In this paper, we enriched Ant Colony Optimization (ACO) with interval outranking to develop a novel multiobjective ACO optimizer to approach problems with many objective functions. This proposal is suitable if the preferences of the Decision Maker (DM) can be modeled through outranking relations. The introduced algorithm (named Interval Outranking-based ACO, IO-ACO) is the first ant-colony optimizer that embeds an outranking model to bear vagueness and ill-definition of DM preferences. This capacity is the most differentiating feature of IO-ACO because this issue is highly relevant in practice. IO-ACO biases the search towards the Region of Interest (RoI), the privileged zone of the Pareto frontier containing the solutions that better match the DM preferences. Two widely studied benchmarks were utilized to measure the efficiency of IO-ACO, i.e., the DTLZ and WFG test suites. Accordingly, IO-ACO was compared with two competitive many-objective optimizers: The Indicator-based Many-Objective ACO and the Multiobjective Evolutionary Algorithm Based on Decomposition. The numerical results show that IO-ACO approximates the Region of Interest (RoI) better than the leading metaheuristics based on approximating the Pareto frontier alone.

中文翻译：

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偏好并入多目标优化：一种基于优胜的蚁群算法

在本文中，我们通过区间优化丰富了蚁群优化（ACO），以开发一种新颖的多目标 ACO 优化器来解决具有许多目标函数的问题。如果决策者 (DM) 的偏好可以通过排名关系建模，则该提议是合适的。引入的算法（命名为基于 Interval Outranking 的 ACO，IO-ACO）是第一个嵌入 outranking 模型以承受 DM 偏好的模糊性和不明确定义的蚁群优化器。这种能力是 IO-ACO 最与众不同的特征，因为这个问题在实践中高度相关。IO-ACO 将搜索偏向于感兴趣区域 (RoI)，这是帕累托边界的特权区域，包含更好地匹配 DM 偏好的解决方案。两个广泛研究的基准被用来衡量 IO-ACO 的效率，即，DTLZ 和 WFG 测试套件。因此，将 IO-ACO 与两个具有竞争力的多目标优化器进行了比较：基于指标的多目标 ACO 和基于分解的多目标进化算法。数值结果表明，IO-ACO 比仅基于近似帕累托边界的领先元启发式算法更好地近似感兴趣区域（RoI）。