Analysis of two variants of the Generalized Differential Evolution algo- rithm with ordered mutation for real world engineering multi-objective optimization problems

Resumo

Differential Evolution (DE) is one of the most powerful commonly used metaheuristics for global multi-
objective optimization. New strategies to improve the DE’s performance are an important and attractive research

study. The third Evolution Step of Generalized Differential Evolution (GDE3) is a widely used DE-based multi-
objective evolutionary algorithm in the literature, especially in real-world multi-objective optimization problems

with two or three conflicting objectives in its formulation. GDE3 uses the most popular mutation strategy of the DE,
DE/rand/1, which randomly selects three candidate solutions from the population without considering any order.
The fourth version of the Generalized Differential Evolution (GDE4) was recently proposed, which presents an
ordered mutation operator based on two well-known schemes: Non-dominated Ranking and Crowding Distance.
Previous studies have shown that GDE4 outperforms GDE3 on a set of many-objective optimization problems.
In this paper, the second version of GDE4 is proposed, GDE4-II, considering a local ordering among the three
randomly selected individuals instead of the entire population as GDE4. Besides, experiments are conducted to
evaluate the performance of the two GDE4 variants in benchmark and engineering multi-objective optimization
problems with two and three objective functions. Metrics such as Hypervolume and Inverted Generational Distance
plus (IGD+) combined with performance profiles are used to point out the robustness of the GDE4 and GDE4-II.