2P network system. Each solution of the inequalities represents a feasible flow control scheme. Motivated by some different managerial objectives, several optimization problems subject to the addition-min inequalities have been recently studied. For example, considering the total efficiency for decreasing the network congestion, the linear objective function was adopted. While considering the fairness among the terminals, the min-max objective function was employed. In this article, combining these two objectives, we establish a corresponding bilevel fuzzy relation programming subject to the addition-min inequalities. For solving the bilevel programming, we first investigate some properties of the first-level programming, using the concept of fixed index set. Based on the properties of the first-level programming, our studied bilevel programming could be equivalently converted into a single-level programming and then solved by the existing linear programming approach. Our resolution approach is carried out by the fixed-index-set based algorithm and illustrated by some numerical examples.

关键词： Addition-min composition bilevel programming fuzzy relation inequality linear objective function min-max objective function

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Instantaneous magnitudes and instantaneous frequencies of signals with their positivity constraints via non-smooth non-convex functional constrained optimisation

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IET SIGNAL PROCESSING 2016年第3期10卷 247-253页

作者： Yang, Zhijing Kuang, Wei-Chao Ling, Bingo Wing-Kuen Dai, Qingyun Guangdong Univ Technol Sch Informat Engn Guangzhou 510006 Guangdong Peoples R China Guangdong Univ Technol Fac Informat Engn Guangzhou 510006 Guangdong Peoples R China

This study proposes an iterative method to approximate an N-dimensional optimisation problem with a weighted Lp norm and L2 norm objective function by a sequence of N independent one-dimensional optimisation problems. This iterative method is inspired by the existing weighted L1 norm and L2 norm separable surrogate functional (SSF) iterative shrinkage algorithm. However, as these independent one-dimensional optimisation problems consist of weighted Lp norm and L2 norm objective functions, these optimisation problems are non-convex and they may have more than one locally optimal solutions. In general, it is very difficult to find their globally optimal solutions. To address this difficulty, this study proposes to partition the feasible set of each approximated problem into various regions such that the sign of the convexity of the objective function in each region remains unchanged. In this case, there is no more than one stationary point in each region. By finding the stationary point in each region, the globally optimal solution of each approximated optimisation problem can be found. Besides, this study also shows that the sequence of the globally optimal solutions of the approximated problems converge to the globally optimal solution of the original optimisation problem.

关键词： signal processing linear programming minimisation concave programming signal instantaneous frequency representation signal instantaneous magnitude representation positivity constraint nonsmooth nonconvex functional constrained optimisation nonconvex functional equality constraint linear functional inequality constraint pth-order derivatives maximum total absolute value minimization linear objective function constraint transcription method

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FILE EVALUATION IN AUXILIARY STORAGE

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INTERNATIONAL JOURNAL OF COMPUTER & INFORMATION SCIENCES 1975年第3期4卷 197-204页

作者： ROSE, LL GOTTERER, MH SUNY SCH ADV TECHNOL BINGHAMTON NY 13901 USA FLORIDA INT UNIV DEPT MATH SCI MIAMI FL USA

This paper investigates, in detail, the evaluation of files in auxiliary storage. We are seeking an evaluation procedure whereby those files most critical to throughput time minimization are exposed. Such a procedure can then be used by a storage management routine to move data so that throughput time is improved. The linear objective function defined here considers parameters not only for the file under evaluation but also for the jobs that reference the file and the overall system needs. Exogenous variables in the evaluation function make it an attractive tool for managers. This particular evaluation function is incorporated in the Dynamic File Management model and significant time savings have been realized under simulation.

关键词： evaluation exogenous variables hierarchial storage Information retrieval linear objective function simulation storage management throughput time

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AN EXACT CHARACTERIZATION OF GREEDY STRUCTURES

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SIAM JOURNAL ON DISCRETE MATHEMATICS 1993年第2期6卷 274-283页

作者： HELMAN, P MORET, BME SHAPIRO, HD

The authors present exact characterizations of structures on which the greedy algorithm produces optimal solutions. Our characterization, which are called matroid embeddings, complete the partial characterizations of Rado [A note on independent functions, Proc. London Math. Soc., 7 (1957), pp. 300-320], Gale [Optimal assignments in an ordered set, J. Combin. Theory, 4 (1968), pp. 176-180], and Edmonds [Matroids and the greedy algorithm, Math. Programming, 1 (1971), pp. 127-136], (matroids), and of Korte and Lovasz [Greedoids and linear object functions, SIAM J. Alg. Discrete Meth., 5 (1984), pp. 239-248] and [Mathematical structures underlying greedy algorithms, in Fundamentals of Computational Theory, LNCS 177, Springer-Verlag, 1981, pp. 205-2091 (greedoids). It is shown that the greedy algorithm optimizes all linear objective functions if and only ff the problem structure (phrased in terms of either accessible set systems or hereditary languages) is a matroid embedding. An exact characterization of the objective functions optimized by the greedy algorithm on matroid embeddings is also presented. Finally, the authors present an exact characterization of the structures on which the greedy algorithm optimizes all bottleneck functions, structures that are less constrained than matroid embeddings.

关键词： ALGORITHMIC PARADIGM BOTTLENECK objective function GREEDY ALGORITHM GREEDOID linear objective function MATROID MATROID EMBEDDING SET SYSTEM

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Techno-economic adequacy for PV-Battery sizing of a residential grid-connected installation 11

Techno-economic adequacy for PV-Battery sizing of a resident...

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11th International Renewable Energy Congress (IREC)

作者： Guidara, Imen Tina, Giuseppe Marco Souissi, Anoir Chaabene, Maher Signal Image & Maitrise Energie SIME Digital Res Ctr Sfax Sfax Tunisia Univ Catania Dept Elect Elect & Comp Engn Catania Italy

ISBN: (纸本)9781728155722

A techno-economic analysis is introduced in this study for the design of a residential grid-connected photovoltaic battery installation in order to determine the sizing of the integrated PV-battery system. The sizing methodology consists in identifying the optimal combination of the photovoltaic surface and the battery capacity. Therefore, a linear objective function is developed to minimize the total cost of the electricity for the considered installation. In that context, the economic metric known as the Levelized Cost of electricity is adopted to evaluate the feasibility of the system over its lifetime. Furthermore, an energy management strategy is developed to control the energy flow. This strategy, based on managing the energy sources, aims to protect the battery and ensure a continuous load supply whilst considering the risk of grid failure. The results have shown that the minimum total cost of electricity is obtained for 90 m(2) of PV array surface and 27 kWh for the battery capacity while providing a maximum of 88% of self-consumption.

关键词： Levelized cost of electricity PV-Battery sizing linear objective function energy management

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Multi-supervised CML for Small Sample Low-resolution Image Matching

Multi-supervised CML for Small Sample Low-resolution Image M...

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Chinese Automation Congress (CAC)

作者： Zou, Guofeng Fu, Guixia Peng, Xiang Liu, Zheng Gao, Mingliang Shandong Univ Technol Coll Elect & Elect Engn Zibo Peoples R China Univ British Columbia Sch Engn Kelowna BC Canada

ISBN: (纸本)9781728140940

The coupled metric learning(CML) is an effective method for low-resolution image matching. However, the existing coupled metrics generally use class label as the supervision, which easily leads to changes in the samples distribution after coupling transformation. These changes affect image matching accuracy seriously. To address this problem, we propose a multi-supervised coupled metric learning method fusing class label and distribution information. In this work, a novel multi-supervised objective function is constructed, which consists of the main and auxiliary objective functions. The class label in the main objective function plays key supervisory role, and the distribution information in the auxiliary objective function plays auxiliary supervisory role. Then, by solving the objective function, the samples with different resolution are transformed into a common space for distance measurement. Experimental results on two image datasets validate the efficacy of the proposed method.

关键词： multi-supervised information coupled metric learning low-resolution image matching linear objective function

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Introducing INTSOSTOOLS: A SOSTOOLS plug-in for integral inequalities

Introducing INTSOSTOOLS: A SOSTOOLS plug-in for integral ine...

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European Control Conference (ECC)

作者： Valmorbida, Giorgio Papachristodoulou, Antonis Univ Oxford Dept Engn Sci Oxford OX1 3PJ England Univ Oxford Somerville Coll Oxford England

ISBN: (纸本)9783952426937

INTSOSTOOLS is a plug-in for the MATLAB toolbox SOSTOOLS for the formulation of optimization problems with constraints of the form of one-dimensional integral inequalities. For polynomial problem data, semidefinite programming can be used to solve the underlying optimization problems. This paper details a method for checking integral inequalities and shows how to use INTSOSTOOLS to cast optimization problems with integral constraints and linear objective functions. Two examples illustrate the potential of the proposed method and of the developed software.

关键词： mathematical programming mathematics computing polynomials INTSOSTOOLS MATLAB toolbox SOSTOOLS integral constraints linear objective function one-dimensional integral inequalities optimization problems polynomial problem data semidefinite programming sum-of-squares Integral equations linear matrix inequalities MATLAB Optimization Polynomials

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Fuzzy multi-objective optimization of linear functions subject to max-arithmetic mean relational inequality constraints

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SCIENTIA IRANICA 2017年第3期24卷 1561-1570页

作者： Kouchakinejad, F. Mashinchi, M. Khorram, E. Grad Univ Adv Technol Dept Math End Haft Bagh E Alavi Highway Kerman Iran Shahid Bahonar Univ Kerman Fac Math & Comp Sci Dept Stat Pajohesh Sq22nd Braman Blvd Kerman Iran Amirkabir Univ Technol Fac Math & Comp Sci 424 Hafez Ave Tehran Iran

The main goal of this work is to find a better solution to a kind of multi objective optimization problem subject to a system of fuzzy relational inequalities with max-arithmetic mean composition. First, this problem is solved and, then, in the case that the decision maker is not satisfied with any of the solutions, by assigning linear membership functions to the inequalities in the constraints and objective functions and using BellmanZadeh decision, a new solution is found. This new solution does not belong to the feasible domain but is considered acceptable based on the decision maker's view. In order to find this solution easier, some simplification processes are given. Afterwards, an algorithm is presented to generate the new solution. Finally, an example is given to illustrate the steps of the algorithm. (C) 2017 Sharif University of Technology. All rights reserved.

关键词： Fuzzy inequality Fuzzy relational inequalities Fuzzy solution linear objective function Max-arithmetic mean composition Multi-objective optimization

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