In this paper, we propose a novel multi-objective ant colony optimizer (called iMOACO\(_{\mathbb {R}}\)) for continuous search spaces, which is based on ACO\(_{\mathbb {R}}\) and the R2 performance indicator. iMOACO\(_{\mathbb {R}}\) is the first multi-objective ant colony optimizer (MOACO) specifically designed to tackle continuous many-objective optimization problems (i.e., multi-objective optimization problems having four or more objectives). Our proposed iMOACO\(_{\mathbb {R}}\) is compared to three state-of-the-art multi-objective evolutionary algorithms (NSGA-III, MOEA/D and SMS-EMOA) and a MOACO algorithm called MOACO\(_{\mathbb {R}}\) using standard test problems and performance indicators taken from the specialized literature. Our experimental results indicate that iMOACO\(_{\mathbb {R}}\) is very competitive with respect to NSGA-III and MOEA/D and it is able to outperform SMS-EMOA and MOACO\(_{\mathbb {R}}\) in most of the test problems adopted.

中文翻译：

---

一种基于指标的多目标蚁群优化器，用于连续搜索空间

在本文中，我们提出了一种基于ACO \（_ {\ mathbb {R}}的新型多目标蚁群优化器（称为iMOACO \（_ {\ mathbb {R}} \））用于连续搜索空间\）和R 2性能指标。iMOACO \（_ {\ mathbb {R}} \）是第一个专门设计用于解决连续多目标优化问题（即具有四个或更多目标的多目标优化问题）的多目标蚁群优化器（MOACO）。我们提出的iMOACO \（_ {\ mathbb {R}} \）与三种最新的多目标进化算法（NSGA-III，MOEA / D和SMS-EMOA）和称为MOACO的MOACO算法进行了比较\（__ \ mathbb {R}} \）使用来自专业文献的标准测试问题和性能指标。我们的实验结果表明，iMOACO \（_ {\ mathbb {R}} \）在NSGA-III和MOEA / D方面非常有竞争力，并且能够胜过SMS-EMOA和MOACO \（_ {\ mathbb {R }} \）在大多数测试问题中采用。