## 1 Introduction  
Optimization problems arise in many real-world applications and various types of intelligent evolutionary optimization methods, such as the Genetic Algorithm (GA) [1], the Particle Swarm Optimization (PSO) [2], the Differential Evolution (DE) [3], and the artificial bee colony (ABC) [4], have been proposed in the literature over the last few decades. The PSO algorithm is based on a simulation of social behavior and has been applied in various optimization problems [5]. The DE algorithm employs the difference of parameter vectors to explore the objective function [6]. The Genetic Algorithm, proposed by [PERSON] in 1975, is an algorithmic model for solving optimization problems and is inspired by genetic evolution. The conventional GA encodes a possible solution in the solution space as a string of binary bits which is treated as (a chromosome of) an individual. It explores the search space for optimal solutions by generating new individuals from an individual in the current population, using a set of operations that mimic genetic mutation in natural evolution. This approach has shown some success in solving complex optimization problems. However, the traditional GA has several drawbacks. It often suffers from a premature convergence to a local optimum when searching in a local area if there is a rapid decrease in population diversity. In addition, the binary bit string encoding usually results in a very long code and therefore, significantly reduces the computational efficiency. Many researchers believe that a promising solution to these problems may lie in the adaptation of more sophisticated natural models that can be incorporated into the framework of the GA algorithms. Hybrid optimization algorithms have recently been proposed to overcome the existing drawbacks of GA [7]. [PERSON] et al. proposed a revised Gravitational Search Algorithm (GSA) [8] powered by evolutionary methods and obtained good results. [PERSON] proposed a hybrid technique known as PSO-GA [9] for solving the constrained optimization problems. On the other hand, mimicking the genetic mechanisms of biological DNA in computation has gained increasing interest in the computer science research community [10]. This was inspired by the fact that, as the major genetic material in life, DNA encodes and processes an enormous amount of genetic information. DNA computing, proposed by [PERSON] [11] in 1994, may potentially provide a promising method for solving complex optimization problems because its parallel computing may efficiently search through a large space for potential solutions [12]. However, using DNA as computing hardware [13] still faces many challenges. For example, current solutions require biological experiments which are expensive and time-consuming. Integrating genetic algorithms with DNA computing can provide a promising alternative for solving complex optimization problems. Extending GA to use DNA encoding and corresponding genetic operations is a natural extension to the GA and DNA-computing techniques, which both aim to solve complex computational problems by mimicking a process in nature. Recent developments in the understanding of biological DNA has provided a solid ground for research. For example, a PID controller [14] and many other applications [15] have been designed using DNA computing. The DNA sequence is arguably more suitable for encoding individuals in a genetic algorithm than simple binary bit strings for solving optimization problems. The current research in this area is focused on developing better DNA encoding [16; 17]. A DNA genetic algorithm (DNA-GA) was initially proposed by [PERSON] [18] and a modified DNA genetic algorithm (MDNA-GA) was subsequently introduced by [PERSON] and [PERSON] [19]. In these algorithms, DNA encoding and two DNA-based operators, the choose crossover and frame-shift mutation, were used. These methods have been shown to be effective in improving the search for global solutions.