［Purposes］ A special kind of multi-objective optimization problem with norm structure is studied, which can be applied to the processing of many practical problems. ［Methods］ Based on the idea of scalarization, an approximate method is proposed to solve this kind of multi-objective optimization problem under some suitable assumptions. ［Findings］ It can obtain Pareto solutions of multi-objective optimization problems by adjusting the ranges of several parameters. ［Conclusions］ The multi-objective optimization model with norm structure and the approximate solution method are used in the setting of basic workload and the assignment of power plant generators in performance management.