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Memetic Algorithms are known to be a powerful technique in solving hardoptimization problems. To design a memetic algorithm one needs to make a hostof decisions; selecting a population size is one of the most important amongthem. Most algorithms in the literature fix the population size to a certainconstant value. This reduces the algorithm's quality since the optimalpopulation size varies for different instances, local search procedures andrunning times. In this paper we propose an adjustable population size. It iscalculated as a function of the running time of the whole algorithm and theaverage running time of the local search for the given instance. Note that inmany applications the running time of a heuristic should be limited andtherefore we use this limit as a parameter of the algorithm. The averagerunning time of the local search procedure is obtained during the algorithm'srun. Some coefficients which are independent with respect to the instance orthe local search are to be tuned before the algorithm run; we provide aprocedure to find these coefficients. The proposed approach was used to developa memetic algorithm for the Multidimensional Assignment Problem (MAP or s-AP inthe case of s dimensions) which is an extension of the well-known assignmentproblem. MAP is NP-hard and has a host of applications. We show that usingadjustable population size makes the algorithm flexible to perform well forinstances of very different sizes and types and for different running times andlocal searches. This allows us to select the most efficient local search forevery instance type. The results of computational experiments for severalinstance families and sizes prove that the proposed algorithm performsefficiently for a wide range of the running times and clearly outperforms thestate-of-the art 3-AP memetic algorithm being given the same time.

A New Approach to Population Sizing for Memetic Algorithms: A Case Study for the Multidimensional Assignment Problem