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Ensemble of multi-objective metaheuristic algorithms for multi-objective unconstrained binary quadratic programming problem

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APPLIED SOFT COMPUTING 2019年 81卷 105485-000页

作者： Zhou, Ying Kong, Lingjing Wu, Ziyan Liu, Shaopeng Cai, Yiqiao Liu, Ye Shenzhen Inst Informat Technol Sch Comp Sci Shenzhen 518172 Peoples R China China Securities Depository & Clearing Corp Ltd S 2012 Shennan Blvd Shenzhen 518038 Peoples R China Guangdong Polytech Normal Univ Dept Comp Sci Guangzhou 510006 Guangdong Peoples R China Huaqiao Univ Coll Comp Sci & Technol Xiamen Fujian Peoples R China Sun Yat Sen Univ Sch Data & Comp Sci Guangzhou 510006 Guangdong Peoples R China

Metaheuristics have been widely utilized for solving NP-hard optimization problems. However, these algorithms usually perform differently from one problem to another, i.e., one may be effective on a problem but performs badly on another problem. Therefore, it is difficult to choose the best algorithm in advance for a given problem. In contrast to selecting the best algorithm for a problem, selection hyper-heuristics aim at performing well on a set of problems (instances). This paper proposes a selection hyper-heuristic based algorithm for multi-objective optimization problems. In the proposed algorithm, multiple metaheuristics exhibiting different search behaviors are managed and controlled as low-level metaheuristics in an algorithm pool, and the most appropriate metaheuristic is selected by means of a performance indicator at each search stage. To assess the performance of the proposed algorithm, an implementation of the algorithm containing four metaheuristics is proposed and tested for solving multi-objective unconstrained binary quadratic programming problem. Experimental results on 50 benchmark instances show that the proposed algorithm can provide better overall performance than single metaheuristics, which demonstrates the effectiveness of the proposed algorithm. (C) 2019 Elsevier B.V. All rights reserved.

关键词： Multi-objective optimization Selection hyper-heuristic Multi-objective unconstrained binary quadratic programming problem

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An efficient optimization algorithm for quadratic programming problem and its applications to mobile robot path planning

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INTERNATIONAL JOURNAL OF ADVANCED ROBOTIC SYSTEMS 2018年第1期15卷

作者： Cai, Lei Yang, Juanjuan Zhao, Li Wu, Lan Henan Inst Sci & Technol Sch Informat Engn Xinxiang 453003 Peoples R China Henan Inst Sci & Technol Sch Math Sci Xinxiang Peoples R China Henan Polytech Univ Sch Mech & Power Engn Jiaozuo Peoples R China Henan Univ Technol Coll Elect Engn Zhengzhou Henan Peoples R China

The quadratic programming problem has broad applications in mobile robot path planning. This article presents an efficient optimization algorithm for globally solving the quadratic programming problem. By utilizing the convexity of univariate quadratic functions, we construct the linear relaxation programming problem of the quadratic programming problem, which can be embedded within a branch-and-bound structure without introducing new variables and constraints. In addition, a new pruning technique is inserted into the branch-and-bound framework for improving the speed of the algorithm. The global convergence of the proposed algorithm is proved. Compared with some known algorithms, numerical experiment not only demonstrates the higher computational efficiency of the proposed algorithm but also proves that the proposed algorithm is an efficient approach to solve the problems of path planning for the mobile robot.

关键词： quadratic programming problem global optimization linear relaxation programming pruning technique branch-and-bound optimization algorithm path planning

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A Newton-Type Method for quadratic programming problem and Variational Equilibrium problem

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Procedia Computer Science 2019年 150卷 636-645页

作者： A.N. Daryina K.Yu. Andrianov B.B. Kulakov Federal Research Centre “Computer Science and Control” of Russian Academy of Sciences Vavilov str. 44 2 Moscow 119333 Russia RUDN University Miklukho-Maklaya str. 6 117198 Moscow Russia

The active-set Newton method developed earlier by the author and her supervisor for mixed complementarity problems is applied to solving the quadratic programming problem with a positive definite matrix of the objective function and for variational equilibrium problem. A theoretical justification is given to the fact that the method is guaranteed to find the exact solution in a finite number of steps. Numerical results indicate that this approach is competitive with other available methods as for quadratic programming problems and for variational equilibrium problem.

关键词： Newton-type method quadratic programming problem variational equilibrium problem error bound semistability

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Generalized quadratic programming problem with Interval Uncertainty

Generalized Quadratic Programming Problem with Interval Unce...

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IEEE International Conference on Fuzzy Systems

作者： P. Kumar G. Panda U. C. Gupta Department of Mathematics Indian Institute of Technology

ISBN: (纸本)9781479900213

In this paper, a quadratic programming model is considered, wherein all parameters and decision variables take values in intervals. Existence of optimal solution for this model with certain acceptable level is justified and a methodology is proposed to derive such a solution. Finally, the theoretical development is illustrated by means of an example of portfolio selection.

关键词： quadratic programming problem Interval Order relation Portfolio selection Risk

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A variables neighborhood search algorithm for solving fuzzy quadratic programming problems using modified Kerre's method

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SOFT COMPUTING 2019年第23期23卷 12305-12315页

作者： Ghanbari, Reza Ghorbani-Moghadam, Khatere Mahdavi-Amiri, Nezam Ferdowsi Univ Mashhad Fac Math Sci Dept Appl Math Mashhad Razavi Khorasan Iran Sharif Univ Technol Fac Math Sci Tehran Iran

To solve a fuzzy optimization problem, we need to compare fuzzy numbers. Here, we make use of our recently proposed modified Kerre's method as an effective approach for comparison of LR fuzzy numbers. Using our new results on LR fuzzy numbers, we show that to compare two LR fuzzy numbers, we do not need to compute the fuzzy maximum of two numbers directly. We propose a new variable neighborhood search approach for solving fuzzy number quadratic programming problems by using the modified Kerre's method. In our algorithm, a local search is performed using descent directions, found by solving five crisp mathematical programming problems. In several available methods, a fuzzy optimization problem is converted to a crisp problem, but in our proposed approach, using our modified Kerre's method, the fuzzy optimization problem is solved directly, without changing it to a crisp program. We give some examples to compare the performance of our proposed algorithm with some available methods and show the effectiveness of our proposed algorithm by using the nonparametric statistical sign test.

关键词： quadratic programming problem Modified Kerre's method Ranking function

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Finite time dual neural networks with a tunable activation function for solving quadratic programming problems and its application

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NEUROCOMPUTING 2014年 143卷 80-89页

作者： Miao, Peng Shen, Yanjun Xia, Xiaohua China Three Gorges Univ Coll Sci Yichang 443002 Hubei Peoples R China China Three Gorges Univ Coll Elect Engn & New Energy Yichang 443002 Hubei Peoples R China Univ Pretoria Dept Elect Elect & Comp Engn ZA-0002 Pretoria South Africa

In this paper, finite time dual neural networks with a new activation function are presented to solve quadratic programming problems. The activation function has two tunable parameters, which give more flexibility to design the neural networks. By Lyapunov theorem, finite-time stability can be derived for the proposed neural networks, and the actual optimal solutions of the quadratic programming problems can be obtained in finite time interval. Different from the existing recurrent neural networks for solving the quadratic programming problems, the neural networks of this paper have a faster convergent speed, at the same time, they can reduce oscillation when delay appears, and have less sensitivity to additive noise with careful selection of the parameters. Simulations are presented to evaluate the performance of the neural networks with the tunable activation function. In addition, the proposed neural networks are applied to estimate parameters for an energy model of belt conveyors. The effectiveness of our methods are validated by theoretical analysis and numerical simulations. (C) 2014 Elsevier B.V. All rights reserved.

关键词： Recurrent neural networks Finite-time stability Tunable activation function quadratic programming problem

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Some properties of solution sets to nonconvex quadratic programming problems

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OPTIMIZATION 2007年第3期56卷 369-383页

作者： Phu, H. X. Inst Math Hanoi Vietnam

This article deals with some properties of the global minimizer set G(Q), the local minimizer set L-Q, and the stationary point set S-Q to the quadratic programming problem (Q) of minimizing the function f(x) =(1/2)x(T)Ax + b(T)x on the polyhedron D = {x is an element of R-n vertical bar C(i)x >= d(i), i is an element of I}, where A is an element of R-nxn, b is an element of R-n, d is an element of R-m, C-i(T) is an element of R-n, i is an element of I = {1, 2, ..., m}. In particular, we investigate the intersection of these solution sets with faces (D) over bar (J) = {x is an element of R-n vertical bar C(i)x >= d(i) for i is an element of J, C(i)x >= d(i) for i is an element of I\J} and pseudofaces D-J = {x is an element of R-n vertical bar C(i)x >= d(i) for i is an element of J, C(i)x = d(i) for i is an element of I\J}, where J subset of I. Some selected results are the following. If G(Q) boolean AND D-J not equal 0 then G(Q) boolean AND D-J and G(Q) boolean AND (D) over bar (J) are relatively affine in the following sense: G(Q) boolean AND D-J = aff(G(Q) boolean AND D-J) boolean AND D-J and G(Q) boolean AND (D) over bar (J) = aff(G(Q) boolean AND (D) over bar (J)) boolean AND D. If L-Q boolean AND D-J not equal 0 then L-Q boolean AND D-J is open relative to aff(L-Q boolean AND (D) over bar (J)) boolean AND D-J, L-Q boolean AND (D) over bar (J) is open relative to aff(L-Q boolean AND (D) over bar (J)) boolean AND D-J and L-Q boolean AND (D) over bar (J) are convex. If G(Q) boolean AND D-J not equal 0 then each stationary point (in particular, each local minimizer) in (D) over bar (J) is a global minimizer. If x(0) is an element of L-Q boolean AND D-J, x(1) is an element of S-Q boolean AND (D) over bar (J), and x(0) not equal x(1), then [x(0), x(1)) subset of L-Q boolean AND D-J subset of L-Q. Let B-m,B-n and C-m,C-n denote the maximal number of nonempty faces and the maximal cardinality of an antichain of nonempty faces of a polyhedron defined as intersection of

关键词： quadratic programming problem solution set global minimizer set local minimizer set stationary point set Kuhn-Tucker point

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Continuity properties of the Karush-Kuhn-Tucker point set in quadratic programming problems

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MATHEMATICAL programming 1999年第1期85卷 193-206页

作者： Tam, NN Yen, ND Hanoi Pedag Inst 2 Dept Math Vinhphuc Vietnam Inst Math Hanoi 10000 Vietnam

We obtain necessary and sufficient conditions for the set of the Karush-Kuhn-Tucker points in a canonical quadratic programming problem to be upper semicontinuous or lower semicontinuous with respect to the problem pa... 详细信息

关键词： quadratic programming problem Karush-Kuhn-Tucker point set upper semicontinuity lower semicontinuity R-0-matrix

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MIXED ENERGY METHOD FOR SOLUTION OF quadratic programming problemS AND ELASTIC-PLASTIC ANALYSIS OF TRUSS STRUCTURES

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Acta Mechanica Solida Sinica 2002年第1期15卷 1-8页

作者： Zhong Wanxie Zhang Hongwu Dalian Univ Technol Dept Mech Engn State Key Lab Struct Anal Ind Equipment Dalian 116024 Peoples R China

A new algorithm for the solution of quadratic programming problemsis put forward in terms of the mixed energy theory and is furtherused for the incremental solution of elastic-plastic trussstructures. The method proposed is different from the traditionalone, for which the unknown variables are selected just in one classsuch as displacements or stresses. The present method selects thevariables in the mixed form with both displacement and stress. As themethod is established in the hybrid space, the information found inthe previous incremental step can be used for the solution of thepresent step, making the algorithm highly effi- cient in thenumerical solution process of quadratic programming problems. Theresults obtained in the exm- ples of the elastic-plastic solution ofthe truss structures verify what has been predicted in thetheoretical anal- ysis.

关键词： elastic-plastic analysis mixed energy method quadratic programming problem

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Using concave optimization methods for inexact quadratic programming problems with an application to waste management

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JOURNAL OF INEQUALITIES AND APPLICATIONS 2021年第1期2021卷 1-19页

作者： Mahajan, Sumati Gupta, S. K. Ahmad, Izhar Al-Homidan, S. Punjab Engn Coll Dept Appl Sci Chandigarh 160012 India Indian Inst Technol Roorkee Dept Math Roorkee 247667 Uttar Pradesh India King Fahd Univ Petr & Minerals Dept Math & Stat Dhahran 31261 Saudi Arabia

quadratic programming is potentially capable of strategic decision making in real world problems. However, practical problems rarely conform to crisp parameters, and hence the prospects of these problems with inexact parameters are inevitably higher. The existing studies regarding public welfare schemes/ organizations reveal that their objectives end up as minimization of cost functions and are governed by linear or concave quadratic programming problems. The present study proposes a method that can be applied to concave type quadratic objective function subject to linear constraints with inexact parameters. A comparison is also drawn with existing methods to establish its simplicity and efficiency. Further, a numerical example is illustrated, and finally, a waste management problem is formulated and solved using the proposed method.

关键词： Concave optimization Waste management Inexact parameters quadratic programming problem

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