Department of Electrical and Computer Engineering, National University of Singapore, 117576, Singapore.
Evol Comput. 2013 Spring;21(1):149-77. doi: 10.1162/EVCO_a_00066. Epub 2012 Mar 12.
Many real-world optimization problems are subjected to uncertainties that may be characterized by the presence of noise in the objective functions. The estimation of distribution algorithm (EDA), which models the global distribution of the population for searching tasks, is one of the evolutionary computation techniques that deals with noisy information. This paper studies the potential of EDAs; particularly an EDA based on restricted Boltzmann machines that handles multi-objective optimization problems in a noisy environment. Noise is introduced to the objective functions in the form of a Gaussian distribution. In order to reduce the detrimental effect of noise, a likelihood correction feature is proposed to tune the marginal probability distribution of each decision variable. The EDA is subsequently hybridized with a particle swarm optimization algorithm in a discrete domain to improve its search ability. The effectiveness of the proposed algorithm is examined via eight benchmark instances with different characteristics and shapes of the Pareto optimal front. The scalability, hybridization, and computational time are rigorously studied. Comparative studies show that the proposed approach outperforms other state of the art algorithms.
许多现实世界的优化问题都受到不确定性的影响，这些不确定性可能表现为目标函数中存在噪声。估计分布算法（EDA）是一种用于搜索任务的全局分布建模的进化计算技术，它可以处理噪声信息。本文研究了 EDAs 的潜力；特别是基于受限玻尔兹曼机的 EDA，它可以在噪声环境中处理多目标优化问题。噪声以高斯分布的形式引入到目标函数中。为了减少噪声的不利影响，提出了一种似然校正特征来调整每个决策变量的边际概率分布。随后，将 EDA 与离散域中的粒子群优化算法进行混合，以提高其搜索能力。通过具有不同 Pareto 最优前沿形状和特征的八个基准实例来检验所提出算法的有效性。严格研究了可扩展性、混合和计算时间。比较研究表明，所提出的方法优于其他最先进的算法。
