Refined Heuristic Swarm Intelligence Algorithm

In this paper, a new metaheuristic algorithm named refined heuristic intelligence swarm (RHIS) algorithm is developed from an existing particle swarm optimization (PSO) algorithm by introducing a disturbing term to the velocity of PSO and modifying the inertia weight, in which the comparison between the two algorithms is also addressed.


Introduction
For the last decade, many researchers in this field have changed direction, leaving aside traditional optimization techniques based on linear and nonlinear programming and embarked in the implementation of the evolutionary algorithm: genetic algorithm; ant colony optimization; simulated annealing; and harmony search among others. Particle swarm optimization (PSO) algorithm was first introduced by Kennedy and Eberhart in 1995 by observing the behavior of animals, e.g., bird flocking and fish schooling. Their movements and communication mechanisms were thoroughly studied [1,2,4].
In comparison with several other population based stochastic optimization methods such as genetic algorithm (GA) and evolutionary programming (EP), PSO performs better in solving various optimization problems with fast and stable convergence rate [3,6].
In this research work a new metaheuristic method is designed which performs better than the existing one.

Particle Swarm Optimization (PSO) Algorithm
The pseudo code for particle swarm algorithm (PSO) is as follows: Step 1: Initialize the population size N p , the dimension of the space c 1 , c 2 , It max , w max , w min Step 2: Set P best,i = x i , Step 3: If iter < It max Step 4: Calculate the inertia weight Step 5: Calculate the velocity of each particle by v t+1 = wv t i + c 1 r 1 (P best,1 − x t i ) + c 2 r 2 (G best − x t i ) Step 6: Calculate the position of each particle by Step 7: Calculate the value of the objective function for each particle f (x t+1 ) Step 8: Step 9: Go to Step 3.
The velocity of particle i at (t + 1) th iteration P t+1 best,i The personal best of particle i at (t + 1) th iteration G best,i The global best r 1 , r 2 Random variable, which is always between o and 1

Algorithm of Refined Heuristic Swarm Intelligence (RHSI)
Just like other global algorithm, PSO converges prematurely and being trapped into a local minimum. This leads to the modification of PSO algorithm called refined heuristic swarm intelligence (RHSI) algorithm which is the major concentration of this paper.

Refined Heuristic Swarm Intelligence (RHSI) Algorithm
RHSI algorithm was developed as a result of the premature convergence of PSO algorithm and being trapped by local minimum.
In this algorithm the natural log of the inertial weight (w) of PSO is being considered as the inertia weight of the algorithm, i.e., Also a disturbing term is introduced to the velocity of PSO which makes the method more efficient. This disturbing term |b(r 3 − 0.5)| is introduced to the velocity, where b is a small number and r is a random number in the range (0, 1). We take b = 0.05 in this paper. Therefore the velocity of each particle is being updated with The pseudo code for algorithm of refined heuristic swarm intelligence (RHSI) is as follows: Step 1: Initialize the population size N p , the dimension of the space Step 2: Set P best,i = x i , Step 3: If iter < It max Step 4: Calculate the inertia weight Step 5: Calculate the velocity of each particle by Step 6: Calculate the position of each particle by Step 7: Calculate the value of the objective function for each particle Step 8: Find P t+1 best,i and G best if f t+1 i > P t best,i then P t+1 best = P t best , i else Step 9: Go to step 3.

Computational Consideration
In this paper we will take the following values for the PSO and RHSI parameters: w max = 0.9, w min = 0.4, It max = 1000, b = 0.05, number of particles=10. The numerical results are presented in Tables 4.1 and it was obtained from the solution of some test problems are presented in this section using MATLAB R2010a (7.10.499) run on the PC Intel(R) samsung, a 32 bit Os Laptop windows 7 operating system.

Computational Results
The computational result is given in Table 4.1.

Discussion on Numerical Results
From the result tabulated in Table 4.1, it can be seen that RHIS proposed in this paper performs better than PSO in terms of value of the objective function.

Conclusion
To improve the performance of PSO algorithm, a modified PSO algorithm (RHSI algorithm) based on disturbing term is introduced in this paper. Two improvement strategies are proposed to generate a new position for each particle, which the strategies are modifying the inertia weight and the velocity of the particle of which it performs better than PSO algorithm. Therefore RHSI algorithm is recommended for solving optimization problems.