Optimization in Uncertain and Complex Dynamic Environments with Evolutionary Methods

In the real world, many of the optimization issues are dynamic, uncertain, and complex in which the objective function or constraints can be changed over time. Consequently, the optimum of these issues is changed nonlinearly. Therefore, the optimization algorithms not only should search the global optimum value in the space but also should follow the path of optimal change in dynamic environment. Accordingly, several researchers believe in the effectiveness of following a series of optimums compared to a global optimum. Therefore, when an environment is changed, following a global optimum in a series of best optimums is more efficient. Evolutionary algorithms (EA) were inspired by biological and natural evolution. Because of changing characteristic of nature, it can be a good option for dynamic optimization. In recent years, different methods have been proposed to improve EA of static environments. One of the most common methods is multi-population method. In this method, the whole space is divided into sub-spaces. Each sub-space covers some local optimums and represents a sub-population. The algorithm updates the particles of each sub-space and searches the best optimum. The most challenging issue of multi-population method is to create the desired number of sub-population and people to cover different sub-spaces in the search space. In the present study, in order to deal with the challenges, a new algorithm based on particle optimization algorithm, which is called decrement and increment particle optimization algorithm, was proposed. The algorithm is able to follow and find the number of time-varied optimum in an environment with invisible changes by increasing or decreasing the number of particles adaptively. Another challenging issue in dynamic optimization is the detection of environmental changes, due to the impossibility of this issue and failure of detection-based algorithms.  In the proposed method, there is no need to detect the environmental changes and it always adapts itself to the environment. Furthermore, the terms of focused search area were defined to emphasize on promising spaces to accelerate the local search process and prevent early convergence. The results of the proposed algorithm were evaluated on moving peaks and compared with several valid algorithms. The results showed the positive effect of decrement/increment mechanism of particles on finding and following time of many optimums compared to other multi-population based optimization algorithm.