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Discrete differential evolution algorithm for integer linear bilevel programming problems 被引量:1
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作者 Hong Li Li Zhang Yongchang Jiao 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2016年第4期912-919,共8页
A discrete differential evolution algorithm combined with the branch and bound method is developed to solve the integer linear bilevel programming problems, in which both upper level and lower level variables are forc... A discrete differential evolution algorithm combined with the branch and bound method is developed to solve the integer linear bilevel programming problems, in which both upper level and lower level variables are forced to be integer. An integer coding for upper level variables is adopted, and then a discrete differential evolution algorithm with an improved feasibility-based comparison is developed to directly explore the integer solution at the upper level. For a given upper level integer variable, the lower level integer programming problem is solved by the existing branch and bound algorithm to obtain the optimal integer solution at the lower level. In the same framework of the algorithm, two other constraint handling methods, i.e. the penalty function method and the feasibility-based comparison method are also tested. The experimental results demonstrate that the discrete differential evolution algorithm with different constraint handling methods is effective in finding the global optimal integer solutions, but the improved constraint handling method performs better than two compared constraint handling methods. 展开更多
关键词 discrete linear bilevel programming problem discrete differential evolution constraint handling method branch and bound algorithm
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A UNIVERSAL APPROACH FOR CONTINUOUS OR DISCRETE NONLINEAR PROGRAMMINGS WITH MULTIPLE VARIABLES AND CONSTRAINTS
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作者 孙焕纯 王跃芳 柴山 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2005年第10期1284-1292,共9页
A universal numerical approach for nonlinear mathematic programming problems is presented with an application of ratios of first-order differentials/differences of objective functions to constraint functions with resp... A universal numerical approach for nonlinear mathematic programming problems is presented with an application of ratios of first-order differentials/differences of objective functions to constraint functions with respect to design variables. This approach can be efficiently used to solve continuous and, in particular, discrete programmings with arbitrary design variables and constraints. As a search method, this approach requires only computations of the functions and their partial derivatives or differences with respect to design variables, rather than any solution of mathematic equations. The present approach has been applied on many numerical examples as well as on some classical operational problems such as one-dimensional and two-dimensional knap-sack problems, one-dimensional and two-dimensional resource-distribution problems, problems of working reliability of composite systems and loading problems of machine, and more efficient and reliable solutions are obtained than traditional methods. The present approach can be used without limitation of modeling scales of the problem. Optimum solutions can be guaranteed as long as the objective function, constraint functions and their First-order derivatives/differences exist in the feasible domain or feasible set. There are no failures of convergence and instability when this approach is adopted. 展开更多
关键词 continuous or discrete nonlinear programming search algorithm relative differential/difference method
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Parametric Duality Models for Semi-infinite Discrete Minmax Fractional Programming Problems Involving Generalized (η,ρ)-Invex Functions 被引量:4
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作者 G.J.Zalmai 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2007年第3期353-376,共24页
A semi-infinite programming problem is a mathematical programming problem with a finite number of variables and infinitely many constraints. Duality theories and generalized convexity concepts are important research t... A semi-infinite programming problem is a mathematical programming problem with a finite number of variables and infinitely many constraints. Duality theories and generalized convexity concepts are important research topics in mathematical programming. In this paper, we discuss a fairly large number of paramet- ric duality results under various generalized (η,ρ)-invexity assumptions for a semi-infinite minmax fractional programming problem. 展开更多
关键词 Semi-infinite programming discrete minmax fractional programming generalized invex functions infinitely many equality and inequality constraints parametric duality models duality theorems
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Parallel power system restoration planning using heuristic initialization and discrete evolutionary programming 被引量:3
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作者 Dian Najihah ABU TALIB Hazlie MOKHLIS +1 位作者 Mohamad Sofian ABU TALIP Kanendra NAIDU 《Journal of Modern Power Systems and Clean Energy》 SCIE EI 2017年第6期991-1003,共13页
This paper proposes a sectionalizing planning for parallel power system restoration after a complete system blackout.Parallel restoration is conducted in order to reduce the total restoration process time.Physical and... This paper proposes a sectionalizing planning for parallel power system restoration after a complete system blackout.Parallel restoration is conducted in order to reduce the total restoration process time.Physical and operation knowledge of the system,operating personnel experience,and computer simulation are combined in this planning to improve the system restoration and serve as a guidance for system operators/planners.Sectionalizing planning is obtained using discrete evolutionary programming optimization method assisted by heuristic initialization and graph theory approach.Set of transmission lines that should not be restored during parallel restoration process(cut set)is determined in order to sectionalize the system into subsystems or islands.Each island with almost similar restoration time is set as an objective function so as to speed up the resynchronization of the islands.Restoration operation and constraints(black start generator availability,load-generation balance and maintaining acceptable voltage magnitude within each island)is also takeninto account in the course of this planning.The method is validated using the IEEE 39-bus and 118-bus system.Promising results in terms of restoration time was compared to other methods reported in the literature. 展开更多
关键词 Sectionalizing planning Parallel power system restoration Graph theory Heuristic initialization discrete evolutionary programming(DEP)optimization method
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Global Parametric Sufficient Optimality Conditions for Semi-infinite Discrete Minmax Fractional Programming Problems Involving Generalized (η,ρ)-invex Functions 被引量:1
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作者 G.J.Zalmai 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2007年第2期217-234,共18页
In this paper, we discuss a large number of sets of global parametric sufficient optimality conditions under various generalized (η,ρ)-invexity assumptions for a semi-infinite minmax fractional programming problem.
关键词 Semi-infinite programming discrete minmax fractional programming generalized invex functions infinitely many equality and inequality constraints sufficient optimality conditions
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