In recent years, multi-modal optimization algorithms have attracted considerable attention, largely because many real-world problems have more than one solution. Multi-modal optimization algorithms are able to find multiple local/global optima (solutions), while unimodal optimization algorithms only find a single global optimum (solution) among the set of the solutions. Niche-based multi-modal optimization approaches have been widely used for solving multi-modal problems. These methods require a predefined niching parameter but estimating the proper value of the niching parameter is challenging without having prior knowledge of the problem space. In this paper, a novel multi-modal optimization algorithm is proposed by extending the unimodal bacterial foraging optimization algorithm. The proposed multi-odal bacterial foraging optimization (MBFO) scheme does not require any additional parameter, including the niching parameter, to be determined in advance. Furthermore, the complexity of this new algorithm is less than its unimodal form because the elimination-dispersal step is excluded, as is any other phase, like a clustering or local search algorithm. The algorithm is compared with six multi-modal optimization algorithms on nine commonly used multi-modal benchmark functions. The experimental results demonstrate that the MBFO algorithm is useful in solving multi-modal optimization problems and outperforms other methods.

近年来，多模式优化算法已引起了广泛的关注，这在很大程度上是因为许多现实世界中的问题都具有多个解决方案。多峰优化算法能够找到多个局部/全局最优（解），而单峰优化算法只能在一组解中找到单个全局最优（解）。基于小生境的多模式优化方法已被广泛用于解决多模式问题。这些方法需要预定义的niching参数，但是在没有问题空间的先验知识的情况下，估计niching参数的适当值是一项挑战。通过扩展单峰细菌觅食优化算法，提出了一种新颖的多峰优化算法。拟议的多对象细菌觅食优化（MBFO）方案不需要任何其他参数（包括固定参数）就可以预先确定。此外，这种新算法的复杂度低于其单峰形式，因为消除消除步骤与任何其他阶段一样都被排除，例如聚类或局部搜索算法。将该算法与六个常用的多模式基准函数上的六个多模式优化算法进行了比较。实验结果表明，MBFO算法在解决多模式优化问题方面很有用，并且优于其他方法。这种新算法的复杂度小于其单峰形式，因为消除消除步骤与任何其他阶段一样都被排除，例如聚类或局部搜索算法。将该算法与六个常用的多模式基准函数上的六个多模式优化算法进行了比较。实验结果表明，MBFO算法在解决多模式优化问题方面非常有用，并且优于其他方法。这种新算法的复杂度小于其单峰形式，因为消除消除步骤与任何其他阶段一样都被排除，例如聚类或局部搜索算法。将该算法与六个常用的多模式基准函数上的六个多模式优化算法进行了比较。实验结果表明，MBFO算法在解决多模式优化问题方面很有用，并且优于其他方法。