Diversified sine–cosine algorithm based on differential evolution for multidimensional knapsack problem

The sine–cosine algorithm (SCA) is one of the simplest and efficient stochastic search algorithms in the field of metaheuristics. It has shown its efficacy in solving several real-life applications. However, in some cases, it shows stagnation at local optima and premature convergence issues due to low exploitation ability and insufficient diversity skills. To overcome these issues from the SCA, its enhanced version named ISCA is developed in this paper. The proposed ISCA is designed based on modifying the original search mechanism of the SCA and hybridizing it with a differential evolution (DE) algorithm. The search procedure in the ISCA switches between the modified search mechanism of the SCA and DE based on the evolutionary states of candidate solutions and a parameter called the switch parameter. The modified SCA enhances the exploitation ability and convergence speed, while the DE maintains the diversity of the population to avoid local optimal solutions. The parameters of the ISCA are tuned in such as way that they could balance the exploration and exploitation features. Validation of the ISCA is conducted on a benchmark set of 23 continuous optimization problems through different performance measures, which reveals its effectiveness as a better optimizer for continuous optimization problems. Furthermore, the proposed ISCA is extended to develop its efficient binary version named BISCA for solving multidimensional knapsack problems. A benchmark collection of 49 instances is used for the performance evaluation of the BISCA. Comparison of results produced by the BISCA with other algorithms and previous studies indicates its better search efficiency and verifies it as an effective alternative for solving the MKP.