*3.3. Proposed Algorithm*

This section outlines the proposed opposition-based arithmetic optimization algorithm (OBAOA). In the field of optimization, local optima avoidance capability and convergence rate are two critical parameters, which define the performance of the algorithm. Most of the metaheuristic algorithms quickly converges and avoids local optimal solution. However, some algorithms fail to explore entire search space and get trapped in local optimal solution. In this area, researchers are exploring new ways such as modification of existing algorithm, hybridization of two or more algorithms to overcome these limitations.

AOA also has poor exploration capability and did not discover a global optimal solution and have slow rate of convergence. Thus, in this article, authors have enhanced the performance of AOA by incorporating the opposition mechanism and have proposed opposition OBAOA. OBL mechanism allows the algorithm to discover global optimal solution and improve convergence rate and thereby boost exploration capability of the algorithm. In OBAOA, the opposition-based principle is first incorporated in the initialization phase and later in the operational phase. The flow chart of OBAOA is shown in Figure 2 and the mathematical model is outlined as follows:

Step 1 Initialization: Generate the random candidate solution in the defined space as:

$$X = \begin{bmatrix} p\_{1,1} & p\_{1,2} & \dots & \dots & p\_{1,d} \\ p\_{2,1} & p\_{2,2} & \dots & \dots & p\_{2,d} \\ p\_{n,1} & p\_{n,2} & \dots & \dots & p\_{n,d} \end{bmatrix} \tag{26}$$

,1 ,2 … … , where *n* is the number of solution and *d* is the dimension.


update position of each candidate solution using the following mechanism.

Implement exploration phase:

if *r*<sup>1</sup> > 0.5;

<sup>1</sup> >

<sup>1</sup> >

<sup>1</sup> <sup>2</sup> <sup>3</sup>

**Figure 2.** Flow chart of opposition-based arithmetic optimization algorithm.
