Abstract
Unbalanced bidding problem with mixed uncertainty of fuzziness and randomness is considered in this paper, where the bidding engineering quantities of each activity are assumed to be fuzzy random variables. Two types of fuzzy random models as expected value maximization model and maximax chance-constrained model are built to satisfy different optimization requirements. Then a hybrid intelligent algorithm integrating fuzzy random simulations, neural network and genetic algorithm is designed to solve these models. Finally, a numerical experiment is given to illustrate its effectiveness of the algorithm. The results show that the algorithm is feasible and effective.
Highlights
In real world, unbalanced bids is a complex problem
Fuzziness and randomness sometimes may co-exist in unbalanced bidding problem
Fuzzy random variable, which was initialized by Kwakernaak (1978, p.1), can be introduced as a useful tool for optimization problems with mixed uncertainty of fuzziness and randomness
Summary
Fuzziness and randomness simultaneously appear in an optimization framework. Let ξ be a fuzzy random variable defined on the probability space (Ω, ∑, Pr). The expected value of the fuzzy random variable is defined by. The present value of the client’s budget price for the total project can be written as n. ∑ f = ki Pi. The present value of the contractor’s bidding price for the total project can be written as n (9). The present value of the contractor’s bidding price for the total project can be written as n (9) As these parameters and basic formulas have been given, we can establish different fuzzy random programming models to satisfy different optimization goals As these parameters and basic formulas have been given in the above section, we can establish different fuzzy random programming models to satisfy different optimization goals
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