A Dual Biogeography-Based Optimization Algorithm for Solving High-Dimensional Global Optimization Problems and Engineering Design Problems

Abstract

Biogeography-based optimization (BBO) cannot effectively solve high-dimensional global optimization problems due to its single migration mechanism and random mutation operator. To get better performance, a dual BBO based on sine cosine algorithm (SCA) and dynamic hybrid mutation is proposed in this work, which named SCBBO. Firstly, the Latin hypercube sampling method is innovatively used to improve the initial population ergodicity. Secondly, a nonlinear transformation parameter and a inertia weight adjustment factor are designed into the position update formula of SCA to make SCBBO suitable for high dimensional environments. Then, a dynamic hybrid mutation operator is designed by combining Laplacian and Gaussian mutation, which helps the algorithm to escape from local optima and balance the exploration and exploitation. Finally, the dual learning strategy is integrated, so the convergence accuracy is further improved by generating dual individuals. Meanwhile, A sequence convergence model is established to prove the algorithm can converge to the global optimal solution with probability 1. Compared with other state-of-the-art evolutionary algorithms, SCBBO effectively improves the optimization accuracy and convergence speed for high-dimensional optimization problems. To further show the superiority of SCBBO, its performance is compared on 1000, 2000, 5000 and 10000 dimensions, respectively. The comparsions show that SCBBO’s optimization results on these dimensions are basically the same. Applying SCBBO to engineering design problems, and the simulation results demonstrate that the proposed method is also effective on constrained optimization problems.

Keywords

• Biogeography-based optimization
• high-dimensional global optimization
• sine cosine algorithm
• dual learning
• engineering design problems