Adaptive Differential Evolution Integration: Algorithm Development and Application to Inverse Heat Conduction

In response to the limitations observed in existing single intelligent optimization algorithms, particularly their shortcomings in their global search capability and population diversity, we propose the Adaptive Differential Evolution Integral (ADEI) algorithm. Drawing inspiration from the collective behaviors observed in social organisms, this algorithm introduces four roles—“leaders”, “followers”, “contemplators”, and “rationalists”—employing a dynamic following strategy to effectively integrate these diverse particles and populations. Specifically, individuals in the Differential Evolution algorithm serve as the leader population, with tailored trial vector generation strategies implemented to enhance the global search capability. Concurrently, improvements are made to the particle swarm optimization algorithm to facilitate its role as the evolution strategy for other populations. By adopting this approach, the algorithm’s population diversity is enhanced, striking a balance between the global and local search performance, thereby augmenting its search efficiency and convergence accuracy. Extensive tests using benchmark functions and engineering problems show that the proposed algorithm excels in over half of the 28 test functions. It demonstrates strong convergence and adaptability for unimodal, multimodal, and composite problems. Experiments on solving inverse heat conduction problems validate its effectiveness in real-world scenarios and highlight its potential for engineering applications.