A Time-varying Mutation Operator for Balancing the Exploration and Exploitation Behaviours of Genetic Algorithm

Abstract

Many real-world combinatorial optimization problems (COPs) are NP-hard and challenging to find the optimal solution using classical linear and convex optimization methods. In addition, the computational complexity of these optimization tasks increases exponentially with the increasing number of decision variables. A further difficulty can be also caused by the search space being intrinsically multimodal and non-convex. In such a case, an effective optimization method is required that can cope better with these problem characteristics. Genetic algorithm (GA) is a widely used method for COPs. The original GA and its variants have been used to solve a number of classic discrete optimization problems. Literature shows that the static mutation probability is commonly used for the GA and its variants which cause the imbalance between exploration and exploitation, limiting the performance of GA. To overcome this problem, this research proposes a time-varying mutation operator for GA. In this paper, the balance between exploration and exploitation of the proposed GA has been verified using the benchmark instances of a well-known combinatorial optimization problem i.e., the 0–1 knapsack problem. The numerical results show that the proposed GA can obtain better results with on average a significant number of function evaluations compared to the well-known metaheuristic methods.