Time-Varying Acceleration Coefficients or TVAC

Apart from each existing fundamental, the idea of time-varying acceleration coefficients or TVAC (φ₁ and φ₂) has been embedded in the basic Particle Swarm Optimization algorithm. Because of the presence of Time Varying Acceleration Coefficients, the search process controls the global best position and assist in establishing an appropriate balance among socio-cognitive components. Because, both social and cognitive components guide the search towards the best solution, contain an accurate control over these components can be acknowledged like a key to determine the best solution efficiently and accurately. Past studies have incorporated a new or latest parameter tuning strategy as like time varying acceleration coefficients that can be embedded in the basic Particle Swarm Optimization algorithm to improve the quality of solution.

Based upon the aforementioned fact, cognitive component is decreased and social component is raised by changing the acceleration coefficient φ₁ and φ₂ utilized in Eqs. 21 and 22 with time Initially, along with the larger cognitive and smaller social component, particles are permitted to move towards the search space quite than moving towards population best, while in latter part of the search, little cognitive and large social component permits the particle to the global minimum to converge. Such modification can be mathematically presented as like:

                                f₁  = (f_{1, l}  - f_{1, s} ) . (iter / max _ iter ) + f_{1, s}.........................Eqn(21)

                                f₂  = (f_{2, l}  - f_{2, s} ) . (iter / max _ iter ) + f_{2, s}.........................Eqn(22)

Here f1, S , f1, l, f2, l and f2, s are constants and there values can be determione in literature as 2.5 to 0.5 and from 0.5 to 2.5. While 'max_iter' is the maximum number of generations and 'iter' is the counter of recent generation.

This modification's application assists in ignoring pre-mature convergence in the early stages of search and improves the best solution throughout latter stages of search.

For i = (1,2,3,4,5) the function crandi (Z), in pseudo-code is the chaotic random number generating function.