To testthe performance ofthe proposed algorithm, we do experiments on 10 benchmark functions. These test functions, which are shown in Table 1, can be classified into two groups. The first five functions f1–f5 are unimodalfunctions. For unimodalfunctions, the convergence rate of an algorithm is more interesting than the final result of optimization. Therefore, we not only give the final achievement but also show the convergence rate of each algorithm. The next five functions f6–f10 are multimodal functions with many local optima. For multimodal functions, we only give the final result
since it reflects an algorithm’s ability of escaping from poor local optima. The functions are used to test the global search ability of the algorithm in avoiding premature convergence. In this paper, all empirical experiments related to the PSO and
its improvements are carried out with a same population size. Furthermore, in order to ensure that the initial values of particles in each algorithm are same, we use the MATLAB command rand(state, sum(i30)). The initial value of i of each run for all algorithms is the same. Parameter s is the interval of the adjacent two inertia weight change in all iterations. The parameters of the BPSO are used as follow.