Design of Optimal CMOS Inverter for Symmetric Switching Characteristics Using Firefly Algorithm with Wavelet Mutation

Design of Optimal CMOS Inverter for Symmetric Switching Characteristics Using Firefly Algorithm with Wavelet Mutation

Bishnu Prasad De (Department of Electronics and Communication Engineering, NIT Durgapur, Durgapur, India), Rajib Kar (Department of Electronics and Communication Engineering, NIT Durgapur, Durgapur, India), Durbadal Mandal (Department of Electronics and Communication Engineering, NIT Durgapur, Durgapur, India) and Sakti Prasad Ghoshal (Department of Electrical Engineering, NIT Durgapur, Durgapur, India)
Copyright: © 2014 |Pages: 36
DOI: 10.4018/ijsir.2014040103
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Abstract

In this article, a population based meta-heuristic search method called Firefly Algorithm with Wavelet Mutation (FAWM) is applied for the optimal switching characterization of CMOS inverter. In Firefly Algorithm (FA), behaviour of flashing firefly towards its competent mate is structured. In this algorithm attractiveness depends on brightness of light and brighter fireflies are considered as more attractive among the population. For the present minimization based optimization problem, brightness varies inversely proportional to the error fitness value, so the position of the brightest firefly gives the optimum result corresponding to the least error fitness in multidimensional search space. FAWM incorporates a new definition of swarm updating with the help of wavelet mutation based on wavelet theory. Wavelet mutation enhances the FA to explore the solution space more effectively compared with the other optimization methods. The performance of FAWM is compared with real coded genetic algorithm (RGA), and conventional PSO reported in the literature. FAWM based design results are also compared with the PSPICE results. The comparative simulation results establish the FAWM as a more competent optimization algorithm to other aforementioned evolutionary algorithms for the examples considered and can be efficiently used for CMOS inverter design.
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1. Introduction

Due to complex growth in VLSI circuits, the task of optimal integrated circuit design by hand is very difficult. Evolutionary computation may be a competent implement for automatic design of digital integrated circuits (IC). A CMOS-based integrated circuit is made up of NMOS and PMOS transistors, where the transistor geometries (i.e., channel length (L) and channel width (W)) and other necessary circuit component values are considered to be the design parameters. The values of the design parameters are to be found out such that the performances of the circuits are optimized. Selection of design parameters is very important in design process. Ideally all the design parameters are taken as variables and the optimal solution is searched.

Two basic but popular evolutionary optimization techniques used for different optimization problems are Genetic Algorithm (GA) which is originated by the Darwin’s “Survival of the Fittest” strategy (Ma & Cowan, 1996), and swarm intelligence such as particle swarm optimization (PSO) and its variants (Luitel & Venayagamoorthy, 2010; Kar, Mandal, Mondal & Ghoshal, 2012). Conventional PSO replicates the behaviour of bird flocking or fish schooling (Luitel & Venayagamoorthy, 2010; Kar, Mandal, Mondal & Ghoshal, 2012; Fang, Sun, & Xu, 2009; Krusienski, & Jenkins, 2003; Upadhyay, Kar, Mandal & Ghoshal, 2014; Saha, Kar, Mandal & Ghoshal 2013).GA is a probabilistic heuristic search optimization technique developed by Holland (Holland, 1975). The characteristics such as multi-objective, coded variable and natural selection made this technique suitable for finding the near global solution to the optimization problem. GA is used for the optimal design of two dimensional recursive filters (Mastorakis, Gonos, & Swamy, 2003) and FIR log filters (Lu & Tzeng, 2000). Genetic Algorithm has also been applied for the synthesis of passive analog circuits to get optimal values of R, L and C elements from a given set of specifications (Das & Vemuri 2007). VLSI circuit partitioning (Gill, Chandel & Chandel, 2009), placement and area optimization of soft modules in VLSI floor plan stage (Tang & Lau, 2007) have been developed using Genetic Algorithm.

PSO is swarm intelligence based evolutionary algorithm developed by Eberhart et al. (Kennedy & Eberhart, 1995; Eberhart & Shi, 1998). PSO is very simple to implement and a few steps are required to implement the algorithm. PSO was efficiently used in various application areas (Chen & Luk, 2010; Gudise & Venayagamoorthy, 2004; Lai, 2006; Ulker, 2008; Vural & Yildirim, 2012; Ling, Iu, Leung & Chan, 2008). Design of digital IIR filter using particle swarm optimization was proposed in (Chen & Luk, 2010). PSO was adopted for the placement and routing of the field programmable gate arrays (FPGA) to minimize the distances between Configurable Logic Blocks (CLBs) (Gudise & Venayagamoorthy, 2004). PSO was used for image segmentation to estimate the parameters in the mixture density function for minimization of the square error between the density function and the actual histogram (Lai, 2006). PSO was also applied for the synthesis of microstrip coupler and single shunt stub matching circuits (Ulker, 2008). Optimal design of analog circuits such as differential amplifier with current mirror load and two stage operational amplifiers were carried out using PSO algorithm in (Vural & Yildirim, 2012).

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