二进制阿基米德优化算法及其应用

Binary Archimedes Optimization Algorithm and Its Application

组合优化问题的研究在各个领域中有着广泛的应用意义。阿基米德优化算法是一种新型的元启发式算法,在求解连续空间的优化问题上应用广泛,但不能直接用于求解离散空间的组合优化问题。因此,提出了二进制阿基米德优化算法用以解决组合优化问题。首先,借鉴部分二进制优化算法,选用转换函数,并以位置距离差作为参数进行空间映射。其次,根据问题对编码的要求,在阿基米德优化算法的基础上选取不同的转换函数和sigmoid函数进行位置更新,同时提出了一种对应S型转换函数的sigmoid函数,以提高最优解的搜索效率与质量。最后,引入北极熊算法的出生与死亡规则,以更好地进行全局搜索,减少陷入局部最优解的次数。通过模拟求解0-1背包问题的仿真实验和在热力管道保温结构优化项目中的应用,验证了二进制阿基米德优化算法具有良好的收敛性、稳定性和搜索速度快等特点,且在对编码有要求时使用S型转换函数较V型转换函数具有更好的效果。

The researches of combinatorial optimization problems have wide application significances in various fields.Archimedes optimization algorithm is a new meta heuristic algorithm.It is widely used in continuous space optimization problems,but it cannot be directly used to solve combinatorial optimization problems in discrete space.But it's difficult to solve combinatorial optimization problems in discrete space.Therefore,a binary Archimedes optimization algorithm is proposed to solve the combinatorial optimization problems.Firstly,referencing some binary optimization algorithms,we take transformation function and choose position distance as parameter to do spatial mapping.Secondly,we propose a new sigmoid function corresponding to S-type transformation function and select different transformation functions and sigmoid functions to improve the search efficiency and quality of the optimal solution,according to requirements.Finally,we conduct global search better and reduce the occurrence of local optimal solutions by introducing the reproduction and extinction rule of polar bear optimization algorithm.It is verified that binary Archimedes optimization algorithm has some advantages and using S-type conversion has better effects function when coding is required in solving combinatorial optimization problems,through the comparative experiment about solving 0-1 knapsack problem and thermal pipe insulation structure composition.