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Solving dynamic optimization problems with an Improved Imperialis Competition Algorithm
Mr Mahdi Sadeghi Moghadam, Dr Samad Nejatian, Dr Hamid Parvin, Dr Karamullah Bagheri Fard, Dr Seyed Hadi Yagoubian,
Volume 22, Issue 2 (9-2025)
Abstract
Optimization issues are often defined statically, assuming constant environmental conditions. However, in many real-world scenarios, problem environments are dynamic and continuously changing. Thus we need optimization algorithms that could solves those issues in dynamic environments as well. Dynamic optimization problems are change(s) that may occur through the time. Such environments are characterized by uncertainty, temporal changes, and structural complexities, which makes the optimization process a significant challenge. In addressing these challenges, evolutionary algorithms have emerged as one of the most effective approaches for solving dynamic optimization problems (DOPs). Among these algorithms, the Imperialist Competitive Algorithm (ICA), designed based on swarm intelligence and competition among imperialist countries, has garnered considerable attention due to its capability in solving static optimization issues. In this research, Imperialist Competitive Algorithms, inspired by the historical and political processes of colonization and assimilation, have been known as one of the efficient evolutionary algorithms. These algorithms face numerous challenges when dealing with dynamic problems , including reduced population diversity, performance degradation in conditions of rapid environmental changes, and limitations in optimal convergence. These cases indicate the need to develop improved and more adaptable versions of these algorithms. Using concepts such as memory, population clustering, and repulsion mechanisms, this algorithm has been able to maintain population diversity at all stages while increasing the speed of convergence in the face of environmental changes. The key feature of the proposed algorithm is the use of memory to store previous optimal solutions, a clustering mechanism to manage population diversity, and repulsion to prevent unnecessary accumulation of solutions in specific regions. Nevertheless, ICA exhibits poor performance in dynamic environments because it lacks mechanisms to maintain diversity, quick adaptation to environmental changes, and new optima track. This study presents an improved version of ICA aimed at overcoming these limitations. The proposed algorithm incorporates a combination of a memory mechanism and a clustering strategy to enhance its adaptability to environmental changes and preserve diversity within the population. The memory mechanism stores information about previous optima and utilizes it under appropriate conditions to accelerate the optimization process.for clustering method is used for clustering. Clustering in the proposed method ensures that diversity is maintained for the population during the execution of the algorithm. In this study, our goal is to solve problems that change the environment in a global way. That means, the fitness of all points in the environment changes. By testing just one point in the environment and comparing the fitness obtained with its previously stored value, we can detect a change in the environment. On the other hand, the clustering strategy, particularly the k-means technique, to maintain maintain population diversity and prevents the convergence of solutions to specific regions. Together, these two components create a balance between exploration and exploitation, thereby improving the algorithm's performance in dynamic environments. To evaluate the performance of the proposed algorithm, the Moving Peaks Benchmark (MPB) was used as a standard metric. Due to its capability to simulate complex and diverse changes in dynamic environments—particularly in Branke's second scenario—MPB is one of the most recognized tools for assessing the performance of dynamic optimization algorithms. The proposed algorithm was evaluated alongside advanced algorithms such as FTmPSO (TMO), RAmQSO-s4, RmNAFSA-s4, TFTmPSO, RFTmPSO, mQSO10 (5+5q), FMSO, CellularPSO, Multi-SwarmPSO, mCPSO, AmQSO*, FTMPSO, almPSO, and CDEPSA. Experimental results demonstrated that the proposed algorithm outperformed other methods in areas such as convergence speed, adaptability to environmental changes, and population diversity preservation. A key feature of the proposed algorithm is its ability to retain identified optima even after environmental changes. Additionally, the use of the k-means clustering technique has ensured that the algorithm effectively avoids excessive focus on specific regions and maintains population diversity while facing complex environmental changes. Another advantage of this algorithm is its scalability in handling dynamic optimization issues with high dimensions and complexities. These findings indicate that the proposed algorithm is not only effective in laboratory settings but also suitable for real-world applications with fast and dynamic changes.

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