Comparative study of power consumption minimization in analog electronic circuit using AI techniques

Today we are living in electronics world. Analog electronics are electronic systems with a continuously variable signal, in contrast to digital electronics where signals usually take only two levels. Although we usually convert the analog information for processing or storage into digital media, we essentially create and consume information in analog domain. Analog circuits can be very elegant designs with many components or they can be very simple. Analog circuit design was developed four decades ago but it is still infancy compared of digital design. In modern days use of analog circuit is increasing day by day, so we need high degree of reliability and accuracy. For the analog design problems, new techniques are developed. Many of these techniques have been based on intelligent system such as logic, neural networks etc. So we need minimization of electronic circuit to increase the system reliability and accuracy and also we need to reduce the value of component as well as the power consumption in circuits. Optimization of circuit is necessary for this purpose.

Optimization is a branch of computational science which can be defined as the process of finding the best solution for a problem (Wang et al., 2018). Over the years, many efforts have been made to solve this problem, incorporating different kinds of constraints or multiple objectives through various mathematical programming and optimization techniques. The conventional methods include Newton- Raphson method, Lambda iteration method, Gradient method etc. The input/output characteristics of modern units are inherently highly nonlinear (Lee & El-Sharkawi, 2007). Consideration of highly nonlinear characteristics of the units requires highly robust algorithms to avoid getting stuck at local optimum. The classical calculus based techniques fail in solving these types of problems (Rani & Latha, 2016) because of these algorithms stuck with local optimum solutions (Sakhrieh et al., 2017). In this respect, stochastic search algorithms like Genetic Algorithm (GA), Particle Swarm Optimization (PSO) (Magrini & Lazzari, 2018; Halber & Chakravarty, 2018) may prove to be very efficient in solving minimization of power consumption problem without any restrictions (Sharma and Rai, 2017; Sen et al., 2017). These are nature inspired algorithms. Alan Turing was the first who used heuristic algorithms in 1948. But 1960s and 1970s were the two decades of development of Evolutionary Algorithms (EA). Today these are very popular to solve the real-world optimization problems (Keshtkar, 2017). Some of recent evolutionary algorithms like Cuckoo Search (CS) have been introduced (Nie & Yue, 2008). This algorithm is inspired by brooding behaviour of cuckoos and based on levy flights and successfully implemented for various optimization problems (Idoumghar & Melkemi, 2011). Later on many researchers have given different techniques to improve performance of the basic algorithm like as Dynamic PSO or Improved PSO or Hybrid Algorithms. In hybrid algorithm merits of two algorithms combine and demerits are removed. Such algorithm has better characteristics (Nie & Yue, 2008; Idoumghar & Melkemi, 2011; Goyal & Mehta, 2004).

In the section-2, objective function of minimization of power consumed in emitter amplifier circuit is formulated. Section-3 describes the evolutionary algorithms viz GA, PSO and a new algorithm i.e. hybrid algorithm. In hybrid algorithm, some characteristics of PSO algorithms and some of GA algorithms are compounded. Section-4 gives a comparative study for power consumption minimization using GA, PSO and hybrid algorithm.

3.1. Genetic algorithm

Genetic Algorithm (GA) is computerized search and optimization algorithm, based on mechanics of neutral genetics and natural selection. It is a population based stochastic global search method and apply the Darwin’s principle of “Survival of fittest” to produce better and better solution. Genetic Algorithms are commonly used to generate high-quality solutions. A GA uses a population of individuals (solutions) instead of a single solution to perform a parallel search in the problem space. The basic elements of natural genetics are reproduction, crossover and mutation (Saini et al., 2017; Sharma & Goyal, 2017).

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Figure 2. Flow chart for genetic algorithm

3.2. Particle swarm optimization (PSO)

Particle Swarm Optimization (PSO) algorithm was first described in 1995 by J. Kennedy and R. C. Eberhart This algorithm is inspired by simulation of social psychological expression. As like people solve their problems by talking with each other and interacts by sharing their beliefs, attitudes, and behaviour changes. In PSO, each individual makes its decisions by his own experience together with other’s experiences. The algorithm of PSO works in a way to have all the particles being located in the optimal position.

Thus, working behaviour of swarm intelligent technique is based on three important factors:

(1) Cohesion—Stick together.

(2) Separation—doesn’t come too close.

(3) Alignment—Follow the general heading of the flock.

3.2.1. Initialization

As like other evolutionary algorithms, PSO is also initialized with some random solutions. In PSO, each individual “i”, called particle, represents a solution to the optimization problem i.e. a vector of decision variables, X_i (Das et al., 2016).

${{X}_{i}}=X_{i}^{\min }+rand()*(X_{i}^{\max }-X_{i}^{\min })$      (3)

Here, NP shows the number of particles, (i=1, 2.....NP)

3.2.2. Update the solution vector

In PSO algorithm particles follow the fittest member of the swarm and move toward historically good areas of the provided space. Each particle tries to modify its position using the following information:

(1) Current positions,

(2) Current velocities,

(3) Difference of current position and individual position

(4) Difference of current position and global best position

In order to modify the solutions vector, each individual is associated with some velocity, v. Starting from some random value, velocity is updated in each iteration by the following equation (Hussein et al., 2014).

$v_{ij}^{t+1}=wv_{ij}^{t}+{{c}_{1}}{{R}_{1}}(Pbes{{t}^{t}}-{{X}^{t}})+{{c}_{2}}{{R}_{2}}(Gbes{{t}^{t}}-{{X}^{t}})$    (4)

Gbest is the global best position in the problem space. Pbest is the best known individual position of a particle.

V^t_ij is velocity of jth member of ith particle at iteration number t which is bounded in its min-max limits (Sharma et al., 2017)

$v_{j}^{\min }\le {{v}_{ij}}\le v_{j}^{\max }$

R₁ & R₂ are the random numbers generated between 0 and 1. On the other hand, C₁& C₂ can vary in range of 0-4 but these are adjusted such as sum of C₁ and C₂ should be 4. Here C₁=C₂= 2 (Cohen et al., 2015).

Here, ѡ is inertia-weight which is given as follows (Leela & Madhavi, 2016):

$w={{w}^{\max }}-\frac{({{w}^{\max }}-{{w}^{\min }})*iteration}{\max iteration}$  (5)

After iteration the position vector of swarms is updated by adding the velocity ‘v’ in the current solution vector and same processes is repeated.

${{X}^{t+1}}={{X}^{t}}+{{v}^{t+1}}$    (6)

3.3. Hybrid algorithm

It is observed that the performance of PSO is problem-dependent. This dependency usually results from the parameters settings in each algorithm. The different parameters for a stochastic search algorithm result in high performance variances. Thus finding the best value for the parameters is not easy task. To overcome the limitations of PSO, hybrid algorithms with GA are proposed. The basis behind this is that such a hybrid approach is expected to have merits of PSO with those of GA. One advantage of PSO over GA is its algorithmic simplicity. Another clear difference between PSO and GA is the ability to control convergence. Crossover and mutation rates can subtly affect the convergence of GA, but these can not be analogous to the level of control achieved through manipulating of the inertia weight. In fact, the decrease of inertia weight dramatically increases the swarm’s convergence.

The proposed algorithm which is a Hybrid of Genetic Algorithm (GA) and Particle Swarm Optimization (PSO). It has following steps:

(1) Initialize random generated population by GA

(2) Evaluation of objective function with initial population.

(3) Finding Pbest and Gbest as per PSO.

(4) Calculate velocity of particles by PSO using equation (4)

$v_{ij}^{t+1}=wv_{ij}^{t}+{{c}_{1}}{{R}_{1}}(Pbes{{t}^{t}}-{{X}^{t}})+{{c}_{2}}{{R}_{2}}(Gbes{{t}^{t}}-{{X}^{t}})$

(5) Generate new population using Genetic Algorithm Operators i.e. (i) Reproduction, (ii) Mutation and (iii) Crossover.

(6) Add the velocity in to solution vector by following equation (6)

${{X}^{t+1}}={{X}^{t}}+{{v}^{t+1}}$

(7) Evaluate again the objective function and update Pbest as well as Gbest.

(8) Repeat the process up-to maximum iteration counter.