A Trust-Region Algorithm for Bi-Objective Stochastic Optimization
A Trust-Region Algorithm for Bi-Objective Stochastic Optimization
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DOI：
10.1016/j.procs.2011.04.153
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
Sujin Kim;Jong-hyun Ryu
中科院分区：
文献类型：
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作者：
Sujin Kim;Jong-hyun Ryu
我们发展了一种新的方法来逼近双目标随机优化问题的Pareto前沿，其中期望目标函数是通过从昂贵的模拟中获取样本平均输出来估计的。在该算法的每一次迭代中，识别一个信任域，并利用样本平均值构造期望目标函数的二次近似函数。为了确定信赖域内的非支配解，基于近似目标函数构造了一个单目标优化问题。在更新非支配解集合后，确定围绕最孤立点的新的信任域来探索尚未访问的区域。当计算预算有限时，每次迭代的大样本量会导致对预期目标函数的更精确的逼近，但算法不能运行足够的迭代来生成一组接近帕累托前沿的解。所提出的可变采样方案考虑了近似误差和优化误差之间的折衷，从而自适应地更新样本量。数值结果表明，本文提出的方法是可行的，选择合适的采样方案可以显著提高系统的性能。
We develop a new method for approximating the Pareto front of a bi-objective stochastic optimization problem in which the expected objective functions are estimated by taking sample averaged outputs from expensive simulations. At each iteration of the proposed algorithm, a trust region is identified and quadratic approximate functions for the expected objective functions are built using the sample average values. To determine non-dominated solutions in the trust region, a single-objective optimization problem is constructed based on the approximate objective functions. After updating the set of non-dominated solutions, a new trust region around the most isolated point is determined to explore areas that have not been visited. When the computational budget is limited, a large sample size at each iteration leads to more accurate approximation of the expected objective functions, but the algorithm is not able to run for enough iterations to generate a set of solutions that are close to the Pareto front. The proposed variable sampling scheme adaptively updates the sample size with consideration for this trade-offetween approximation and optimization errors. The numerical results show that our proposed method is feasible, and the performance can be significantly improved with an appropriate sampling scheme.