A real-world multiobjective optimization problem (MOP) usually has differently scaled objectives. Objective space normalization has been widely used in multiobjective optimization evolutionary algorithms (MOEAs). Without objective space normalization, most of the MOEAs may fail to obtain uniformly distributed and well-converged solutions on MOPs with differently scaled objectives. Objective space normalization requires information on the Pareto front (PF) range, which can be acquired from the ideal and nadir points. Since the ideal and nadir points of a real-world MOP are usually not known a priori , many recently proposed MOEAs tend to estimate and update the two points adaptively during the evolutionary process. Different methods to estimate ideal and nadir points have been proposed in the literature. Due to inaccurate estimation of the two points (i.e., inaccurate estimation of the PF range), objective space normalization may deteriorate the performance of an MOEA. Different methods have also been proposed to alleviate the negative effects of inaccurate estimation. This article presents a comprehensive survey of objective space normalization methods, including ideal point estimation methods, nadir point estimation methods, and different methods based on the utilization of the estimated PF range.

中文翻译：

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多目标进化算法中的归一化方法综述

现实世界的多目标优化问题 (MOP) 通常具有不同比例的目标。目标空间归一化已广泛应用于多目标优化进化算法 (MOEA)。如果没有目标空间归一化，大多数 MOEA 可能无法在具有不同尺度目标的 MOP 上获得均匀分布和良好收敛的解决方案。目标空间归一化需要有关帕累托前沿 (PF) 范围的信息，这些信息可以从理想点和最低点获得。由于通常不知道现实世界 MOP 的理想点和最低点先验地，许多最近提出的 MOEA 倾向于在进化过程中自适应地估计和更新这两个点。文献中提出了估计理想点和最低点的不同方法。由于两点估计不准确（即PF范围估计不准确），客观空间归一化可能会降低MOEA的性能。还提出了不同的方法来减轻不准确估计的负面影响。本文全面介绍了客观空间归一化方法，包括理想点估计方法、最低点估计方法以及基于估计PF范围利用的不同方法。