Combining Approximation Algorithm with Genetic Algorithm at the Initial Population for NP-complete Problem

In Genetic Algorithm (GA), the prevalent approach to population initialization are heuristics and randomization. Unlike approximation algorithms (AA), these methods do not provide a guarantee to the generated individual's quality in terms of optimality. Surprisingly, no literature to this date has attempted using AA as a population initialization method. Hence, we seek to improve upon the state of the art for NP-complete problem by presenting an implementation of AA at a GA's initial population. We tested this approach by sampling the populations for some Set Covering Problems from OR Library using the randomized rounding method (AAR) and compared them with that sampled using a randomized heuristics (R) in terms of redundancy rate, diversity and closeness to the optimal solution (OPT). Then, we tested three types of GA; R-GA with R-sampled initial population, AAR-GA with AAR-sampled initial population and S-GA with a combined R-AAR initial population and their performances are compared in terms of the best solution found(BFS) and the average number of iterations required to reach BFS. Results suggested that AAR has the potential of generating better starting populations compared to the traditional random heuristics.