*3.9.4 Demerits*

Convergence is major issue in MFO.

### *3.9.5 Applications*

MFO advantages have been incorporated in many domains. Navigation approach to solve the inequality and equality constrained optimization are real problem, to optimize real function for constrained selected variables. Chemical identification to improve single level production which can be extended to incorporate as include in determination of optimal production portfolio in other industries, applied in agriculture based to recognize problems of tomato [52]. Applied for medical field to improve time consuming Alhemeris disease, detection and diagnosis of breast cancer, to train networks RBFN [42], deployment of Wifi, determination of optimal solution in placement, location problem solution.


**Figure 11.** *MFO algorithms & flowchart.*

### **3.10 Grey wolf optimization (GWO) algorithm**

Grey wolf optimization, a meta-heuristic swarm technique, introduced for first time by Simon Fong [86]. Hunting behaviour in pack of wolf inspired in design of grey wolf optimization. Wolves in pack will not communicate physically during hunting, each wolf identify and attack prey individually silently. They follow levy flights model in search of food during hunting. Wolves unify to another pack of wolves or to new location if they find new food location better and suitable compared to their current dwelling place. A random hunter will be selected among pack to hunt for prey. The hunter identifies potential position itself to catch prey from current line of sight.

#### *3.10.1 Concept*

The social hierarchy consists of four levels in GWO. The level one called Alpha. They are the leaders of the pack, and they are male and female. They are responsible for making decisions about hunting time to walk, sleeping place and soon. The pack members have to dictate the alpha decisions and they acknowledge the alpha by holding their tails down. The alpha wolf is considered the dominant wolf in the pack and all his/her orders should be followed by the pack members. Next level group is labeled as Beta. The betas are subordinate wolves, which help the alpha in decision making. They can be either male or females. If consider the best candidate to both alpha when the alpha passes away or becomes very old. The beta reinforces the alpha's commands throughput the pack and gives the feedback to alpha. The third group of wolves is called Delta. They are subordinates. They need to submit their work report to alpha and beta. Scouts are responsible for watching boundaries of the territory and warning the pack in case of any danger. Sentinels are responsible for protecting the pack. Hunters are response got helping the alphas and beta involves beta in hunting and provide food for the pack. They are not important individuals in the pack, and they are allowed wolves were outwards. They are fighting i the case of loss.

Wolf search has been used to select two relay nodes: inter and intra relay nodes. Within a cluster, cluster members sense and transmit sensed data directly to the CH irrespective of their distance from CH. Hence, the nodes far away from CH dissipate more energy resulting in reduced network lifespan. To overcome this problem, the Wolf search is used in order to identify intra relay nodes for every cluster. The cluster member will send the sensed data to intra relay node and it in turm to CH. Similarly, all CHs communicate directly to BS irrespective of distance between CHs and BS. Hence, the CHs far away from BS dissipate more energy which leads to selection of new CHs resulting in next iteration, resulting very low network lifespan. To overcome this PEGASIS protocol introduced inter relay node as final node to communicate with BS. In proposed work, Wolf search is used to identify the inter relay nodes. The working principles of Wolf search for identification of inter and intra relay nodes are described in this section. The pseudo code of Wolf search is described in Algorithm 2.11.2.

ð Þ *X*, *Y* are the coordinates of unknown node/target node and *xi*, *yi* are the coordinates of the *i th* anchor node in the neighbourhood. The computations of WS) for encircling, and hunting process are shown below.

*Bio-inspired Optimization: Algorithm, Analysis and Scope of Application DOI: http://dx.doi.org/10.5772/intechopen.106014*

Eqs. (49)–(54) used in WSO are as follows.

$$d\_i = \sqrt{\left(\mathbf{X} - \mathbf{x}\_i\right)^2} + \sqrt{\left(\mathbf{Y} - \mathbf{y}\_i\right)^2} \tag{49}$$

$$D = \left| C \ast X\_p(t) - X(t) \right| \tag{50}$$

$$C = \mathcal{Z} \ast r \tag{51}$$

$$A = \mathbf{2} \ast \mathbf{a} \ast \mathbf{r} - a \tag{52}$$

$$X(t+1) = X\_p(t) - A \ast D \tag{53}$$

$$r = 0.5 + \frac{\sin 2\sqrt{\varkappa^2 + y^2 - 0.5}}{\left(1 + 0.001X(\varkappa^2 + y^2)\right)^2} \tag{54}$$

where *t* represents the current iteration, *A* and *C* are coefficient vectors, position vector of the prey is represented *Xp*, X the position vector, ∣ ∣ is the absolute value, and is an element-by-element multiplication, *a* is linearly decreased from 2 to 0 in each iteration and *r* is a random vector in 0, 1 ½ �.

#### *3.10.2 Flowchart and algorithm*

The algorithm and flow of operation of GWO is presented in **Figure 12**.

**Figure 12.** *GWO algorithm & flowchart.*
