Free Search with Adaptive Differential Evolution Exploitation and Quantum-Inspired Exploration

Recently an interesting evolutionary mechanism, sensibility, inherited from a concept model of Free Search (FS) was introduced and used for solving network problems. Unfortunately, the original FS is not easy to implement because it requires key knowledge that is not clearly defined in the existing literature to determine the neighborhood space that profoundly affects the performance of the original FS. This paper thus designs a new implementation for the concept model of FS, and proposes a new algorithm, called Free Search with Adaptive Differential Evolution Exploitation and Quantum-Inspired Exploration (ADEQFS) to address this issue. In ADEQFS, we focus on designing a new mutation strategy by employing adaptive differential evolution techniques as well as concepts and principles from real-coded quantum-inspired evolutionary algorithm. In addition, we use the crossover operation from the traditional Differential Evolution scheme to alleviate the premature convergence for the proposed algorithm. Furthermore, we employ the greedy mechanism to preserve the best solutions found at each generation. The convergence analysis of the proposed algorithm is also presented in this paper. We give the proof of convergence by using the Markov chain model. Thirty-four optimization test functions with different mathematical characteristics are employed as benchmark set to test the performance of ADEQFS. The numerical results highlight the improved convergence rate and computation reliability.