Dynamic Robust Particle Swarm Optimization Algorithm Based on Hybrid Strategy

Introduction

Optimization problems are subject to change in response to the dynamics and uncertainty of the environment, leading to what are known as dynamic optimization problems (DOPs) (Jin & Branke, 2005). Most of the current research in this area has focused on tracking moving optimization (TMO) (Parrott & Li, 2006; Chen et al., 2023; Falahiazar et al., 2022), which involves an algorithm that seeks to identify a new optimal solution after each environmental modification. Despite its effectiveness in addressing dynamic optimization problems, this approach may present some limitations in practical applications. Firstly, it may face challenges in quickly identifying the optimal solution in each dynamic environment within a limited timeframe. Secondly, even if it manages to identify the optimal solution in the new environment, it will require a considerable amount of computational resources.

Based on the aforementioned considerations, Yu et al. (2010) introduced the concept of robust optimization over time (ROOT) with the primary aim of discovering a set of robust solutions that can adapt to multiple dynamic environments both in the present and future. Following this, Jin et al. (2012) proposed a framework for tackling dynamic robust problems, which involves an optimizer, a database containing historical information, an approximator, and a predictor. Along with robustness, the ROOT approach also takes into account switching costs, which was considered in literature (Huang et al., 2017) that proposed dynamic robust optimization algorithm (robust optimization over time considering switching cost, ROOT/SC).

However, the ROOT/SC algorithm has two limitations: 1) the search dimensions cannot be expanded sufficiently, leading to considerable practical restrictions; 2) the feasible solutions from non-dominated solution sets cannot be sought using the algorithm. To address these problems, Huang et al. (2020) proposed a more efficient dynamic robust multi-objective algorithm named ROOT/SCII (improved ROOT/SC), which incorporates minimizing switching costs as an additional objective by weighing the robustness of the high-dimensional decision space and switching costs. Yazdani et al. (2019) applied multiple swarm methods to the ROOT problem, using multi-swarm PSO to identify and track optimal values while collecting information about peaks in the decision space over time, which was used to select the next robust solution. Moreover, most dynamic robust algorithms employ prediction models to solve ROOT problems; however, the accuracy of such models in practical applications is dependent on the availability of data. In addition, for dynamic problems with high-dimensional search spaces and high change frequencies, a large amount of data is often required to obtain accurate predictions. Consequently, Yazdani et al. (2017) proposed a new ROOT framework that eliminates the original predictor in ROOT (Jin et al., 2012) and substitutes the prediction of future fitness values with the prediction of future behavior of peaks, using the behavioral information of peaks to predict robust feasible solutions that satisfy the future dynamic environment when the resulting feasible solution does not satisfy the dynamic environment.

It has been demonstrated that the effectiveness of search engines is crucial to addressing dynamic robust problems. To further enhance the ability to solve such problems, this article proposes a dynamic robust optimization of particle swarm optimization algorithm based on a hybrid strategy (HS-DRPSO). In the HS-DRPSO algorithm, the two variation strategies of the differential evolution algorithm, i.e., “DE/rand/1” and “DE/best/1,” are first combined with the particle swarm algorithm in each search period using a weight dynamic adjustment strategy. The population is then clustered, and the variation strategy of the brainstorming algorithm is used to select the central variation of the clusters to generate new individuals in the population and improve population diversity. By comparing the results with two other dynamic robust optimization algorithms across five dynamic standard test functions, it is demonstrated that the proposed algorithm’s overall performance is superior.