中文摘要：

研究了以总路程与总收益之比为目标函数的最小比率旅行商问题,提出了求解该问题的离散蝙蝠算法。介绍了蝙蝠算法的基本思想,重新定义了位置与位置的减法操作算子、实数与位置的乘法操作算子以及速度与位置的加法操作算子,引入了城市子序列逆序策略来对线路进行局部搜索。给出了算法的具体实现方案,并通过仿真和比较实验验证算法的优化性能,实验结果表明该算法可以有效求解最小比率旅行商问题。

英文摘要：

This paper studied minimum ratio traveling salesman problem（ MRTSP）, which objective function was the ratio between the total distances and total benefits, and presented a discrete bat algorithm for solving MRTSP. In this improved bat algorithm, on the one hand, it redefined the subtraction operator of location and location, the multiplication operator of real number and location, and the addition operator of velocity and location. On the other hand, it introduced the reversing the city subsequence in order to perform the route＇ s local search. The experimental results show that this improved bat algorithm is feasible and can effectively solve the MRTSP instances.