This paper proposes a new nonlinear interval programming method that can be used to handle uncertain optimization problems when there are dependencies among the interval variables. The uncertain domain is modeled usin...
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This paper proposes a new nonlinear interval programming method that can be used to handle uncertain optimization problems when there are dependencies among the interval variables. The uncertain domain is modeled using a multidimensional parallelepiped interval model. The model depicts single-variable uncertainty using a marginal interval and depicts the degree of dependencies among the interval variables using correlation angles and correlation coefficients. Based on the order relation of interval and the possibility degree of interval, the uncertain optimization problem is converted to a deterministic two-layer nesting optimization problem. The affine coordinate is then introduced to convert the uncertain domain of a multidimensional parallelepiped interval model to a standard interval uncertain domain. A highly efficient iterative algorithm is formulated to generate an efficient solution for the multi-layer nesting optimization problem after the conversion. Three computational examples are given to verify the effectiveness of the proposed method. (C) 2014 Elsevier B.V. All rights reserved.
Based on decoupling strategy, a novel efficient method is proposed to solve the nonlinearinterval uncertainty optimization problem with correlated interval design variables or parameters. This method is applicable to...
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Based on decoupling strategy, a novel efficient method is proposed to solve the nonlinearinterval uncertainty optimization problem with correlated interval design variables or parameters. This method is applicable to cases where both objective function and constraints are nonlinear with uncertain parameters, and design variables and parameters can be correlated or independent. The uncertainty of design variables and interval parameters is expressed by a multidimensional parallelepiped model, with which the correlated variables and parameters can be converted into independent interval parameters, thus constituting the traditional interval optimization model for independent interval parameters. Based on the idea of sequential optimization and reliability assessment (SORA), the two-layer nested optimization involved in the above interval optimization model can be converted into a single loop problem which can be solved efficiently by the sequential deterministic optimization algorithm. Finally, three numerical examples are investigated to demonstrate the effectiveness of the proposed model.
Efficient cross -regional allocation of hydropower is critical for the low -carbon energy transition. However, cooptimizing bidding curves for different regional markets presents significant challenges for hydropower ...
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Efficient cross -regional allocation of hydropower is critical for the low -carbon energy transition. However, cooptimizing bidding curves for different regional markets presents significant challenges for hydropower producers, due to the complex interplay of bidding strategies, multiple factors that contribute to uncertainty, and the diversity of regional markets. This paper proposes a novel bi-level model to optimize the bidding curves of cascade hydropower plants for multi -regional electricity markets with detailed modeling of their spatio-temporal correlations. The proposed model can adapt to regional markets with varying information transparency by employing a flexible approach to market modeling. A modified intervalprogramming method is proposed to address the multiple uncertainties in the bidding, which mitigates the excessive conservatism inherent in traditional intervalprogramming while preserving its robustness to the distribution estimation error. To efficiently solve the mathematical model, the complex nonlinear dependencies among interval variables are first eliminated through Taylor expansion and a modified multi -dimensional interpolation method. Subsequently, the order relation of interval and Karush-Kuhn-Tucker conditions are utilized to reformulate the proposed model into a tractable mixed -integer linear programming model. Numerical tests conducted on a real cascade hydropower system located in China validate the effectiveness and advantages of the proposed method.
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