Hierarchy relaxations for robust equilibrium constrained polynomial problems and applications to electric vehicle charging scheduling

IF 1.8 3区 数学 Q1 Mathematics Journal of Global Optimization Pub Date : 2024-07-20 DOI:10.1007/s10898-024-01421-0
Thai Doan Chuong, Xinghuo Yu, Andrew Eberhard, Chaojie Li, Chen Liu
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Abstract

In this paper, we consider a polynomial problem with equilibrium constraints in which the constraint functions and the equilibrium constraints involve data uncertainties. Employing a robust optimization approach, we examine the uncertain equilibrium constrained polynomial optimization problem by establishing lower bound approximations and asymptotic convergences of bounded degree diagonally dominant sum-of-squares (DSOS), scaled diagonally dominant sum-of-squares (SDSOS) and sum-of-squares (SOS) polynomial relaxations for the robust equilibrium constrained polynomial optimization problem. We also provide numerical examples to illustrate how the optimal value of a robust equilibrium constrained problem can be calculated by solving associated relaxation problems. Furthermore, an application to electric vehicle charging scheduling problems under uncertain discharging supplies shows that for the lower relaxation degrees, the DSOS, SDSOS and SOS relaxations obtain reasonable charging costs and for the higher relaxation degrees, the SDSOS relaxation scheme has the best performance, making it desirable for practical applications.

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稳健均衡约束多项式问题的层次松弛及在电动汽车充电调度中的应用
在本文中,我们考虑了一个具有均衡约束的多项式问题,其中约束函数和均衡约束涉及数据的不确定性。我们采用稳健优化方法,通过建立稳健均衡约束多项式优化问题的有界度对角显性平方和(DSOS)、缩放对角显性平方和(SDSOS)和平方和(SOS)多项式松弛的下界近似和渐近收敛,研究了不确定均衡约束多项式优化问题。我们还提供了数值示例,说明如何通过求解相关松弛问题来计算稳健均衡约束问题的最优值。此外,在不确定放电供应情况下的电动汽车充电调度问题中的应用表明,对于较低的松弛度,DSOS、SDSOS 和 SOS 松弛方案可获得合理的充电成本,而对于较高的松弛度,SDSOS 松弛方案的性能最佳,因此非常适合实际应用。
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来源期刊
Journal of Global Optimization
Journal of Global Optimization 数学-应用数学
CiteScore
0.10
自引率
5.60%
发文量
137
审稿时长
6 months
期刊介绍: The Journal of Global Optimization publishes carefully refereed papers that encompass theoretical, computational, and applied aspects of global optimization. While the focus is on original research contributions dealing with the search for global optima of non-convex, multi-extremal problems, the journal’s scope covers optimization in the widest sense, including nonlinear, mixed integer, combinatorial, stochastic, robust, multi-objective optimization, computational geometry, and equilibrium problems. Relevant works on data-driven methods and optimization-based data mining are of special interest. In addition to papers covering theory and algorithms of global optimization, the journal publishes significant papers on numerical experiments, new testbeds, and applications in engineering, management, and the sciences. Applications of particular interest include healthcare, computational biochemistry, energy systems, telecommunications, and finance. Apart from full-length articles, the journal features short communications on both open and solved global optimization problems. It also offers reviews of relevant books and publishes special issues.
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