Improved differential evolution algorithm to solve the advertising method selection problem

This article proposes a methodology to resolve the advertising method selection problem (AdSP). The use of different advertising methods for the same product can generate different responses in terms of the product's sales volume. Companies selling products have limited resources for advertising, with challenges such as budget and time constraints. It is necessary that the correct advertising method is selected in order to increase the maximum profit, given these limited resources. In the present study, a mathematical model was developed to represent the AdSP, and optimization software (OS) was utilized to optimally resolve it. However, a larger problem can prevent OS from optimally resolving the problem within a reasonable timeframe. To overcome this challenge, the authors developed a metaheuristic called the improved differential evolution algorithm (IDE), which combines three metaheuristics: (1) The differential evolution algorithm (DE); (2) the iterated local search (ILS); and (3) the adaptive large neighborhood search (ALNS). The performance of IDE reflects the best elements of these three methods. The computational results show that IDE can generate solutions that are similar to the optimal solutions obtained by OS while using 69.25% less computational time than OS. IDE improved the efficiency compared with the three original component methods. Moreover, IDE also found better solutions than those found by the original DE, ILS, and ALNS.