An adaptive bivariate decomposition method for interval optimization problems with multiple uncertain parameters

Tonghui Wei

doi:10.1007/s00366-021-01589-z

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An adaptive bivariate decomposition method for interval optimization problems with multiple uncertain parameters

2022-01-27

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Tonghui Wei

李峰 (Feng Li) *

DOI：10.1007/s00366-021-01589-z

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Abstract

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A novel interval optimization method based on an adaptive bivariate decomposition algorithm is developed to solve the engineering uncertain optimization problems with multiple interval parameters. Unlike the traditional highly time-consuming nested optimization approach, the interval perturbation method-based interval optimization avoids tedious inner optimization, nonetheless, it faces huge computational challenges in the optimization issues with large uncertainties and requires derivative information that may be unavailable for complex engineering systems. To overcome these shortcomings, an adaptive bivariate decomposition method (ABDM) is proposed to compute the interval ranges of the uncertain function. In the optimization, the objective function and constraints are decomposed by ABDM into a sum of several one- and two-dimensional subsystems. The extrema of the subsystems are approximately calculated through subinterval analysis, and an adaptive convergence strategy is applied to guarantee the accuracy of the obtained bounds. Based on the interval order relation and the reliability-based possibility degree of interval, the interval uncertain optimization model is converted into a deterministic optimization one. To effectively solve the deterministic optimization model, a robust optimization solver known as lightning attachment procedure optimization is employed in the optimization algorithm. Finally, a numerical example and two engineering applications illustrate the accuracy and effectiveness of the method for uncertain optimization issues with multiple interval parameters. Moreover, the new method does not need to determine the derivative information of the uncertain objective and constraints, and thus applies to different engineering optimization issues.

Keywords:

Uncertain optimization

Interval analysis

Bivariate decomposition method

Adaptive convergence strategy

Lightning attachment procedure optimization