Abstract: A solving method for constrained optimization problem based on adaptive penalty function and improved bats algorithm is designed. An adaptive penalty function method is proposed, which both takes the circumstances of constraint violations and characteristics of evolutionary process into consideration. The more frequently a constraint is violated, the more powerful it is, the larger penalty coefficient is given to it. The more infeasible solutions in the population, the smaller the constrain should be, in other words, the smaller the penalty coefficient should be, in order to keep the diversity of the population. An improved bats algorithm is proposed, which generates the initial population by using the ergodicity of chaos, and enhances the quality of the initial population and diversity of population. In the local search of bats algorithm which takes the pulse loudness into consideration, crossover operation is added. In order to prevent the algorithm from falling into local optimal solution in the late, variation operation is added, which ensures the diversity of the population. Then adaptive penalty function and improved bats algorithm are mixed to solve constrained optimization problem, and 4 complex standard test functions and 2 practical engineering problems prove the feasibility and effectiveness of the solving methods for constrained optimization problem.

Key words: bats algorithm, adaptive penalty function, constrained optimization problem

摘要： 设计了一种基于自适应罚函数法和改进蝙蝠算法的约束优化问题求解方法。提出了一种自适应罚函数法，该处理方法综合考虑了约束违反的情况和进化过程的特点，如果某个约束违反的次数越多，则证明该约束越强，赋予惩罚系数越大；种群中的不可行解的数量越多，为保持种群的多样性，则约束应该取较小的值，即惩罚系数取较小的值。提出了一种改进的蝙蝠算法，利用混沌的遍历性特点产生初始种群，增强了初始种群的多样性和种群的质量；在考虑了脉冲响度的蝙蝠算法局部搜索中，融入了交叉操作；为防止算法在后期陷入局部最优解，引进了变异操作，保证了群体的多样性。将自适应罚函数法与改进的蝙蝠算法融合起来求解约束优化问题，4个复杂的标准测试函数和2个工程实际问题证明了该约束优化求解方法的可行性和有效性。

关键词: 蝙蝠算法, 自适应罚函数, 约束优化问题