## 2 Previous Work  
Many research studies proposed different variants based on initialization techniques and we have discussed some of them in detail in this chapter. Initialization of the swarm in a good way helps the PSO to search more efficiently [41]. In this work, the initialization of swarm with nonlinear simplex method (NSM) has been done. NSM requires only function evaluations without any derivatives for computation. NSM starts with initial simplex and produces sequence of steps moving the highest function value vertex in opposite direction of the lowest one. They initialized the particle with the initial simplex in the D dimensional search areas, where D + 1 vertices of the simplex are D + 1 particle of the swarm and the MSN method is applied for N-D + 1 steps for N size swarm. In this way, each particle in the swarm has the information of the region. In the last, they compared their results with simple PSO and found significant improvement. This variant was introduced by [PERSON] and [PERSON] in 2004. In their work [42], they proposed to use centroidal Voronoi tessellations for initializing the swarm. Voronoi tessellations is a technique of partitioning any region into compartments, each partition contains group of generators. Each partition is associated with one generator and it consists of all the particles closer to that generator. In the same way, the generators are selected for the initial position of the particle. In this way, they initializedthe particle swarm optimization algorithm. They compared it with basic SPO on many benchmark functions and found improved performance in high-dimensional spaces. Halton sampling was introduced by [PERSON], [PERSON], and [PERSON] in 2007 [43]. Halton sequence is a low discrepancy deterministic sequence used to generate point in space. Halton sequence is not a fully random. To randomize, [PERSON] and [PERSON] proposed a new function called randomize Haltom sequence by using von Neuman-Kakutani transformation. They used this sequence to initialize the global best of the PSO. They performed a test on various benchmark functions and compared the result with the PSO and initialized with uniform random numbers. They found better performance especially for complex and smaller populations. VC\(-\)PSO was introduced by [PERSON] et al. in 2008. They used Vandor Corput sequence for initializing the swarm for large dimensions' search [44] ([PERSON], [PERSON], [PERSON], and [PERSON], 2008). The Vandor Corput and Sobol sequence generates semi random number which is more suitable for computational purposes. They tested the new variant with different benchmark functions and compared the result with BPSO and SOPSO and found significant improvement especially for large search space dimension. The main purpose of this variant is to see the performance of large search space problems. That is why they used search space with different dimensions ranging [\(-\)5.12, 5.12] to [\(-\)1000, 1000]. The performance is showing prominent when the dimension increases to [\(-\)100, 100]. SMPO was introduced by [PERSON] et al. in 2008. They used quasi-random Sobol sequence to initialize the particles instead of normal random numbers [45]. They used a new operator called systematic mutation operator which is used to improve the performance of the PSO. Instead of using the normal random number, the new operator uses the quasi-random Sobol sequence to initialize the swarm as the QRS is less random as compared to pseudorandom sequences which is helpful for computational methods. They proposed two variants, SM-PSO1 and SM-PSO2. The main difference between the two versions is that in MSPSO1, the best particle is mutated while in MS-PSO2, the worst particle is mutated. They found better results comparing with BPSO and other variants. This work is done by [PERSON] et al. 2011 [46]. In this paper, researchers proposed a new method of initialization. In their work, they added the functionality to detect automatically when the particle is prematurely converged and initializes the swarm.