*3.3.3 Merits*

FSA similar to GBC has got increased convergence power and flexible. In addition, it exhibits fault to tolerant and accuracy feature. Global search ability, tolerance of parameter setting and robustness are other merits of FSA. It solves nonlinear and multi modal problems.

### *3.3.4 Demerits*

FSA exhibits high complexity, lack of balance among one is ineffective if lack balance between local search. Not suitable for global convergence problem. The information transfer if experience low search rate. As good robustness, global search ability, tolerance of parameter setting, and it is also proved to be insensitive to initial values

### *3.3.5 Applications*

FSA has been applied for network related problems, control of resources, image processing related problems. In order to increase evolutionary capabilities of FSA, in few swarm solutions hybrid to FSA.

FSA incorporate to solutions in wireless sensor networks [30, 32, 33], tracking [34], medical estimations [35–37], segmentation [32], clustering [33], regression [38], image processing [39, 40], calibration [35], localization [41], power systems [36, 42].

### **3.4 Cat swarm optimization (CSO)**

Chu et al. introduced cat swarm optimization technique to solve most of engineering problems inspired by the movement of cats. The process is carried on in two different modes seeking and tracing modes. Nodes virtually move in fixed areas as cats to determine optimal solution. Number of virtual cats are fixed in both modes and predefined in few cases ratio known as MR. the N virtual cats is placed randomly. Processed and unprocessed cats are identified for each dimension based on its value of MR set either to 0 or 1 for tracing or seeking in coming rounds. Every cat compute fitness function in evaluation then among the existing best will be chosen initially existing is compared if It best retained for fitness function otherwise coordinates will be changed to new best cat. The movement of cat adjusted towards solution space identified as identified in initially. Choose for unprocessed cats in tracing mode through permutation. Tracing mode ends if no more cats are left. Traced coordinate nodes will be selected as best solution at end. In seeking mode, cats' movement will be slow and conformist. Essential parameters of seeking mode are seeking memory pool, Ra range of identified dimension, counts of dimensions to change and self-position. Improved CSO algorithm proposed by Tsai et al. supports parallel information exchange in tracing mode. The parallelizing of virtual agents is adopted in PCSO [43, 44]. PCSO finds application in parallel processing inspired by colonies of cats tracing for food.

#### *3.4.1 Concept*

CSO identification of optimized solution is described in this sub section step by step. The seeking feature of cats carried in five processing steps. In first step, j copies of cat generated is recognized applying Eq. (16). Addition or decrement of SRD value on selected search space defined by Eqs. (17)–(19) in step two. In next step, fitness value for all candidates is selected. In step four, calculation of probability of cat performed by Eq (20). Sort and select best solution by roulette wheel selection in last step. In tracking mode cats imitate movement of prey during tracing. This process can be discrete into three operational steps. In first step, velocity of each cat is updated as in equation 6 for given search space. The random value for cat adjusted in range 0-1. In step 2, the valued are rearranged based on velocities of cat. Velocities are set to maximum velocity value. Position of cat is updated selecting by Eq. (7) in last step.

$$j = \begin{cases} \text{SMP} & \text{SPC} = \text{"true"} \\ \text{SMP-1} & \text{SPC} = \text{"false"} \end{cases} \tag{16}$$

$$M = Modify \cup (1 - Modify) \tag{17}$$

$$|Mod\hat{y}| = \text{CDC} \ast M\tag{18}$$

$$\mathbf{x}\_{jd} = \begin{cases} \mathbf{x}\_{jd} & d \not\models Mod \mathbf{ify} \\ (\mathbf{1} + rand \ast SRD) \ast \mathbf{x}\_{jd} & d \in Mod \mathbf{ify} \end{cases} \tag{19}$$

$$p\_i = \begin{cases} 1 & \text{when } F\mathbb{S}\_{\max} = F\mathbb{S}\_{\min} \\ \frac{|F\mathbb{S}\_i - F\mathbb{S}\_b|}{F\mathbb{S}\_{\max} - F\mathbb{S}\_{\min}}, & \text{where } 0 < i < j, \text{ otherwise} \end{cases} \tag{20}$$

$$
\upsilon\_{k,d} = \upsilon\_{k,d} + r.c.(\varkappa\_{\text{best},d} - \varkappa\_{k,d}), d = \textbf{1}, \textbf{2} \dots \textbf{M} \tag{21}
$$

$$\mathbf{x}\_{k,d} = \mathbf{x}\_{k,d} + \mathbf{v}\_{k,d} \tag{22}$$

#### *3.4.2 Algorithm and flowchart*

The algorithms and flow of operations of CSO is summarized in **Figure 6**.

#### *3.4.3 Merits*

COA is Simple to construct and have minimal parameters to adjust. COA has got ability to execute in parallel system. The design is robust. Can converge fast, find global solution, overlap and mutate. Have computational time less. Find accurate mathematical models. Discover good and rapid solutions. Adapt changes in new system and dependent on random decisions.

### *3.4.4 Demerits*

Definition of initial parameters is time consuming. COA does not work better for scattering problems and can converge at faster rate if trapped in complex problems. The time to converge and towards convergence for multi objective and larger sized problem is more.

**Figure 6.** *COA algorithm & flowchart.*

### *3.4.5 Applications*

CSO optimization is being incorporated in media for information hiding [44], aircraft scheduling recovery in limited processing time [45]. Voltage stability, economically dispatch in transmission system, hybrid generation systems, task allocation, data mining, project scheduling, optimal contract capacity, global numeric optimization problems. Applied for clustering technique in green expression classification, travelling salesman problem, data hiding, graph coloring, SVM, K means. CAO even find its application in stock market and supply chain in currency exchange rate analysis and stock prediction. COA is applied in image processing for machinery fault detection, plant modeling, image edge enhancement, water marking and single bit map. COA extended application in electronics for cognitive radio engine cooperative, spectrum sensing, linear antenna array synthesis, aircraft maintenance, routing for wireless sensor network.
