**3.3 Hybrid Particle Swarm optimization**

The Hybrid Particle Swarm algorithm with Mutation (HPSOM) incorporates the mutation process often used in genetic algorithm in PSO (Esmin et al., 2005). This process will allow the particles can escape a local optimum point and perform searches in different area in the search space. This process starts by random choice in Particle Swarm and move to a new different position within the search space. The process of mutation used is given by the following equation:

$$mut(p[k]) = p([k]^\ast - 1) + o\tag{10}$$

Where the *p*[*k*] is the randomly chosen particle swarm of and is also obtained from a random order within the following scale: [0, 0.1(*xmax – xmin*)] representing 0.1 times the length of the search space. The HPSOM algorithm has the following pseudocode.

#### **begin**

Create and initialise*: While ( stop condition is false) begin evalaute update velocity and position mutation*   **end end** 
