*3.2. Opposition-Based Learning*

In 2005, Tizhoosh et al. introduced the phenomenon of opposition-based learning (OBL) [49]. The basic principle of OBL is that it imitates the opposite relationship among agents. Over the last few years, artificial intelligence field has experienced tremendous growth and researchers are exploring and building innovative algorithms so as to enhance the performance of existing algorithms. OBL is one of the novel concepts that finds application in metaheuristic [50] and other artificial intelligence algorithms. OBL considers agents and their opposite counterpart in order to better explore the search space and find global optimal solution. Figure 1 shows the mechanism of OBL. The fundamental concept of OBL is outlined as follows:

Let *N* be a real number in the search space [*kL*, *kU*], then its opposite counterpart is defined as follows: <sup>→</sup>

$$
\dot{N} = k\_L + k\_{\rm II} - N \tag{24}
$$

In the higher dimensional space, the *N* is expressed as:

*N<sup>k</sup>* = [*Nk*<sup>1</sup> , *Nk*<sup>2</sup> , . . . , *Nk<sup>t</sup>* ] and defined in the search space [*kLt*, *kUt*], where *t* = 1, 2, 3, . . . , *n*. Then, the opposite points are defined as:

$$
\stackrel{\rightarrow}{N}\_{k} = k\_{Lt} + k\_{llt} - \left[ \stackrel{\rightarrow}{N}\_{k1}, \stackrel{\rightarrow}{N}\_{k2}, \dots, \dots, \dots, \dots, \dots, \stackrel{\rightarrow}{N}\_{kt} \right] \tag{25}
$$

 ⃗

= <sup>1</sup> <sup>2</sup> …

=1, 2, 3, …

 ⃗

= + − [

= + −

⃗ ]

, … … … … … …

⃗ 1 , ⃗ 2

**Figure 1.** Illustration of opposition-based learning mechanism [2].
