The flowchart of the proposed algorithm is presented in Fig. 2. The RSRP of serving cell is compared with the threshold value. If the signal goes down, then the user equipment finds neighbor base stations satisfying RSRP condition. The speed of the user is compared with the threshold speed. The high-speed users are switched to macrocell. For the low-speed users, data types are checked. The high-rate data traffics are handed over to femtocell base stations and low-rate data traffics are delivered to macrocell base stations. Then, a list of femtocells is prepared and it is solved as the optimization problem using PSO and PSOPC algorithm.
In this paper, the main goal is to reduce the handovers and total energy consumptions using PSO and PSOPC algorithm.
The state of macrocell and femtocell is classified as on and off, as in equations:
$${S_{mc}}=\left\{ \begin{gathered} 1,\,\,\,if\,{B_{mc}}\,is\,ON\,state \hfill \\ 0,\,\,otherwise \hfill \\ \end{gathered} \right.$$
6.1
$${S_{fc}}=\left\{ \begin{gathered} 1,\,\,\,if\,{B_{fc}}\,is\,ON\,state \hfill \\ 0,\,\,otherwise \hfill \\ \end{gathered} \right.$$
6.2
The service state of k UEs in a macrocell and femtocell is described as:
$${a_{mc,k}}=\left\{ \begin{gathered} 1,\,\,\,if\,{u_k}\,is\,provided\,by\,{B_{mc}} \hfill \\ 0,\,\,otherwise \hfill \\ \end{gathered} \right.$$
6.3
$${a_{fc,k}}=\left\{ \begin{gathered} 1,\,\,\,if\,{u_k}\,is\,provided\,by\,{B_{fc}} \hfill \\ 0,\,\,otherwise \hfill \\ \end{gathered} \right.$$
6.4
The presence of data services, the data type, and the speed of k UEs are described as:
$$d{s_k}=\left\{ \begin{gathered} 1,\,\,\,if\,{u_k}\,needs\,data\,sevices \hfill \\ 0,\,\,otherwise \hfill \\ \end{gathered} \right.$$
6.5
$$d{t_k}=\left\{ \begin{gathered} 1,\,\,\,if\,{u_k}\,needs\,\,high\,\,rate\,\,data\,\,traffic \hfill \\ 0,\,\,otherwise \hfill \\ \end{gathered} \right.$$
6.6
$${v_k}=\left\{ \begin{gathered} 1,\,\,\,for\,\,high\,\,speed\,\,velocity \hfill \\ 0,\,\,for\,\,low\,\,speed\,\,velocity \hfill \\ \end{gathered} \right.\,$$
6.7
The total possible handovers include all these four cases.
3.1 Particle Swarm Optimization
PSO optimization technique was first familiarized in 1995 by Dr. Russel C. Eberhart and Dr. James Kennedy [26], that was propelled by the social conduct of animals such as bird grouping and fish shoaling. PSO optimization technique has roots in bogus life, social psychology, and in engineering. It uses a “population” of particles that operate over the issue hyperspace with allowing speeds. The PSO optimization technique is a robust technique based on social psychological analogy; a society of the individual known as particles. This optimization technique is a computational intelligence-based technique that isn’t generally influenced by the content and non-linearity of the issue and can encounter to the best solution in numerous issues where maximum logical strategies flop to combine. “Swarm” originates from the uneven shifting of the particles in the issue space, presently further like to swarm of mosquitoes instead of a group of birds or fish. “Particles” indicates to the population members which are massless and volume less and are bound to speeds and raising velocities approaching a superior mode of behavior.
PSO optimization technique was initially proposed for investigating social behavior, but the optimization technique was interpreted and it was concluded that the particles were really achieving optimization. The advantages of PSO optimization technique is to solve difficult problems with fast convergence rate and it is simple to implement.
PSO optimization technique addresses the issue by keeping a population of candidate results called particles and stimulating these particles in each search-space as per the method. The mobility of the particles is managed by the best positions in the search space that are constantly being refreshed as best position. The interaction between ith particles and the global best position (gbest) is shown in in Fig. 6.3.
The pseudocode for the PSO optimization technique is:
Assume be the cost function that must be decreased. Assume that the amount of particles in the swarm is, each having a position \({X_i}\) belonging to real numbers in the search space and velocity \({V_i}\) belonging to real numbers. Assume that the particle’s i best position is \({P_i}\) be and the global best position is\({g_i}\). Then, the PSO optimization algorithm is:
● for all particles \(i=1,2,.....,S\)
do:
● Initialization of particle’s position: where is a uniformly distributed random vector and\({B_{lo}}\), \({B_{up}}\)are the lower and upper boundaries respectively of the search space.
● Initialization of particle’s best position: \({P_i} \leftarrow {X_i}\)
● Initialization of velocity:![](https://myfiles.space/user_files/120476_695e7dc7a8d3b6b1/120476_custom_files/img1656257560.png)
● Initialization of the global best position of the swarm: \({g_i} \leftarrow \arg \;\hbox{min} f\left( {{P_i}} \right)\)
● Until a finale criterion is met (e.g., number of iterations completed),
repeat:
● for all particles \(i=1,2,.....,S\)
do:
● Initialize a random vectors ![](https://myfiles.space/user_files/120476_695e7dc7a8d3b6b1/120476_custom_files/img1656257648.png)
● Revise the particle’s velocity:\({V_{i1}}=w.{V_i}+{c_1}.{r_p}\left[ {{P_i} - {X_i}} \right]+{c_2}.{r_g}\left[ {{g_i} - {X_i}} \right]\)
● Revise the particle’s position:\({X_{i1}}={X_i}+{V_{i1}}\)
● If \(\left( {f\left( {{X_i}} \right) \prec f\left( {{P_i}} \right)} \right)\), upgrade the best position of particles:\({P_i}={X_i}\)
● If \(\left( {f\left( {{X_i}} \right) \prec f\left( {{g_i}} \right)} \right)\), upgrade the global best position of swarm: \({g_i}={P_i}\)
● now \({g_i}\) keeps the global best solution.
The parameters \(w,{c_1},{c_2}\)are chosen to control the behavior and efficiency of the PSO method.
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3.2 Particle Swarm Optimization with Passive Congregation
Passive congregation was introduced by He et al. [27], a system that enables creatures to assemble into groups. PSOPC optimization technique was introduced to increase the efficiency and convergence speed of PSO optimization technique. The involvement of passive congregation is to revise the particle’s velocity equation to
\({V_{i1}}=w.{V_i}+{c_1}.{r_p}\left[ {{P_i} - {X_i}} \right]+{c_2}.{r_g}\left[ {{g_i} - {X_i}} \right]+{c_3}.{r_3}\left[ {{R_i} - {X_i}} \right]\) \({X_{i1}}={X_i}+{V_{i1}}\) (6.8)
where, \({r_p},{r_g},{r_3}\) are random numbers in the range 0 and 1. The passive congregation coefficient is\({c_3}\), and \({R_i}\) is the randomly selected particle from the swarm. The interactions between particles of PSOPC optimization technique are shown in Fig. 4.
However, the work defined by He et al. [27] exclude the details for the estimation of the congregation coefficient or how it influences the functioning of the optimization technique. These two points are the essential features for future analysis.