Abstract
This paper presents an innovative Fuzzy-Stochastic Approach (FSA) to solve Binary Linear Programming (BLP) problems under uncertainties. An Interval-coefficient Fuzzy Binary Linear Programming (IFBLP) model is applied here to reflect two different types of uncertainty in a BLP problem. In the proposed IFBLP model the interval coefficient is used to reflect parameter uncertainty, and the fuzzy goal & fuzzy constraints are used to represent model structure uncertainty. The proposed FSA would de-fuzzify the fuzzy constraints in an IFBLP model by considering its fuzzy goal; and then derive two linear BLPs with extreme crisp-coefficients from the IFBLP model, which here are called as a best optimum BLP and a worst optimum BLP. The results of the two-extreme linear BLPs are used to bound the outcome distribution of the IFBLP model. The proposed FSA is applied into a long-term traffic noise control planning to present its applicability.
Highlights
Uncertainty is a major difficulty in solving optimization problems
The proposed Fuzzy-Stochastic Approach (FSA) would de-fuzzify the fuzzy constraints in an Interval-coefficient Fuzzy Binary Linear Programming (IFBLP) model by considering its fuzzy goal; and derive two linear Binary Linear Programming (BLP) with extreme crisp-coefficients from the IFBLP model, which here are called as a best optimum BLP and a worst optimum BLP
The fuzzy constraints and interval coefficients are designed in the developed IFBLP model, in which the interval coefficients reflect parameter uncertainty and the fuzzy goal & fuzzy constraints represent model structure uncertainty
Summary
Uncertainty is a major difficulty in solving optimization problems. It may exist in the parameters and/or in the structure in an optimization model, which are called as “parameter uncertainty” and “structure uncertainty” respectively. In the Binary Linear Programming (BLP) area, for example, Yu and Li (2001) proposed a fuzzy method to solve a fuzzy BLP ( called as FBLP) problem, in which the model contains fuzzy coefficients in the objective function and constraints Their model doesn’t consider the model structure uncertainty, which may result in low efficiency to solve uncertainty in the right-hand side of constraints. The proposed FSA novelty consists in: (1) utilizing the T-operator technique to defuzzify the fuzzy constraints with considering the fuzzy goal; (2) using a stochastic simulation model to find the range of optimal alpha solutions; and (3) preforming a crisping process to transfer the interval-coefficient BLP into two extreme auxiliary parametric BLPs. The IFBLP is applied into a long-term traffic noise control planning to demonstrate the applicability.
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