Decomposition-based many-objective evolutionary algorithms need to adjust reference vectors when solving problems with irregular Pareto fronts. To avoid this complicated operation, this paper proposes a many-objective evolutionary algorithm based on clustering and the sum of objectives referred to as CSEA. This algorithm introduces a periodically updated external population to store non-dominated solutions, which guides the evolving directions of the current population through clustering and maintains the diversity of the current population. When selecting solutions, CSEA evaluates convergence according to Pareto dominance and the sum of objectives, and then select well-converged solutions according to non-dominated sorting and fitness-based sorting. Compared with seven algorithms on two many-objective optimization test suites, CSEA is effective on many-objective optimization problems with various shapes of Pareto fronts.