一种新的模因算法种群规模确定方法--以多维指派问题为例
A New Approach to Population Sizing for Memetic Algorithms: A Case Study for the Multidimensional Assignment Problem
摘要：
模因算法是解决困难优化问题的一种强大技术。要设计一个模因算法，需要做出许多决定;选择种群规模是其中最重要的一个。文献中的大多数算法将种群规模固定为某个常数值。这降低了算法的质量，因为最佳种群大小因不同的实例、局部搜索过程和运行时间而异。在本文中，我们提出了一个可调整的人口规模。它被计算为整个算法的运行时间和给定实例的局部搜索的平均运行时间的函数。请注意，在许多应用程序中，启发式算法的运行时间应该是有限的，因此我们使用此限制作为算法的参数。在算法运行过程中，得到了局部搜索过程的平均运行时间。一些系数是独立的实例或局部搜索的算法运行前进行调整，我们提供了一个程序来找到这些系数。所提出的方法被用来开发一个模因算法的多维分配问题（MAP或s-AP的情况下，s维），这是一个著名的分配问题的扩展。MAP是NP难的，有很多应用。我们表明，使用可调整的人口规模，使算法灵活地执行非常不同的大小和类型的实例，并为不同的运行时间和本地搜索。这允许我们为每个实例类型选择最有效的本地搜索。对多个实例族和实例规模的计算实验结果表明，该算法在较宽的运行时间范围内都能有效地执行，并且明显优于相同时间下的最新3-AP模因算法.
英文摘要：
Memetic Algorithms are known to be a powerful technique in solving hard optimization problems. To design a memetic algorithm one needs to make a host of decisions; selecting a population size is one of the most important among them. Most algorithms in the literature fix the population size to a certain constant value. This reduces the algorithm's quality since the optimal population size varies for different instances, local search procedures and running times. In this paper we propose an adjustable population size. It is calculated as a function of the running time of the whole algorithm and the average running time of the local search for the given instance. Note that in many applications the running time of a heuristic should be limited and therefore we use this limit as a parameter of the algorithm. The average running time of the local search procedure is obtained during the algorithm's run. Some coefficients which are independent with respect to the instance or the local search are to be tuned before the algorithm run; we provide a procedure to find these coefficients. The proposed approach was used to develop a memetic algorithm for the Multidimensional Assignment Problem (MAP or s-AP in the case of s dimensions) which is an extension of the well-known assignment problem. MAP is NP-hard and has a host of applications. We show that using adjustable population size makes the algorithm flexible to perform well for instances of very different sizes and types and for different running times and local searches. This allows us to select the most efficient local search for every instance type. The results of computational experiments for several instance families and sizes prove that the proposed algorithm performs efficiently for a wide range of the running times and clearly outperforms the state-of-the art 3-AP memetic algorithm being given the same time.
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