*Article* **Hybrid Annealing Krill Herd and Quantum-Behaved Particle Swarm Optimization**

**Cheng-Long Wei 1 and Gai-Ge Wang 1,2,3,4,\***


Received: 27 July 2020; Accepted: 17 August 2020; Published: 21 August 2020

**Abstract:** The particle swarm optimization algorithm (PSO) is not good at dealing with discrete optimization problems, and for the krill herd algorithm (KH), the ability of local search is relatively poor. In this paper, we optimized PSO by quantum behavior and optimized KH by simulated annealing, so a new hybrid algorithm, named the annealing krill quantum particle swarm optimization (AKQPSO) algorithm, is proposed, and is based on the annealing krill herd algorithm (AKH) and quantum particle swarm optimization algorithm (QPSO). QPSO has better performance in exploitation and AKH has better performance in exploration, so AKQPSO proposed on this basis increases the diversity of population individuals, and shows better performance in both exploitation and exploration. In addition, the quantum behavior increased the diversity of the population, and the simulated annealing strategy made the algorithm avoid falling into the local optimal value, which made the algorithm obtain better performance. The test set used in this paper is a classic 100-Digit Challenge problem, which was proposed at 2019 IEEE Congress on Evolutionary Computation (CEC 2019), and AKQPSO has achieved better performance on benchmark problems.

**Keywords:** swarm intelligence; simulated annealing; krill herd; particle swarm optimization; quantum
