Bernstein-based oppositional-multiple learning and differential enhanced exponential distribution optimizer for real-world optimization problems

Abstract

Meta-heuristic algorithms play an essential role in solving real-world optimization problems. However, their performance is limited by the complexity and variability of the problems. Hence, various efficient algorithms are being actively explored. The exponential distribution optimizer (EDO), having attracted attention for its efficient search performance, has been extended to several applications. However, it suffers from falling into local optima and weak exploitation. Meanwhile, it cannot be directly applied to solve binary optimization problems. To address these challenges, this paper proposes an enhanced EDO called BOMLDEDO. The Bernstein-assisted oppositional-multiple learning strategy is proposed to avoid falling into local optimality. The Bernstein-based adaptive differential strategy is developed to improve exploitation capability. Moreover, by introducing a transfer function, repair method, and binary-to-real operation, BOMLDEDO is extended to a binary version. The IEEE (Institute of Electrical and Electronics Engineers) CEC (Congress on Evolutionary Computation) test functions and engineering problems are used to evaluate BOMLDEDO's optimization performance for continuous problems. Compared to its competitors, BOMLDEDO ranks first on more than 8 out of 10 IEEE CEC 2020 functions and more than 10 out of 12 IEEE CEC 2022 functions. Meanwhile, it achieves the global optimum in 91% of engineering problems. Furthermore, the 0–1 knapsack problems are applied to verify BOMLDEDO's binary optimization capabilities, and the results show that BOMLDEDO is successfully utilized in 14 knapsack instances. The above results demonstrate that incorporating multiple strategies helps improve the performance of BOMLDEDO, making it more reliable and applicable in solving continuous optimization problems and 0–1 knapsack problems.