An application of adaptive genetic algorithm in financial knapsack problem

Abstract

We apply adaptive genetic algorithm to the financial knapsack problem, which aims at maximizing the profit from investment with limited capital. Since the performance of genetic algorithms is critically determined by the architecture and parameters involved in the evolution process, an adaptive control is implemented on the parameter governing the relative percentage of preserved (survived) individuals and reproduced individuals (offspring). The portion of preserved individuals is kept to a proportion to the difference between the fitness of the best and average values of individuals in the population. Numerical experiments on knapsack problems with N (150 ≤ N ≤ 300 ) items are analyzed using the mean-absolute deviation generations against the median first passage generations to solutions. Results show strong evidence that our adaptive genetic algorithm can achieve the Markowitz investment frontier: the risk of missing the global optimum can be minimized by reducing the persevered popolution with increasing difficulty of the problem.