Large-Scale Heliostat Field Optimization for Solar Power Tower System Using Matrix-Based Differential Evolution

Intelligent optimization of a solar power tower heliostat field (SPTHF) is critical for harnessing solar energy in various scenarios. However, existing SPTHF optimization methods are typically based on specific geometric layout constraints and assume that each heliostat has the same size and height. As a result, these methods are not flexible or practical in many real-world SPTHF application scenarios. Therefore, this paper proposes a novel flexible SPTHF (FSPTHF) model that is more practical and involves fewer assumptions. This model enables the use of different layouts and simultaneous optimization of the parameters of each heliostat. As an FSPTHF can involve hundreds or even thousands of heliostats, optimizing the parameters of all heliostats results in a challenging large-scale optimization problem. To efficiently solve this problem, this paper proposes a matrix-based differential evolution algorithm, called HMDE, for large-scale heliostat design. The HMDE uses a matrix-based encoding and representation method to improve optimization accuracy and convergence speed, incorporating two novel designs. First, a dual elite-based mutation method is proposed to enhance the convergence speed of HMDE by learning from multiple elite individuals. Second, a multi-level crossover method is proposed to improve the optimization accuracy and convergence speed by integrating element-level and vector-level crossover based on matrix representation. Extensive experiments were conducted on 30 problem instances based on real-world data with three different layouts and problem dimensions up to 12,000, where state-of-the-art algorithms were used for comparison. The experimental results show that the proposed HMDE can effectively solve large-scale FSPTHF optimization problems.