Adaptive weight-vector adjustment has been explored to compensate for the weakness of the evolutionary many-objective algorithms based on decomposition in solving problems with irregular Pareto-optimal fronts. One essential issue is that the distribution of previously visited solutions likely mismatches the irregular Pareto-optimal front, and the weight vectors are misled towards inappropriate regions. The fact above motivated us to design a novel many-objective evolutionary algorithm by performing local searches on an external archive, namely, LSEA. Specifically, the LSEA contains a new selection mechanism without weight vectors to alleviate the adverse effects of inappropriate weight vectors, progressively improving both the convergence and diversity of the archive. The solutions in the archive also feed back the weight-vector adjustment. Moreover, the LSEA selects a solution with good diversity but relatively poor convergence from the archive and then perturbs the decision variables of the selected solution one by one to search for solutions with better diversity and convergence. At last, the LSEA is compared with five baseline algorithms in the context of 36 widely-used benchmarks with irregular Pareto-optimal fronts. The comparison results demonstrate the competitive performance of the LSEA, as it outperforms the five baselines on 22 benchmarks with respect to metric hypervolume.

Workflow scheduling is essential to simultaneously optimize the makespan and economic cost for cloud services and has attracted intensive interest. Most of the existing multi-objective cloud workflow scheduling algorithms regard the focused problems as black-boxes and design evolutionary operators to perform random searches, which are inefficient in dealing with the elasticity and heterogeneity of cloud resources as well as complex workflow structures. This study explores the characteristics of cloud resources and workflow structures to design a knowledge-based evolutionary optimization operator, named KEOO, with two novel features. First, we develop a task consolidation mechanism to reduce the number of cloud resources used, reducing the economic cost of workflow execution without delaying its finish time. Then, we develop a critical task adjustment mechanism to selectively move the critical predecessors of some tasks to the same resources to eliminate the data transmission overhead between them, striving to improve the economic cost and finish time simultaneously. At last, we embed the proposed KEOO into four classical multi-objective algorithms, i.e., NSGA-II, HypE, MOEA/D, and RVEA, forming four variants: KEOO-NSGA-II, KEOO-HypE, KEOO-MOEA/D, and KEOO-RVEA, for comparative experiments. The comparison results demonstrate the effectiveness of the KEOO in improving these four algorithms in solving cloud workflow scheduling problems.