**3.5 Whale optimization algorithm (WOA)**

Whale optimization algorithm proposed by Mirjalili et al. WOA is also based on population of whale. It simulates bubble-net attacking method of humpback whales when hunting their preys. Whales are intelligent due to the spindle cells in their brain. They live in group and are able to develop their own dialect. Whale optimization algorithm consists of two modes of operation. The two modes of operation named as exploitation and exploration. In first prey encircling and position update in spiral manner carried on. Searching for prey randomly done in second phase [46–48]. WHO exploitation phase for prey encircling is mathematically equalized as bubble net attack system. Humpback characteristics of whales considered for phase one behaviour. Whales encircle prey with identification of them in an undefined search space. Initial solution of nearby prey or ideal assumed as best further best solution will be updated once exploration begins. Distance between prey and whales calculated initially then, updates for spiral positioned distance to it. WOA has modified and incorporated improvements by many researchers [49–53]. Few notable changes included in AWOA, IWOA, chaotic WOA, ILWOA, and MWOA research work. WOA hybridized with other meta-heuristic algorithms PSO, BA, and others in order to improve local search [34, 54–56].

#### *3.5.1 Concept*

Whale has a special hunting mechanism which is called bubble-net feeding method. This foraging behaviour is done by creating special bubbles in a spiral shape or nine shape path. Humpback whales know the location of prey and encircle them. They consider the current best candidate solution is best obtained solution and near the optimal solution. After assigning the best candidate, the other agents try to update their positions towards the best search agent as computed by Eq. (23). In Eqs. (23) and (24), t is the current iteration, A and C are coefficients vectors, X\* is the position vector of the best solution. The vector A and C are calculated using Eqs. (25) and (26). In Eqs. (25) and (26) a are linearly decreased from 2 to 0 over the course of iterations and r is random vector in [0, 1]. The humpback whales attack the prey with the bubble-net mechanism in exploitation phase. In shrinking encircling mechanism, the value of A is a random value in interval [-a, a] and the value of a is decreased from 2 to 0 over the course of iterations. Spiral updating position mechanism calculate the distance between the whale location and the prey location is calculated then the helix-shaped movement of humpback is created using Eq. (28). D' = |X\*(t) – X(t)| is distance between the prey and the ith whale, be is a constant, l is random number in [�1, 1]. Whale selectively applies swim around prey techniques suitably. The mathematical model of these two mechanisms assumes to choose between these two mechanisms to update the position of whale as in Eq. (29). In steady exploitation phase the humpback whales search for prey and change their position of whale. The force the search away from reference whale the mathematical model of exploration is computed as in Eqs. (29) and (30).

$$X(t+1) = \begin{cases} \begin{array}{c} X \ast (t) - A > D \text{ if } < 0.5\\ D^t x^{bl} . \cos \left( 2 \pi l \right) + X \ast (t) \text{ if } p \ge 0.5 \end{array} \tag{23}$$

$$D = |\mathbb{C}X \* (t) - X(t)|\tag{24}$$

$$X(t+1) = X\*(t) - A.D\tag{25}$$

$$A = \mathbf{2}a.r.a\tag{26}$$

$$\mathbf{C} = \mathbf{2}.\\r \tag{27}$$

$$\mathbf{X}(\mathbf{t}+\mathbf{1}) = D^t e^{bl}. \cos\left(2\pi l\right) + X\*\left(l\right) \tag{28}$$

$$D = |cX\_{rand\,X}|\tag{29}$$

$$X(t+1) = X\_{rand} - A.D\tag{30}$$

#### *3.5.2 Algorithm and flowchart*

The detailed workflow and algorithms is presented in **Figure 7**.

**Figure 7.** *WOA algorithm & flowchart.*

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

#### *3.5.3 Merits*

Whale optimisation avoid problem of local optima have got ability to compute local and global optima for any constrained or unconstrained optimization applications. During the process, it even does not require any structural are parametric rearrangement or alteration in value. The exploration for best solution computed simply and easily at faster rate. Improve quality of generated population and converge at faster rate.

### *3.5.4 Demerits*

WOA is not suitable for larger spaced problem incurs more time to explore and converge. The accuracy of solution is questionable. The optimal solution cannot be recognized for optimization of problems to solve high dimensional problem. Randomization technique of core WOA solution is complex. Balance among process of exploration and exploitation is lacking. The encircle mechanism slows WOA to jump from one local optima to another yielding low performance. Application problems of classification and dimensional reduction problem

#### *3.5.5 Applications*

WOA has ability to incorporate in dynamic applications. Most of researchers applied WOA for electrical, mechanical and management problems. WOA has been used to solve problem in engineering, multi objective, binary, identification classification and scheduling. WOA has found problems Power plants and systems scheduling [57] has confirmed to standard radial systems. Verify test system in execution of IEEE 30-bus [58, 59]. Size of pillars and optimization to increase efficiency of building is analysed [60]. Energy rise of solar energy to get importance in design of photovoltaic cells. WOA benefit solar cell and photovoltaic cells [61] by calculating internal parameters automatically. The partially cloudy atmosphere traced to get highest power region by a modified artificial killer whale optimization algorithm MAKWO [62]. Medical image analysis for classification and diagnose liver and cluster based abdominal to avoid intensity values to overlap [63]. WOA incorporated in economic and emission dispatch [64], vehicle fuel consumption [65], mobile robot path planning [66], optimal allocation of an ameliorative of water resource [67], design problem [68], heat and power economic dispatch [69].

#### **3.6 Artificial Algae Algorithm (AAA)**

Artificial Algae Algorithm initially proposed in 2015 by Uymaz et al. is also a meta-heuristic bio inspired algorithm. Microalgae growth and reproduction in presence of sunlight behaviour are considered in algorithm AAA. Algae swim towards presence of sunlight for food production following process as photosynthesis. The movement of algae towards sunlight will be in helical manner. They live in groups as algae colonies. The algae identify best sunlight presence to carry on photosynthesis itself considering largest size and reproduce algae's with highest energy. In case sunlight presence is less, then size of algal colony and energy level is less and starts for high starvation level. If sunlight is less algae colony tries to adopt itself in environment for its survival otherwise algae cells die because of starvation. The adaptation of algae

cells in unsupportive environment is known as evolution [70]. Uymaz et al. developed AAA then they modified to perform better [71]. From then many researchers contributed for AAA by incorporating AAA in different fields. Multi-objective optimization for AAA designed by Babalık et al. [72]. Binary version presented by Zhang et al. [73]. AAA applied in various fields from processing to manufacturing and in applications ranging from agriculture to home [74]. Few researcher improved AAA through hybridization [75].

#### *3.6.1 Concept*

AAA proposed for first by Uymaz et al. deals with considering advantages of research area of the properties found in algae. Algae moves from helically towards lighter sources. Algae adopt in nature to adapt and reproduce forming colonies which represent a solution. Colony of algae consists set of cells which dwell together. The colony exposed to external forces. The algae are divided into group and each become new colony as can move jointly, under in appropriate circumstance to from new colony. AAA process incorporated by three parts: Evolutionary, adaptation and helical movement. In evolutionary process, algae colony grows and flourish to get sufficient light, and benefit conditions. The algae undergo mitosis to result in two new algae. If not algae will perish under less nutrition and lighter conditions. In few scenarios if algae cannot grow in an environment due to lack of supporting factors. In such environments algae adapt by itself to environment in order to survive as other species. Finally, algae if it could not adapt then moves toward large grouped algae. If starvation occurs algae stop to adopt. Algaes move in helical movement by swim. In order to live they try to remain close to surface of water to get light. The search capacity will not remain same. Algae growth is more in region where frictional surface is more. The chance of algae movement is more in fluid. Helical motion supports to move algae at higher rate. The energy in different surfaces is not constant and is directly proportional to quantity of food and type of nutrient available in the environment. Capability and survival of algae existence depend on its adaptation and movement. The algae survival process mathematically applied in functional parts. Initially fix size of algae by Eq. (31). Evaluate fitness value of algae and size of colony by Eq. (32). Adaptation of algae is through growth of algae and use of nutrients by Eq. (33). The energy of algae computation inclusion of frictional force is computed applying Eqs. (33) and (34). During adaptation process algae build itself under non favorable or movement to nearby stronger and larger algae colony part. The optimization for given problem can be computed by Eqs. (35)–(38). The three subgroups of algae considered for adaptation. Identification of starvation be Eqs. (39) and (40). Section of best solution is selected by Eq. (41).

$$X\_{\vec{\eta}} = LB\_{\vec{\eta}} + \left(UB\_{\vec{\eta}}LB\_{\vec{\eta}}\right)RAND\ i = 1,2,3\ldots \\ \dots \\ N; j = 1,2,3\ldots D \tag{31}$$

$$
\mu\_i = \frac{\mathcal{S}}{K\_s + \mathcal{S}} \tag{32}
$$

$$\mathbf{G}\_{i}^{t+1} = \mu\_{i}^{t} \mathbf{G}\_{i}^{t} \text{ i = 1,2,3,...,N} \tag{33}$$

$$
\pi(\mathbf{x}\_i) = 2\pi \sqrt[3]{\frac{3G\_i}{4\pi}} \tag{34}
$$

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

$$GE^{t+1} = norm\left(\left(rank(G^t)\right)^2\right) \tag{35}$$

$$X\_{i\_m}^{t+1} = X\_{i\_m}^t + \left(X\_{j\_k}^t - X\_{i\_k}^t\right) (\Delta - \tau^t(X\_i))P\tag{36}$$

$$X\_{i\_k}^{t+1} = X\_{i\_k}^t + \left(X\_{j\_k}^t - X\_{i\_k}^t\right) (\Delta - \pi^t(X\_i)) \cos a \tag{37}$$

$$\mathbf{X}\_{i\_l}^{t+1} = \mathbf{X}\_{i\_l}^t + \left(\mathbf{X}\_{j\_l}^t - \mathbf{X}\_{i\_l}^t\right) (\Delta - \boldsymbol{\tau}^t(\mathbf{X}\_i)) \sin \beta \tag{38}$$

$$\text{Starting}^t = \max A\_i^t \; i = 1, 2, 3, \dots \dots N \tag{39}$$

$$\text{Starting}^{t+1} = \text{Starting}^t + (\text{Bigest}^t - \text{Starving}^t).rand \tag{40}$$

$$i \text{ biggest}^t = \max A\_i^t \, i = 1, 2, 3 \dots \dots \dots N \tag{41}$$

#### *3.6.2 Algorithm and flowchart*

The algorithm and flow of operation of AAA is shown in **Figure 8**.

#### *3.6.3 Merits*

AAA exhibits accuracy for identified colonies. Converge faster towards local and global solution compared to ACO or PSO. Algorithm is convenient and efficient. The method helps find efficient and high accurate result. Produce robust algorithm for real-time optimization problems. Main benefit for gradient-based problems provide by an efficient optimize in few steps and simple to generate.

**Figure 8.** *AAA algorithm & flowchart.*

#### *3.6.4 Demerits*

Major problem of AAA is its expensive apparatus, consumption of time and specialized operator. If data and input size increases accuracy will be minimized. They tend to stick to local optima, increased dependency. AAA apply randomness by this methodology is simple but result accuracy is questionable. Hence applications involved in AAA are complex and provide unstable result.

#### *3.6.5 Applications*

In optimal placement distributed power flow controller (DPFC) with MCFC, optimal coverage, routing and selection of cluster head in wireless sensor network.

#### **3.7 Elephant search algorithm (ESA)**

Elephant search algorithm developed by Adams et al. is inspired by elephant search for water. Normally elephants search for water in drought within swarm. Elephant swarm together search water source. Each elephant swarm consists of leader responsible to make decision regarding movement of whole group. Elephant is identified by its particular position and velocity in each group very similar to other swarm techniques. Leader elephant informs rest of elephants in group in case best water source is identified. The communication is through chemical, tactile, acoustic or visual means. The fitness function is computed considering water source quality and quantity. The elephants' group can move from one water source to another and visits previous also if necessary as they got good memory. Group visit previous water source in case older identified is best solution in compassion to new water source. Elephants search for best solution locally and globally then best solution will be identified in given solution space following long and short distance communication. Switching probability is key controller in considering water search either local or global.

#### *3.7.1 Concept*

EHO is meta-heuristic simulated behaviour in herds of elephants [24] introduced by Wang. Optimize solution for global optimization tasks [5]. Each solution I in each clan ci is updated considering current information such as position and matriarch. The generations are updated by algorithm execution through separating operators. Each individual in heard represent vectors in 2D. The dimensions in unknown population are included. The population is divided into n clans. Updating operator is modeled by increment or decrement each solution i in the clan by ci by influence of ci to identify best fitness value in generation. Fitness update solution in each clan ci represented in Eq. (42). New and old position in clan, incremental factor based on influence of matriarch are parameters included of Eq. (43). In 2D the central clan is computed through Eq. (44). It updates individual value of elephants in heard. The total search space indicates number of solutions in clan. The separating search space and nci indicates number of solutions in clan in ci. The separate operator is applied at each generation for execution on worst individual in population. Choose random population [0-1] be uniform distribution range within lower and upper limits of the position of the individual by Eq. (45).

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

$$\mathcal{X}\_{new,\mathcal{L},\dot{j}} = \mathcal{X}\_{\mathcal{C}i,\dot{j}} + a. \left(\mathfrak{x}\_{\text{best},\mathcal{L}\_i} - \mathfrak{x}\_{\mathcal{C}\_i\dot{j}}\right).r \tag{42}$$

$$
\boldsymbol{\omega}\_{new,ci,j} = \boldsymbol{\beta} \,\boldsymbol{\omega}\_{center,c\_i} \tag{43}
$$

$$\varkappa\_{center,ci,d} = \frac{1}{n\_{ci}} \cdot \sum\_{j=1}^{d} \varkappa\_{cj,d} \tag{44}$$

$$
\boldsymbol{\omega}\_{\text{wort},\boldsymbol{c}\_{i}} = \boldsymbol{\omega}\_{\text{min}} + \boldsymbol{\omega}\_{\text{max}} - \boldsymbol{\omega}\_{\text{min}} + \mathbf{1}) \ast \boldsymbol{r} \, \text{and} \tag{45}
$$

### *3.7.2 Algorithm and flowchart*

The detailed algorithms and flow of operation of EHOA is presented in **Figures 9** and **10**.

#### *3.7.3 Merits*

EHOA is more performance stable than other meta-heuristic algorithms such as PSO. Convergence is faster because they are in herd. Have ability to search a population in parallel. Rapidly discover good solutions similarly adapt to changes such as distance. The computation is simple. EHOA is efficient in solving problem which are difficult to find accurate mathematical models. Computational time is less and overlap is avoided.

#### *3.7.4 Demerits*

Probability can change for each iteration, theoretical analysis is difficult, and sequence of random decisions are major hindering factors of EHOA. Time requirement for convergence is uncertain.

**Figure 9.** *EHOA algorithm & flowchart.*

**Figure 10.** *CSO algorithm & flowchart.*

#### *3.7.5 Applications*

EHO applied to optimize training artificial neural network, selection structure and weight for neural networks, training neural netwosk, optimizing underwater sensor networks, unmanned aerial vehicle path planning, clustering, support vector machine, control problem.

### **3.8 Cuckoo search optimization algorithm (CSOA)**

Yang and Deb introduced cuckoo optimization in 2009 a meta-heuristic algorithm. Later Gandomi, Yang, and Alavi and Yang and Deb extended to solve single or multiobjective problems involved in any constraints or complexity. The solution is capable to resolve potential solutions of any randomly selected population in habitants of cuckoo. The function of CSOA is global optimality, real-world problems are NP-hard for problem used in any problem. Construct workable solution required to be globally optimal solution replicating behaviour of cuckoos. They lay eggs in nest of other birds and obliterate eggs of birds to guarantee hatching of its breed. Cuckoos brood parasitism is simulated in three different ways: Intra-specific brood parasitism, nest take
