**5. Conclusion**

In this chapter, a stochastically perturbed particle swarm optimization algorithm (SPPSO) is proposed for identical parallel machine scheduling (PMS) problems. The SPPSO has all major characteristics of the classical PSO. However, the search strategy of SPPSO is different. The algorithm is applied to (PMS) problem and compared with two recent PSO algorithms. The algorithms are kept standard and not extended by embedding any local search. It is concluded that SPPSO produced better results than DPSO and PSOspv in terms of number of optimum solutions obtained. In terms of average relative percent deviation, there is no significant difference between SPPSO and PSOspv. However, they are better than DPSO.

It also should be noted that, since PSOspv considers each particle based on three key vectors; position (Xi), velocity (Vi), and permutation (Πi), it consumes more memory than SPPSO. In addition, since DPSO uses one and two cut crossover operators in every iteration, implementation of DPSO to combinatorial optimization problems is rather cumbersome. The proposed algorithm can be applied to other combinatorial optimization problems such as flow shop scheduling, job shop scheduling etc. as future work.
