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Engineering design optimization in real life is a challenging global optimization problem, and many meta-heuristic algorithms have been proposed to obtain the global best solutions. An excellent meta-heuristic algorithm has two symmetric search capabilities: local search and global search. In this paper, an improved Butterfly Optimization Algorithm (BOA) is developed by embedding the cross-entropy (CE) method into the original BOA. Based on a co-evolution technique, this new method achieves a proper balance between exploration and exploitation to enhance its global search capability, and effectively avoid it falling into a local optimum. The performance of the proposed approach was evaluated on 19 well-known benchmark test functions and three classical engineering design problems. The results of the test functions show that the proposed algorithm can provide very competitive results in terms of improved exploration, local optima avoidance, exploitation, and convergence rate. The results of the engineering problems prove that the new approach is applicable to challenging problems with constrained and unknown search spaces.

An Improved Butterfly Optimization Algorithm for Engineering Design Problems Using the Cross-Entropy Method