Abstract:  By using the properties of absolute value function, this paper proposes a new constraint handling method, which reforms inequality constraint into equality constraint without any parameter. Then, by constructing a static penalty function of original problem, this paper develops an unconstrained optimization, which is solved by heuristic method named novel global harmony search (NGHS) algorithm. This algorithm simulates the music of the musicians with their own memory, by repeatedly adjusting the pitch of the instruments in the band, eventually reaches a wonderful state of the sound process. The NGHS algorithm utilizes position updating and mutation strategy with low probability. After solving 13 benchmark functions with constrains, the results demonstrate that the constraint-handling technique is effective. Finally the algorithm is applied to solve tension-compression spring design problem.

Key words: absolute value function, constraint handling, inequality constraint, constrained optimization, global harmony search, benchmark functions, tension-compression spring design

摘要： 利用绝对值函数的性质给出了一种约束处理方法：将不等式约束转化为等式约束，该转化无需增加任何参数；进而通过构造静态罚函数将原问题转化为无约束优化，采用全局和声搜索算法求解。该算法模拟了音乐创作中乐师们凭借自己的记忆，通过反复调整乐队中各乐器的音调，最终达到一个美妙的和声状态的过程；全局和声搜索算法嵌入了位置更新和小概率变异策略。求解13个带有约束的非线性规划标准测试函数，结果表明该约束处理方法是有效的。最后将该算法应用于求解伸缩绳设计优化问题。

关键词: 绝对值函数, 约束处理, 不等式约束, 约束优化, 全局和声搜索, 标准测试函数, 伸缩绳设计