The multi-objective energy consumption scheduling problem based on the third-party management is one essential issue of smart grid. The minimal energy cost and the maximal utility are two optimization objectives. One characteristic of the multi-objective energy consumption scheduling problem is that the magnitude difference between the two objectives increases as the number of users increases. The difference affects the quality of the solution set in the sense that it is harder to obtain the uniformly distributed solutions with good convergence and diversity for problems with a larger difference. In this paper, we propose a decomposition algorithm based on the non-uniform weight vector. The weight vector is designed based on the relationship of the magnitude difference between the two optimization objectives. The weight vector consists of two parts. One is the balance factor that can maintain the diversity of the solutions. The other is the scale factor that further enhances the searching ability with a large number of users. With the non-uniform weight vector, our algorithm can effectively deal with the magnitude difference between the two optimization objectives. The simulation illustrates that the proposed algorithm is very useful for solving large-scale energy consumption scheduling problems. In addition, the modified standard ZDT problems with apparent magnitude differences between two objectives are used to illustrate the versatility and stability of the proposed algorithms based on the non-uniform weight vector. 
Multi-objective energy consumption scheduling based on decomposition algorithm with the non-uniform weight vector