Exploring the Impact of Grouping Strategies on Cooperative Co-evolutionary Algorithms for Solving the Advertising Budget Allocation Problem

The large-scale optimization problem (LSOP), which evolves high-dimensional decision variables, exists in many industrial situations. With the increasing number of decision variables, the performance of traditional evolutionary algorithms deteriorates obviously due to the huge search space and sophisticated optimal hyperplane. To solve the LSOP, many improved cooperative co-evolutionary algorithms are proposed, whose main idea is to group the decision variables into sub-components and evolve each component alternately to obtain the global optimal solution. The grouping strategy plays a core role in these algorithms, however, most of the comparative studies are conducted in experimental environments and a rare of them are conducted in real-world applications. In this paper, to explore the performance of different strategies, we compare four popular grouping strategies in a real-world problem, i.e., the Advertising Budget Allocation Problem. Experiments show that the grouping strategies indeed improve the performance of evolutionary algorithms and Differential Grouping performs effectively and efficiently in our experiment.

I. Introduction

Recently, the optimization problem has drawn much attention from both academic and engineering areas since it widely exists in real-world applications [1] [2]. In reality, the dimension of decision variables is usually high, e.g., in thousands. Generally, we call the optimization problem whose number of decision variables beyond 100 the Large-scale Optimization Problem (LSOP [2]). In LSOP, the increasing number of dimensions dramatically enlarges the search space and results in a sophisticated optimal hyperplane, making it hard for traditional evolutionary algorithms to find the global optimal points of the problem.