This paper intends to demonstrate use of Genetic Algorithm for solving fractional programming and which can be extended for DEA. Genetic Algorithm is one of the non-traditional algorithms for solving optimization prob...
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(纸本)9781479944453
This paper intends to demonstrate use of Genetic Algorithm for solving fractional programming and which can be extended for DEA. Genetic Algorithm is one of the non-traditional algorithms for solving optimization problems. The multivariable fraction may have multiple optimum points. Genetic algorithm does not run the risk of getting trapped into the local minimum or maximum. The traditional optimization algorithms have difficulty in computing the derivatives and second order partial derivatives for fractional form. Though there are numerical algorithms but they become computationally intensive. The issues of discontinuity seriously affect traditional algorithms. The genetic algorithm may not be very efficient but a generalized way to find optimal points of multivariate fractional function. Two short and simple experiments have been conducted to illustrate the positions. In the second illustration effect of crossover position on the gain of objective function has been studied.
In this paper, we present sufficient optimality conditions and duality results for a class of nonlinear fractional programming problems. Our results are based on the properties of sublinear functionals and generalized...
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In this paper, we present sufficient optimality conditions and duality results for a class of nonlinear fractional programming problems. Our results are based on the properties of sublinear functionals and generalized convex functions.
A Mond-Weir type dual for a class of nondifferentiable minimax fractional programming problem is considered. Appropriate duality results are proved involving (F,alpha,rho,d)-pseudoconvex functions. (c) 2005 Elsevier I...
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A Mond-Weir type dual for a class of nondifferentiable minimax fractional programming problem is considered. Appropriate duality results are proved involving (F,alpha,rho,d)-pseudoconvex functions. (c) 2005 Elsevier Inc. All rights reserved.
Fuzzy multiple objective fractional programming (FMOFP) is an important technique for solving many real-world problems involving the nature of vagueness, imprecision and/or random. Following the idea of binary behavio...
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Fuzzy multiple objective fractional programming (FMOFP) is an important technique for solving many real-world problems involving the nature of vagueness, imprecision and/or random. Following the idea of binary behaviour of fuzzy programming (Chang 2007), there may exist a situation where a decision-maker would like to make a decision on FMOFP involving the achievement of fuzzy goals, in which some of them may meet the behaviour of fuzzy programming (i.e. level achieved) or the behaviour of binary programming (i.e. completely not achieved). This is turned into a fuzzy multiple objective mixed binary fractional programming (FMOMBFP) problem. However, to the best of our knowledge, this problem is not well formulated by mathematical programming. Therefore, this article proposes a linearisation strategy to formulate the FMOMBFP problem in which extra binary variable is not required. In addition, achieving the highest membership value of each fuzzy goal defined for the fractional objective function, the proposed method can alleviate the computational difficulties when solving the FMOMBFP problem. To demonstrate the usefulness of the proposed method, a real-world case is also included.
In this study, an inexact mixed-integer fractional energy system planning (IMIF-EP) model is developed for supporting sustainable energy system management under uncertainty. Based on a hybrid of interval-parameter pro...
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In this study, an inexact mixed-integer fractional energy system planning (IMIF-EP) model is developed for supporting sustainable energy system management under uncertainty. Based on a hybrid of interval-parameter programming (IPP), fractional programming (FP) and mixed integer linear programming (MILP) techniques, IMIF-EP can systematically reflect various complexities in energy management systems. It not only handles imprecise uncertainties and dynamic features associated with power generation expansion planning, but also optimizes the system efficiency represented as output/input ratios. An interactive transform algorithm is proposed to solve the IMIF-EP model. For demonstrating effectiveness of the developed approach, IMIF-EP is applied to support long-term planning for an energy system. The results indicate that interval solutions obtained from IMIF-EP can provide flexible schemes of resource allocations and facility expansions towards sustainable energy management (SEM) under multiple complexities. A comparative economical energy management (EEM) system is also provided. Compared with least-cost models that optimize single criterion, IMIF-EP can better characterize practical energy management problems by optimizing a ratio between criteria of two magnitudes. In application, IMIF-EP is advantageous in balancing conflicting objectives and reflecting complicated relationships among multiple system factors. (C) 2013 Elsevier Ltd. All rights reserved.
In this paper, we present an efficient branch and bound method for general linear fractional problem (GFP). First, by using a transformation technique, an equivalent problem (EP) of GFP is derived, then by exploiting ...
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In this paper, we present an efficient branch and bound method for general linear fractional problem (GFP). First, by using a transformation technique, an equivalent problem (EP) of GFP is derived, then by exploiting structure of EP, a linear relaxation programming (LRP) of EP is obtained. To implement the algorithm, the main computation involve solving a sequence of linear programming problem, which can be solved efficiently. The proposed algorithm is convergent to the global maximum through the successive refinement of the solutions of a series of linear programming problems. Numerical experiments are reported to show the feasibility of our algorithm. (C) 2008 Elsevier Inc. All rights reserved.
Structural redundancies in mathematical programming models are nothing uncommon and nonlinear programming problems are no exception. Over the past few decades numerous papers have been written on redundancy. Redundanc...
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Structural redundancies in mathematical programming models are nothing uncommon and nonlinear programming problems are no exception. Over the past few decades numerous papers have been written on redundancy. Redundancy in constraints and variables are usually studied in a class of mathematical programming problems. However, main emphasis has so far been given only to linear programming problems. In this paper, an algorithm that identifies redundant objective function(s) and redundant constraint(s) simultaneously in multi-objective nonlinear stochastic fractional programming problems is provided. A solution procedure is also illustrated with numerical examples. The proposed algorithm reduces the number of nonlinear fractional objective functions and constraints in cases where redundancy exists. (C) 2009 Elsevier B.V. All rights reserved.
In solving real life fractional programming problem, we often face the state of uncertainty as well as hesitation due to various uncontrollable factors. To overcome these limitations, the fuzzy rough approach is appli...
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In solving real life fractional programming problem, we often face the state of uncertainty as well as hesitation due to various uncontrollable factors. To overcome these limitations, the fuzzy rough approach is applied to this problem. In this paper, an efficient method is proposed for solving fuzzy rough multiobjective integer linear fractional programming problem where all the variables and parameters are fuzzy rough numbers. Here, the fuzzy rough multiobjective problem transformed into an equivalent multiobjective integer linear fractional programming problem. Furthermore, from the obtained problem, five crisp multiobjective integer linear fractional programming problems are constructed and the resultant problems are solved as a crisp integer linear programming problem by using Dinkelbach concept. Finally, the effectiveness of the proposed procedure is illustrated through numerical examples.
This paper presents a novel recurrent time continuous neural network model which performs nonlinear fractional optimization subject to interval constraints on each of the optimization variables. The network is proved ...
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This paper presents a novel recurrent time continuous neural network model which performs nonlinear fractional optimization subject to interval constraints on each of the optimization variables. The network is proved to be complete in the sense that the set of optima of the objective function to be minimized with interval constraints coincides with the set of equilibria of the neural network. It is also shown that the network is primal and globally convergent in the sense that its trajectory cannot escape from the feasible region and will converge to an exact optimal solution for any initial point being chosen in the feasible interval region. Simulation results are given to demonstrate further the global convergence and good performance of the proposing neural network for nonlinear fractional programming problems with interval constraints.
Uncertainties arising from extreme climate events and human activities pose a challenge to the efficient allocation of water resources. In this study, a type-2 fuzzy chance-constrained linear fractional programming (T...
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Uncertainties arising from extreme climate events and human activities pose a challenge to the efficient allocation of water resources. In this study, a type-2 fuzzy chance-constrained linear fractional programming (T2F-CCLFP) is developed to support the water resource management system under uncertainty by incorporating type-2 fuzzy sets, chance-constrained programming, and fractional programming into a comprehensive multi-objective optimization framework. The model enables the trade-off between economic, social, and environmental sustainability and provides water supply solutions associated with different levels of fuzzy uncertainty and risk of violating constraints. The T2F-CCLFP model is applied to Taiyuan, Shanxi Province, China, to support its water resource management. Results reveal that: (i) the industrial structure is transitioning toward diverse industries from energy and heavy industry dominance;(ii) external water transfer will be the major water-supply sources for the city in the future, accounting for 55 and 50% of the total water supply in 2025 and 2030, respectively;(iii) the water-supply security of the city is enhanced by provoking the utilization of reclaimed water (the annual growth rate is 13.9%). The results are helpful for managers in adjusting the current industry structure, enhancing water supply security, and contributing to the sustainable development of socio-economic and water systems.
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