A fuzzy approach for bi-level integer non-linear programming problem

Emam, O. E.

doi:10.1016/j.amc.2005.01.149

Cited by 41 publications

(23 citation statements)

References 9 publications

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“…During the past few decades, the mixed-integer linear programming (MILP) method has been widely used for solving the above problems (Baetz 1990;Huang et al 1997;Glen 2003;Emam 2006;Chen 2007). Since conventional MILP methods cannot reasonably address the complex uncertainties, a number of interval-parameter MILP (IMILP) methods have been developed and applied in MSW management and planning (Chi and Huang 1998;Huang et al 1997Huang et al , 1993a.…”

Section: Introductionmentioning

confidence: 99%

ISMISIP: an inexact stochastic mixed integer linear semi-infinite programming approach for solid waste management and planning under uncertainty

Guo

Huang

2007

Stoch Environ Res Risk Assess

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An inexact stochastic mixed integer linear semi-infinite programming (ISMISIP) model is developed for municipal solid waste (MSW) management under uncertainty. By incorporating stochastic programming (SP), integer programming and interval semi-infinite programming (ISIP) within a general waste management problem, the model can simultaneously handle programming problems with coefficients expressed as probability distribution functions, intervals and functional intervals. Compared with those inexact programming models without introducing functional interval coefficients, the ISMISIP model has the following advantages that: (1) since parameters are represented as functional intervals, the parameter's dynamic feature (i.e., the constraint should be satisfied under all possible levels within its range) can be reflected, and (2) it is applicable to practical problems as the solution method does not generate more complicated intermediate models (He and Huang, Technical Report, 2004; He et al. J Air Waste Manage Assoc, 2007). Moreover, the ISMISIP model is proposed upon the previous inexact mixed integer linear semi-infinite programming (IMISIP) model by assuming capacities of the landfill, WTE and composting facilities to be stochastic. Thus it has the improved capabilities in (1) identifying schemes regarding to the waste allocation and facility expansions with a minimized system cost and (2) addressing tradeoffs among environmental, economic and system reliability level.

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Section: Introductionmentioning

confidence: 99%

ISMISIP: an inexact stochastic mixed integer linear semi-infinite programming approach for solid waste management and planning under uncertainty

Guo

Huang

2007

Stoch Environ Res Risk Assess

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“…They proposed a mixed-discrete fuzzy nonlinear programming approach that combines the fuzzy -formulation with a hybrid genetic algorithm using mathematical techniques for finding the minimum cost design of a welded beam. Eman (2006) [20] investigated a fuzzy approach for a bi-level integer nonlinear programming problem (BLI-NLP), which consists of the higher-level decision-maker (HLDM) and the lower-level decision-maker (LLDM). The paper was focused on two planner integer models and a solution method for solving the problem using the concept of tolerance membership function and a set of Pareto optimal solutions.…”

Section: Introductionmentioning

confidence: 99%

Uncertain Analysis of a Stationary Solar Compound Parabolic Concentrator PV Collector System Using Fuzzy Set Theory

Lee

Rao

2018

Journal of Renewable Energy

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The uncertain analysis of fixed solar compound parabolic concentrator (CPC) collector system is investigated for use in combination with solar PV cells. Within solar CPC PV collector systems, any radiation within the collector acceptance angle enters through the aperture and finds its way to the absorber surface by multiple internal reflections. It is essential that the design of any solar collector aims to maximize PV performance since this will elicit a higher collection of solar radiation. In order to analyze uncertainty of the solar CPC collector system in the optimization problem formulation, three objectives are outlined. Seasonal demands are considered for maximizing two of these objectives, the annual average incident solar energy and the lowest month incident solar energy during winter; the lowest cost of the CPC collector system is approached as a third objective. This study investigates uncertain analysis of a solar CPC PV collector system using fuzzy set theory. The fuzzy analysis methodology is suitable for ambiguous problems to predict variations. Uncertain parameters are treated as random variables or uncertain inputs to predict performance. The fuzzy membership functions are used for modeling uncertain or imprecise design parameters of a solar PV collector system. Triangular membership functions are used to represent the uncertain parameters as fuzzy quantities. A fuzzy set analysis methodology is used for analyzing the three objective constrained optimization problems.

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“…Let ∈ , ( = 1, 2, 3),be a vector of variables which indicates the first decision level's choice, thesecond decision level's choice and the third decision level's choice andF i : 2,3),be the first level objective function, the second level objective function and the third level objective function, respectively. Assume thatthe first level decision maker is (FLDM),the secondlevel decision maker is(SLDM) and the third level decision maker is(TLDM).…”

Section: Problem Formulation and Solution Conceptmentioning

confidence: 99%

A Multi-Level Multi-Objective Quadratic Programming Problem with Fuzzy Parameters on Objective Functions

Emam

2016

IJCT

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A fuzzy approach for bi-level integer non-linear programming problem

Cited by 41 publications

References 9 publications

ISMISIP: an inexact stochastic mixed integer linear semi-infinite programming approach for solid waste management and planning under uncertainty

ISMISIP: an inexact stochastic mixed integer linear semi-infinite programming approach for solid waste management and planning under uncertainty

Uncertain Analysis of a Stationary Solar Compound Parabolic Concentrator PV Collector System Using Fuzzy Set Theory

A Multi-Level Multi-Objective Quadratic Programming Problem with Fuzzy Parameters on Objective Functions

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