Minimization of Combinational Digital Circuit Using Genetic Algorithm Peeyush Sharma Department of Electronics and Communication National Institute of Technology Kurukshetra, India peeyush89sharma@gmail.com Trailokya Nath Sasamal Department of Electronics and Communication National Institute of Technology Kurukshetra, India tnsasamal.ece@nitkkr.ac.in Abstract— Evolutionary Algorithm (EA) methods are proved more effective for solving complex digital circuit design problems and evaluating the fitness of combinational circuits. They optimize circuits in terms of less number of gates and transistors. In the proposed method, we have calculated the best fitness of the circuit from the designed algorithm by adjusting the parameters of Genetic Algorithm (GA) like mutation rate, crossover rate and number of generations. Then the least fitness, average fitness and worst fitness of the algorithm are evaluated. The digital gates fitness approaches to its maximum for different input parameters in different number of generations. In this method we have defined fitness function which is giving digital gate fitness in less number of generations and also optimizing the total number of gates. Experimental results are showing that proposed EA optimized the digital circuit with less number of gates and maximum fitness is evolved with less number of generations. Keywords—Genetic algorithm, Optimization, Digital circuit encoding, Evolutionary algorithm, Optimum design, Fitness function. I. INTRODUCTION In a digital circuit design the main aim of a designer is to reduce the number of elements that are being used in the circuit. We mainly focus on reducing the total number of gates and transistors used in digital circuit, because it automatically reduces the overall cost of the digital circuit design in many ways. In the combinational circuit design the optimization is based on two criteria: Based on the number of gates, and based on the number of transistors. By reducing the number of gates in a design will automatically reduce the circuit size, power consumed by overall circuit and it will reduce the parasitic effects in the circuit. For the simple combinational circuit minimization most popularly used methods are Karnaugh Maps and Quine- McCluskey. But when it comes to minimization of complex circuits or large circuits, these methods are not efficient. Also, these methods can’t use XOR or XNOR gates, which are useful in reducing the gates in a circuit. For complex optimization problems we use Evolutionary algorithm [1] [2]. Genetic algorithm (GA) is one of the search techniques of Evolutionary algorithm (EA) [3]. Genetic Algorithms can be used in different area of applications. One of the main applications of GA is the optimization. Optimization is to make something better. In the process of optimization, we make adjustment in the input to a design or the characteristics of that design. Evolutionary process for the optimization of digital circuits is totally different from the basic methods, because this is not depending upon the person’s knowledge or experience but it totally depends upon the evolution process [4]. This evolutionary method has lesser bounds than that of human designers. A human designer is not only limited by the technology in which the circuit is evolved but also by routines, capacity of imagination and limited creativity. The GA gives the advantage over these limitations and opens doors for new choices and possibilities. Rest of this paper is arranged in the following order: Section II describing details of the existing work in the field of evolutionary design of combinational digital circuits, different methods and algorithms: Section III presents the proposed GA method for the optimization of digital circuit and chromosome representation of the gate matrix structure. In Section IV experimental results and comparison between ascending fitness of the circuit structure are provided. Section V & VI represent conclusion and future scope respectively. II. EXISTING WORK Starting work in the field of combinational digital circuits designing was done by Louis with the use of GA, in this author gives the idea of arranging the gates in 2D (Two Dimensional) structure [5] [6] [15]. Koza also used GA to design digital circuits using AND, OR, NOR gates. But their methods were restricted only to make functional circuit design, but the optimization of the design was missing. In starting Binary Genetic Algorithms (BGA) were used, but they can’t be applied for large growing chromosomes size along with the growing size of dimensionality, therefore another number systems were used for evolutionary design. Coello, design GA with different dimensionality and was named as: N-Cardinality GA (N-GA), and results of NGA method were improved as compared to BGA [6]. Kalgonova added a forward step in evolutionary algorithm design. Author included more number of gate set and one bit adder circuit was designed. Then he gives EA with enhanced quality of circuit, evolved by using GA. For this author used multi-objective fitness function and evolving circuit, the results shows that the adaptable circuit layout is necessary if the circuit is to be evolved with minimum number of gates [7]. Coello gives a new algorithm design named as Multi-Objective Genetic