A Reinforced Whale Optimization Algorithm for Solving Mathematical Optimization Problems

Abstract

The whale optimization algorithm has several advantages, such as simple operation, few control parameters, and a strong ability to jump out of the local optimum, and has been used to solve various practical optimization problems. In order to improve its convergence speed and solution quality, a reinforced whale optimization algorithm (RWOA) was designed. Firstly, an opposition-based learning strategy is used to generate other optima based on the best optimal solution found during the algorithm's iteration, which can increase the diversity of the optimal solution and accelerate the convergence speed. Secondly, a dynamic adaptive coefficient is introduced in the two stages of prey and bubble net, which can balance exploration and exploitation. Finally, a kind of individual information-reinforced mechanism is utilized during the encircling prey stage to improve the solution quality. The performance of the RWOA is validated using 23 benchmark test functions, 29 CEC-2017 test functions, and 12 CEC-2022 test functions. Experiment results demonstrate that the RWOA exhibits better convergence accuracy and algorithm stability than the WOA on 20 benchmark test functions, 21 CEC-2017 test functions, and 8 CEC-2022 test functions, separately. Wilcoxon's rank sum test shows that there are significant statistical differences between the RWOA and other algorithms.

Keywords: CEC test functions; exploration and exploitation; opposition-based learning strategy; whale optimization algorithm.

Figure 1

Trajectory diagram of w.

Figure 2

Flowchart of RWOA.

Figure 3

Comparison of convergence curves of WOA and RWOA.

Figure 4

Convergence curves at dimension = 10.

Figure 5

Convergence curves at dimension = 50.

Figure 5

Convergence curves at dimension = 50.

Figure 6

Convergence curves at dimension = 100.