Optimization is more and more significant due to its application in the real engineering problems. The recently proposed imperialist competitive algorithm (ICA) is a successful method in mono-objective optimization. Nevertheless, ICA cannot handle simultaneously the conflicting objectives in multi-objective design problem. In addition, the ICA has the drawback of trapping in local optimum solutions when used for high-dimensional or complex multimodal functions. In order to deal with these situations, in this work, an improved ICA, named modified multi-objective imperialist competitive algorithm (MOMICA) is proposed. In MOMICA, an attraction and repulsion (AR) concept is implemented in the assimilation phase to improve the performances of the algorithm to reach the global optimal position. Moreover, in contrast to ICA, the proposed algorithm integrates the sorting non-dominated strategy (SND) to store the Pareto optimal solutions of multiple conflicting functions. Three performance metrics are used to evaluate the performance of the proposed algorithm: (a) convergence to the true Pareto-optimal set, (b) solutions diversity and (c) robustness, characterized by the variance over 10 runs. The results presented in this paper show that the MOMICA algorithm outperforms the other popular techniques in terms of convergence characteristics and global search ability, for both benchmark functions optimization and multi-objective engineering optimization problems.

由于其在实际工程问题中的应用，优化变得越来越重要。最近提出的帝国主义竞争算法（ICA）是一种成功的单目标优化方法。但是，ICA无法同时处理多目标设计问题中的冲突目标。此外，ICA在用于高维或复杂的多峰函数时，存在陷入局部最优解的缺点。为了应对这些情况，在这项工作中，提出了一种改进的ICA，称为改进的多目标帝国主义竞争算法（MOMICA）。在MOMICA中，在同化阶段实现了吸引和排斥（AR）概念，以提高算法的性能以达到全局最优位置。而且，与ICA相比，该算法集成了排序非主导策略（SND）来存储多个冲突函数的Pareto最优解。使用三个性能指标来评估所提出算法的性能：（a）收敛到真正的帕累托最优集，（b）解多样性和（c）健壮性，其特征是超过10次运行的方差。本文给出的结果表明，对于基准函数优化和多目标工程优化问题，MOMICA算法在收敛特性和全局搜索能力方面均优于其他流行技术。（a）收敛到真实的Pareto最优集合，（b）解的多样性和（c）鲁棒性，其特征在于10次运行的方差。本文给出的结果表明，对于基准函数优化和多目标工程优化问题，MOMICA算法在收敛特性和全局搜索能力方面均优于其他流行技术。（a）收敛到真实的Pareto最优集合，（b）解的多样性和（c）鲁棒性，其特征在于10次运行的方差。本文给出的结果表明，对于基准函数优化和多目标工程优化问题，MOMICA算法在收敛特性和全局搜索能力方面均优于其他流行技术。