Abstract
Multiobjective evolutionary algorithms (MOEAs) have witnessed prosperity in solving many-objective optimization problems (MaOPs) over the past three decades. Unfortunately, no one single MOEA equipped with given parameter settings, mating-variation operator, and environmental selection mechanism is suitable for obtaining a set of solutions with excellent convergence and diversity for various types of MaOPs. The reality is that different MOEAs show great differences in handling certain types of MaOPs. Aiming at these characteristics, this paper proposes a flexible ensemble framework, namely, ASES, which is highly scalable for embedding any number of MOEAs to promote their advantages. To alleviate the undesirable phenomenon that some promising solutions are discarded during the evolution process, a big archive that number of contained solutions be far larger than population size is integrated into this ensemble framework to record large-scale nondominated solutions, and also an efficient maintenance strategy is developed to update the archive. Furthermore, the knowledge coming from updating archive is exploited to guide the evolutionary process for different MOEAs, allocating limited computational resources for efficient algorithms. A large number of numerical experimental studies demonstrated superior performance of the proposed ASES. Among 52 test instances, the ASES performs better than all the six baseline algorithms on at least half of the test instances with respect to both metrics hypervolume and inverted generational distance.
Highlights
No one single Multiobjective evolutionary algorithms (MOEAs) equipped with given parameter settings, mating and variation operators, and environmental selection mechanism is suitable for obtaining a set of solutions with excellent convergence and diversity for various types of many-objective optimization problems (MaOPs). e reality is that different MOEAs show great differences in handling certain types of MaOPs. e analyses in [29, 30] demonstrate that
The seven MaOEAs, i.e., RVEA, VaEA, SPEA2 + SDE, NSGA-III, MOEA/DD, MOEA/D-AM2M, and ASES, are repeated 31 times on all the test instances, and the mean and variance of inverted generational distance (IGD) and HV values are reported in Tables 1 and 2
Work is paper focuses on the issue that no one single MOEA is suitable for solving various types of MaOPs
Summary
In real-world applications, various kinds of optimization problems [1,2,3] have multiple conflicting objectives, such as design hybrid renewable energy systems [4], resource management for intelligent traffic [5, 6], optimization of wireless networks [7, 8], resource allocation for radar system [9, 10], and workflow scheduling in distributed environments [11]. On the basis of their environment selection mechanisms, these existing works generally fall into the following three categories: decomposition-based, indicator-based, and dominance relation-based MOEAs [18,19,20]. To achieve better overall performance in solving a diverse range of MaOPs, up to present, there exist some works devoted to combining strengths of different MOEAs via ensemble of multiple mating operators, variation operators, or environmental selection strategies. An adaptive strategy is proposed to online reward competitive mating and variation operators to generate more offspring solutions, such combining their advantages for solving various MOPs. ree representative algorithms (i.e., RVEA [15], VaEA [35], and SPEA2+SDE [28]) are selected to realize a prototype for the proposed framework.
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