*3.1.3 Demerits of PSO*

• PSO fails to resolve problem which lack in storage and not able to may clear distinction between previous and next particle positions.

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


### *3.1.4 Applications*

PSO has been applied in most domains to optimize solutions from agriculture to industry. PSO has been extensively applied in different geotechnical engineering aspects such as slope stability analysis, pile and foundation engineering, rock and soil mechanics, and tunnelling and underground space design [17]. PSO has been widely used in various kinds of planning problems, especially in the area of substation locating and sizing [14]. But in the area of heating supply, PSO is mainly applied in heating load forecasting [18–20], but rarely used in Heat System Planning. PSO can be applied for various optimization problems, for example, Energy-Storage Optimization. PSO can simulate the movement of a particle swarm and can be applied in visual effects like those special effects in Hollywood film.

#### **3.2 Genetic bee colony (GBC) algorithm**

Bee food identification and collection intelligent swarm technique is defined in artificial bee colony. The best bee for the required problem is selected through parameters communication link, task allocation, reproduction, dance, placement mating and movement. GBC is optimised towards solution iteratively in an attempt to increase efficiency for any critical problem. Bee swarm is categorized as employee, onlooker and scouts. The employee bee identifies fresh sources of food. Scout bees job is to assign fitness quotient to entrust job of random search for employee bee identified spots. The assignment is random-based. If freshly identified food is better than earlier findings then, bees will collect from fresh location. Constantly employee bees look for best site for food collection. The onlooker bee is responsible to identify the best food source considering quantitative factor of food availability [21, 22].

#### *3.2.1 Concept*

The ABC algorithm consists of four main steps: initialization, employed bee phase, onlooker bee phase, and scout bee phase. After the initialization step, the other three main steps of the algorithm are carried out repeatedly in a loop until the termination condition is met. The main steps of the ABC algorithm are as follows.

*Step 1 (initialization).* In the initialization step, the ABC generates a randomly distributed population of *SN* solutions (food sources), where *SN* also denotes the number of employed or onlooker bees. Let *φ* represent the ith food source, where is the problem size. Each food source is generated within the limited range of ith index by where*φ* ¼ 1,2, … *SN*,*j* ¼ 1,2, … *:D*,*φi*,*j* , is a uniformly distributed random real number in , xmin and xmax and are the lower and upper bounds for the dimension , respectively. Moreover, a trial counter for each food source is initialized as in Eq. (7).

$$\mathbf{x}\_{i,j} = \mathbf{x}\_j^{\min} + \boldsymbol{\varrho}\_{i,j} \left( \mathbf{x}\_j^{\max} - \mathbf{x}\_j^{\min} \right) \tag{7}$$

*Step 2 (employed bee phase).* In the employed bee phase, each employed bee visits a food source and generates a neighboring food source in the vicinity of the selected food source. Employed bees search a new solution, by performing a local search around each food source as follows: where is a randomly selected index and is a randomly chosen food source that is not equal to; that is, is a random number within the range generated specifically for each and combination. A greedy selection is applied between and by selecting the better one as in Eq. (8).

$$
\omega\_{i,j} = \varkappa\_{i,j} + \mathcal{Q}(\varkappa\_{i,j} - \varkappa\_{r1,j} \tag{8})
$$

*Step 3 (onlooker bee phase).* Unlike the employed bees, onlooker bees select a food source depending on the probability value, which is determined by nectar amount associated with that food source. The value is calculated for the food source as follows considering Eqs. (9) and (10): where the fitness value of solution and calculated as in (4) for minimization problems. Different fitness functions are employed for maximization problems. By using this type of roulette wheel based probabilistic selection, better food sources will more likely be visited by onlooker bees. Therefore, onlooker bees try to find new candidate food sources around good solutions. Once the onlooker bee chooses the food source, it generates a new solution using (2). Similar to the employed bee phase, a greedy selection is carried out between.

$$p\_i = \frac{fit\_i}{\sum\_{j=1}^{\text{SN}} \mathbf{fit}\_i} \tag{9}$$

$$\begin{aligned} \,\_1f\dot{t}\_i = \begin{cases} \frac{i}{1+f\dot{t}t\_i} \, f\dot{t} \ge 0\\ \mathbf{1} + \, abs(\dot{f}t)\dot{f}\dot{t} < 0 \end{cases} \end{aligned} \tag{10}$$

*Step 4 (scout bee phase).* A trial counter is associated with each food source, which depicts the number of tries that the food source cannot be improved. If a food source cannot be improved for a predetermined number of tries (limit) during the onlooker and employed bee phases, then the employed bee associated with that food source becomes a scout bee. Then, the scout bee finds a new food source using (1). By implementing the scout bee phase, the ABC algorithm easily escapes from minimums and improves its diversification performance.

It should be noted that, in the employed bee phase, a local search is applied to each food source, whereas in the onlooker bee phase better food sources will more likely be updated. Therefore, in ABC algorithm, the employed bee phase is responsible for diversification whereas the onlooker bee phase is responsible of intensification. The flow chart of the ABC is given in **Figure 3**.

#### *3.2.2 Merits of GBC*

The ABC algorithm is a population-based algorithm with the advantages of finding global optimization solution, being simple and flexible, and using very few control parameters. The ABC algorithm has been applied to many real-world applications, for example, function optimization, real-parameter optimization, digital filter design, clustering, and neural network training. ABC algorithm-based applications are easy to *Bio-inspired Optimization: Algorithm, Analysis and Scope of Application DOI: http://dx.doi.org/10.5772/intechopen.106014*

build, robust, converge fast, flexible and time efficient. Compared to PSO ACO parameters considered in ABC is less.
