Amplified and quantum based brain storm optimization algorithms for real power loss reduction

Received Jan 3, 2020 Revised Feb 19, 2020 Accepted Mar 3, 2020 In this work amplified brain storm optimization (ABS) algorithm and quantum based brain storm (QBS) optimization algorithm is applied to solve the problem. A node is arbitrarily chosen from the graph as the preliminary point to form a Hamiltonian cycle. At generation t and t+1, Lt and Lt+1 are the length of Hamiltonian cycle correspondingly. In the QBS algorithm a Quantum state of an idea is illustrated by a wave function ( ⃗ ) as an alternative of the position modernized only in brain storm optimization algorithm. Monte Carlo simulation method is used, to measure the position for each idea from the quantum state to the traditional one. Proposed ABS algorithm and QBS optimization algorithm has been tested in standard IEEE 57 bus test system and real power loss reduced effectively.


INTRODUCTION
In this work minimizing true power loss is the main objective of the problem. A variety of methods [1][2][3][4][5][6] have been applied to solve the problem. Subsequently various evolutionary methods [7][8][9][10][11][12][13][14][15][16] applied to solve the problem, in that many algorithms stuck in local optimal solution In this work amplified brain storm optimization (ABS) algorithm and quantum based brain storm (QBS) optimization algorithm is used for solving optimal reactive power problem. Brain storm optimization (BSO) algorithm gets trapped into local optima when applied to different optimization problems. In the mathematical field of graph theory, a Hamiltonian path is a path in an undirected or directed graph that visits each vertex exactly once. In the proposed algorithm Hamiltonian cycle will improve the explore abilities and also stay away from local optimal solution. In QBS algorithm completely, the mechanism of quantum behavior, which causes uncertain of every idea lead to a superior capability to bounce out of the local optimal solution. Proposed ABS algorithm and QBS optimization algorithm has been tested in standard IEEE 57 bus test system.

AMPLIFIED BRAIN STORM OPTIMIZATION ALGORITHM
BSO [17] gets trapped into local optima when applied to different optimization problems. In the projected amplified brain storm optimization algorithm Hamiltonian cycle has been applied to improve the search abilities and also to avoid of trap in local optimal solution. A node is arbitrarily chosen from the graph as the preliminary point to form a Hamiltonian cycle. At generation t and t+1, L t and L t+1 are the length of Hamiltonian cycle correspondingly. Their ratio r at generation t(r t ) can be described as: Hamilton cycle algorithm as follows:
Step 2: is chosen and is picked with least weight linking , then the is obtained.
Step 3: when i+1<n, subsequently i+1 is used to substitute i, and revisit to Step 2; condition not occurred , then revisit to the final Hamiltonian cycle then go back to Step 4.
Step 6: compute the extent of the Hamiltonian cycle C.

End for i
In the proposed amplified brain storm optimization (ABSO) algorithm Hamiltonian cycle will improve the explore abilities and also stay away from local optimal solution.

Commence
Step 1: "n" potential solutions are arbitrarily engendered Step 2: "n" individuals are clustered into "m" clusters Step 3: "n" individuals will be appraised Step 4: In every cluster rank the individuals then the most excellent individual's are recorded as cluster center Step 5: Between 0 and 1 arbitrarily a value will be engendered; If the value is smaller than a probability; then i. a cluster center has been Arbitrarily chosen; ii. To swap the certain cluster center arbitrarily engender an individual Step 1: node v1 chosen as initial point, Step 2: is chosen and is picked with least weight linking , then the is obtained.
Step 3: when i+1<n, subsequently i+1 is used to substitute i, and revisit to Step 2 Step 4: for all i and j in cycle Step 5: C is substituted by C1, and revisit Step 4.
Step 6: compute the extent of the Hamiltonian cycle C. Step 7: when "n" new-fangled individuals are engendered, then go to Step 8; or else go to Step 6.
Step 8:end conditions met ; or else go to Step 2. End

QUANTUM BASED BRAIN STORM OPTIMIZATION ALGORITHM
In BSO algorithm population is indicated as swarm moreover every individual is described as an idea. Originally, every idea is arbitrarily initialized inside the exploration space. Subsequently most excellent one in every cluster is selected as the cluster centre. Sporadically, an arbitrarily chosen centre is swapped by a recently engendered idea, by that the swarm has been kept away from the local optimum.
is a factor used in the evolution process and can be articulated as, Quantum state of an idea is illustrated by a wave function ( ⃗ ) as an alternative of the position modernized only in Brain storm optimization algorithm. By using Schrödinger equation probability density function of the position is identified such that each idea is located. Monte Carlo simulation method is used, to measure the position for each idea from the quantum state to the traditional one. Step a: Initialize the parameters.
Step b: Arbitrarily produce "n" ideas Step c: By k-means algorithm cluster "n" ideas.
Step d: With a predetermined probability modernize the centre of a capriciously chosen cluster.
Step e: Individual generation created.
Step f: Quantum mechanism is exploited based on the chosen idea Step g: Crossover operator is implemented Step h: evaluate the new-fangled idea with the older one, Step i: If "n" ideas have been engender, then go to Step 9. Or else go to Step 5.
Step j: Stop whether the present number of iterations Nc attain the Ncmax. or else, go to

SIMULATION STUDY
Proposed ABS optimization algorithm and QBS optimization algorithm has been tested, in IEEE 57 Bus system [18]. Table 1 shows the comparison results.

CONCLUSION
In this paper ABS optimization algorithm and QBS optimization algorithm successfully solved the optimal reactive power problem. In projetced ABS algorithm to escape BSO from local optima and to maintain the optimization process Hamiltonian cycle has been utilized. In the mathematical field of graph theory, a Hamiltonian path is a path in an undirected or directed graph that visits each vertex exactly once. In QBS approach by using Schrödinger equation probability density function of the position is identified such that each idea is located. Monte Carlo simulation method is used, to measure the position for each idea from the quantum state to the traditional one. Proposed ABS algorithm and QBS optimization algorithm has been tested in standard IEEE 57 bus test system and simulation results show the projected algorithms reduced the real power loss efficiently.