# An Overview of Variants and Advancements of PSO Algorithm
## 4 Advances on Particle Swarm Optimization (PSO) Algorithm
### Extensions of Applications of PSO  
Since its origin in 1995, researchers have also widened/extended the range of application of the original PSO algorithm to a variety of optimization problems, such as constrained, multi objective, multi modal, discrete and binary optimization. To solve the multi-objective optimization problems, [PERSON] et al. [31] introduced a modified variant of the PSO algorithm, namely the homogeneous particle swarm optimizer (HPSO). The authors proved the excellent exploration ability of the proposed algorithm with other multi-objective PSO algorithms by making a comparison study. The authors, [PERSON] and [PERSON] [32], extended the application of the original particle swarm optimization (PSO) to solve the multi-objective optimization problems by using a Pareto dominance approach to determine the flight direction of the particle. By testing it with some standard test functions, the authors concluded that their approach was highly competitive in comparison to the other multi-objective optimization techniques. [PERSON] et al. [33] proposed a new algorithm by hybridizing particle swarm optimization (PSO) with two other statistical techniques--Ranking and Selection (R&S), and Mean Square Error Criterion (MSE), in order to solve the stochastic optimization problems, called (STPSO). The authors proved the robustness of their proposed algorithm with experimental results. In order to solve the NP hard knapsack problems (KPs), [PERSON] and [PERSON] [34] designed a modified binary particle swarm optimization (MBPSO) algorithm. The authors tested this new modified binary PSO version on 10 benchmark problems, and by comparing the results with both the binary particle swarm optimization (BPSO) and the genotype phenotype-modified binary particle swarm optimization (GPMBPSO), showed its effectiveness in terms of reliability, cost and the quality of the solution obtained over the other algorithms. To efficiently solve the different problems on power systems, [PERSON] et al. [35] proposed an evolutionary modified particle swarm optimization. On the basis of numerical experiments, the authors proved that their proposed algorithm was efficiently able to solve the constrained economic dispatch (ED) problem with a comparatively higher rate of convergence than the basic PSO. To efficiently solve the clustering problem, [PERSON] and [PERSON] [36] proposed a new cooperative algorithm that utilized the global search ability of the PSO algorithm and the local search ability of k-means. The authors made a comparison of their proposed algorithm with other algorithms, such as PSO with constriction factor (CF-PSO) and k-means algorithms and revealed the convergence efficiency of their proposed algorithm. In order to solve the university course timetabling problems using PSO, the authors, [PERSON] and [PERSON] [37], introduced a new algorithm, using transition probability into the basic PSO algorithm. With the help of the experimental results, the authors demonstrated the effectiveness of their proposed algorithm over evolutionary strategy to solve the time-table problems. [PERSON] and [PERSON] [38] presented a new PSO algorithm by using a linear SVM (support vector machine) approach to solve both small and large scale classification problems. On the basis of the experiments, the authors concluded that their proposed PSO-LinSVM approach gave comparatively better results than other similar approaches. The basic PSO algorithm does not work well for solving problems of mobile robot path planning, due to its slow convergence and limitations on application. To overcome this, the authors, [PERSON] et al. [39], derived the improved particle swarm optimization (IPSO) algorithm. By making a comparative study with other approaches on the standard benchmark functions, the authors proved that their derived algorithm gave a better solution with a lower number of iterations. In order to monitor the conditions of the surge arrester, [PERSON] et al.