**6. References**

[1] Garey MR, Johnson DS (1979) Computers and intractability: a guide to the theory of NP completeness. Freeman, San Francisco, California

380 Bio-Inspired Computational Algorithms and Their Applications

The results for the instances with different sizes are shown in Table 3 and Table 4, where the minimum, average and maximum of the C/LB ratio are presented. Each line summarizes the values for the 10 instances of each problem size, where 10 replications are performed for

The result for the experiment E1, in which processing times are generated by using U(1,100) are summarized in Table 2. In this experiment, it is found that the minimum, average and maximum values of the ratios are quite similar for SPPSO and PSOspv. On the other hand,

The result for the experiment E2 in which processing times are generated by using U(100,800) are summarized in Table 3. In this experiment, there is also no significant difference between SPPSO and PSOspv. However, in terms of max ratio performance SPPSO performed slightly better than PSOspv. In addition, PSOspv and SPPSO are also better than

Table 4 shows the number of times the optimum is reached within the group (nopt) for each algorithm and their average CPU times in seconds for each experiment. Total number of optimum solutions obtained by PSOspv, DPSO and SPPSO for the both experiment are summarized as (148,148,172) and (117, 94,126) respectively. Here, the superiority of SPPSO over PSOspv and DPSO is more pronounced in terms of number of total optimum solutions

In terms of the average CPU, SPPSO shows better performance than PSOspv and DSPO. SPPSO (0.598, 0.727) is about 15 times faster than PSOspv (8.922, 14,395) and about 2 times

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

[1] Garey MR, Johnson DS (1979) Computers and intractability: a guide to the theory of NP

as flow shop scheduling, job shop scheduling etc. as future work.

completeness. Freeman, San Francisco, California

each instance.

obtained.

**5. Conclusion** 

**6. References** 

SPPSO and PSOspv performed better than DPSO.

DPSO for all the three ratios in this experiment.

faster than DPSO (1.305, 1.634) in both experiments.


**Part 4** 

**Hybrid Bio-Inspired Computational Algorithms** 

