# Bird Swarm Algorithm Analysis

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a1 and a2 are two positive constants in [0, 2],

〖pfit〗_i, denotes the ith bird’s best fitness value and Sumfit represents the sum of the swarm’s best fitness value. E, which is used to avoid zero-division error, is the smallest constant in the computer. 〖mean〗_j, denotes the jth element of the average position of the whole swarm.

Flight behaviour (exploration and exploitation):

Birds after foraging on their previous site would try to move to a different site in search of more food and also to save themselves from the predator’s attack. The two flight groups are producers and scroungers in which producers try to search for food and scroungers are the group of members who depends on the food found by the producers. The behaviours of the producers and scroungers can be described mathematically as follows, respectively:

〖 x〗_(i,j)^(t+1)=x_(i,j)^t+randn(0,1)*x_(i,j)^t (10)

〖 x〗_(i,j)^(t+1)=x_(i,j)^t+(x_(k,j)^t-x_(i,j)^t )*FL*rand(0,1) (11) where randn(0,1) denotes Gaussian distributed random number with mean 0 and standard deviation 1, kϵ[1,2,3……N], k≠i , FL(FL∈[0,2]), means that the scrounger would follow the producer to search for

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Step 7: The termination is done when a maximum number of iteration met.

IMPLEMENTATION OF BSA TO ELD PROBLEM:

In this section, the BSA algorithm is implemented to solve the different types of ELD problems. The various steps of solving the ELD problem using BSA are described below:

Step1: Initialization of population N, each comprising Ng number of generating units and define the related parameters a1, a2, FQ, c1, c2.

Step2: Generation values of each generating units is randomly initialized within their lower and upper operating limits except the last unit. The generation value of last unit is evaluated using equation (3). The infeasible solutions that violated the constraints are reinitialized. The position matrix is created as follow:

P = [█(█(■(P_1^1, P_2^1,&⋯&P_Ng^1@P_1^2, P_2^2,&…&P_Ng^2@⋮ ⋮& ⋯&⋮)@⋮ ⋮ … ⋮@⋮ ⋮ … ⋮)@P_1^N, P_2^N, … P_Ng^N )]

Step3: Calculate N individual fitness value of all the birds using objective function from the equations (1-2) and find the best solution.

Step4: Evaluate foraging, vigilance and flight behavior of birds using equations 8, 9, 10 and 11 and new positions are generated using the four searching