| Summary: | Decomposition-based evolutionary algorithms, especially the branch based on objective space division using a set of uniformly distributed reference vectors, are widely envisioned as a promising technique to solve many-objective optimization problems. Nevertheless, their performance deteriorates severely when solving problems with irregular Pareto fronts (PFs), such as inverted, degenerated, and discontinuous PF shapes. So far, there are some works trying to design reference vector adjustment approaches to make up for such deficiencies of decomposition-based evolutionary algorithms. Unfortunately, the task of designing effective reference vector adjustment approaches adapting to irregular PFs remains challenging. To tackle this challenge, we propose a Two-Stage Adjustment Strategy, namely TSAS, for space division based many-objective evolutionary optimization to deal with the irregular PFs. To be specific, the first stage attempts to approach the boundaries of objective spaces having solutions by inserting new reference vectors between obtained solutions and reference vectors; for achieving better diversity, the second stage adjusts the reference vectors on the basis of both the reference vectors having solutions and the objective vectors of solutions with better diversity, and also adds some reference vectors to explore the sparse sub-spaces. To verify the effectiveness of the proposed TSAS, extensive experiments on benchmarks are carried out to compare it with five recent representative algorithms using three widely-used metrics. The compared results demonstrate the superior performance of our proposal, especially it significantly outperforms all the five algorithms in 45 out of 65 test instances with respect to Inverted Generational Distance (IGD) metric. Furthermore, to test the performance of TSAS in solving real-world problems, 6 test instances from agile satellite task planning are used to compare its performance with five other algorithms. The experimental results show that the TSAS has the best performance on 5 out of 6 test instances.
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