ε constrained differential evolution with pre-estimated comparison using gradient-based approximation for constrained optimization problems

• An improved algorithm is proposed for constrained optimization problems.
• Pre-estimated comparison using gradient-based approximation is proposed.
• The experimental results illustrate the effectiveness of the proposed algorithm.

Many real-world problems can be categorized as constrained optimization problems. So, designing effective algorithms for constrained optimization problems become more and more important. In designing algorithms, how to guide the individuals moving more efficiently towards the feasible region is one of the most important aspects on finding the optimum of constrained optimization problems. In this paper, we propose an improved ε constrained differential evolution, which combines with pre-estimated comparison gradient based approximation. The proposed algorithm uses gradient matrix to determine whether the trail vector generated by differential evolution algorithm is worth using the fitness function to evaluate it or not. Pre-estimated comparison gradient based approximation is used as a detector to find the promising offspring and in this way can we guide the individuals moving towards the feasible region. The proposed method is tested both on twenty-four benchmark functions and four well-known engineering optimization problems. Experimental results show that the proposed algorithm is highly competitive in comparing with other state-of-the-art algorithms. The proposed algorithm offers higher accuracy in engineering optimization problems for constrained optimization problems.