Differential evolution with bi-strategy co-deployment framework and diversity improvement

Differential Evolution (DE) has been adopted as the baseline optimizer for problems with continuous search space because of its stable optimization performance and fast convergence speed. When tackling complex optimization problems, DE faces limitations in its non-adaptive form and fails to utilize the potential information of stagnant individuals to improve the search performance. To address these shortcomings, this paper proposes Differential Evolution with Bi-strategy co-deployment framework and Diversity improvement (BDDE) to enhance the search capacity of DE-based variants. First, a bi-strategy co-deployment framework (BCF) is constructed, which combines a probability-based trial vector generation strategy with a parameter adaptation scheme to leverage their respective advantages. Second, a diversity improvement strategy based on gradient descent is proposed, where diversity level and stagnation detection are both measured. For stagnant individuals at excessively low diversity levels, a gradient descent scheme is introduced to update them, guiding individuals to escape local optima and increasing the population diversity. The performance of BDDE is rigorously evaluated on the standard benchmark test suites developed for the 2013, 2014, 2017, and 2022 Congress on Evolutionary Computation (CEC) real-parameter optimization competitions. In addition, the population diversity of BDDE variants is visualized, and an exploration-exploitation analysis of BDDE is conducted to illustrate the effects of its components. Extensive experimental results indicate that BDDE can outperform other advanced algorithms and achieve highly competitive performance for real-world problems.