A binary reptile search algorithm based on transfer functions with a new stochastic repair method for 0–1 knapsack problems

Abstract

The Reptile Search Algorithm (RSA), inspired by crocodiles' hunting behavior, is a recently introduced nature-inspired algorithm. Although the original version of the RSA shows outstanding performance in optimizing continuous applications, it is not suitable for discrete optimization problems like 0–1 knapsack problems (0–1 KP). To extend RSA to binary optimization issues, binary RSA (BinRSA) is proposed in this study. A wide range of transfer functions (TFs), including the largely used s-shaped and v-shaped, and recently introduced z-shaped, u-shaped, and taper-shaped, are investigated in the proposed algorithm to map the continuous values into binary. In addition, a novel repair method is introduced to cope with infeasible solutions for 0–1 KP and discussed in detail regarding its efficacy in reaching the optimal solution. The proposed method is validated on three benchmark datasets with 63 instances of 0–1 KP. First, the impact of 25 different transfer functions under six categories on the performance of the proposed binary algorithm is thoroughly investigated, and the results indicate that the taper-shaped T1 transfer function is superior to the other variants of the BinRSA. Then, the effectiveness of the proposed BinRSA with T1 transfer function is compared with some well-known and state-of-art algorithms, including Harris hawks optimization (HHO), slime mould algorithm (SMA), and marine predators algorithm (MPA). The experimental results show that compared to other methods, BinRSA considerably increased the solution accuracy and robustness for solving 0–1 KP.