A Controlled Strengthened Dominance Relation for Evolutionary Many-Objective Optimization

Shen, Jiangtao; Wang, Peng; Wang, Xinjing

doi:10.1109/tcyb.2020.3015998

Cited by 35 publications

(14 citation statements)

References 53 publications

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“…In [24,25], the modified dominance relationships, namely SDR and CSDR, are employed in the environmental selection, in addition to the mating selection. However, in the current work, the environmental selection is based on traditional Pareto dominance so that the environmental selection process is not biased to any section of the PF.…”

Section: Environmental Selectionmentioning

confidence: 99%

“…However, in SDR there is a possibility that some dominated solutions may be considered as non-dominated. To overcome this, a modification to SDR referred to as the controlled strengthened dominance relation (CSDR) was proposed in [25], where SDR is combined with traditional Pareto dominance. In addition, CSDR introduces two parameters k and a into convergence degree and niche size, to control the dominance area and to be adapted based on the generation count.…”

Section: Introductionmentioning

confidence: 99%

“…On the other hand, for 0 < k < 1, corner solutions (B) away from the centre of objective space have a better convergence degree. Based on the observation in [25], it can be concluded that (1) larger values of k enhance the convergence pressure, and (2) small values of k enhance diversity.…”

mentioning

confidence: 99%

“…However, the lower and the upper bounds of a niche have to be restricted. In [25], it is justified that the values around 50 would be better, mostly a range from 40 to 60. This is based on the intuition that the environmental selection consistently chooses half of the combined population acquired at each generation in the majority of current MOEAs, the target of adapting 𝜃 is to guarantee that the ratio of the non-dominated solutions in a given candidate set is around 0.5.…”

mentioning

confidence: 99%

“…where k max and a max are predefined initial values, ∆k and ∆a are the variations of k and a, respectively, and t max is the maximum number of generations. The parameter settings are detailed in [25]. The decrease of parameters k and a with respect to the generation count is based on the notion that dynamic dominance relations would improve the performance of MOEAs.…”

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confidence: 99%

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A Mating Selection Based on Modified Strengthened Dominance Relation for NSGA-III

Dutta

Mallipeddi

et al. 2021

Mathematics

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In multi/many-objective evolutionary algorithms (MOEAs), to alleviate the degraded convergence pressure of Pareto dominance with the increase in the number of objectives, numerous modified dominance relationships were proposed. Recently, the strengthened dominance relation (SDR) has been proposed, where the dominance area of a solution is determined by convergence degree and niche size (θ¯). Later, in controlled SDR (CSDR), θ¯ and an additional parameter (k) associated with the convergence degree are dynamically adjusted depending on the iteration count. Depending on the problem characteristics and the distribution of the current population, different situations require different values of k, rendering the linear reduction of k based on the generation count ineffective. This is because a particular value of k is expected to bias the dominance relationship towards a particular region on the Pareto front (PF). In addition, due to the same reason, using SDR or CSDR in the environmental selection cannot preserve the diversity of solutions required to cover the entire PF. Therefore, we propose an MOEA, referred to as NSGA-III*, where (1) a modified SDR (MSDR)-based mating selection with an adaptive ensemble of parameter k would prioritize parents from specific sections of the PF depending on k, and (2) the traditional weight vector and non-dominated sorting-based environmental selection of NSGA-III would protect the solutions corresponding to the entire PF. The performance of NSGA-III* is favourably compared with state-of-the-art MOEAs on DTLZ and WFG test suites with up to 10 objectives.

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Section: Environmental Selectionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A Mating Selection Based on Modified Strengthened Dominance Relation for NSGA-III

Dutta

Mallipeddi

et al. 2021

Mathematics

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Distributed cooperative neural control of a class of nonlinear multi‐agent systems with unknown time‐varying control coefficient

Wang

2021

Adaptive Control & Signal

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This article studies the leader-follower cooperative tracking problem of a class of multi-agent systems with unknown nonlinear dynamics. As the load of the following agent may be changing throughout the whole work process, we consider the control coefficient of the following agent to be time-varying and nonlinear instead of constant, which is more practical. All agents are connected by the directed communication graph with weighted topology. The followers can have unknown nonidentical nonlinear dynamics and external disturbances. The nonautonomous leader generates the reference trajectory for only part of the followers and others can only receive the information from their neighbors. To achieve the ultimate synchronization of all following agents to the leader, the novel cooperative adaptive control protocols are designed based on the neural approximation and adaptive updating mechanism. A novel singularity-avoided adaptive updating law is proposed to estimate the control coefficient and compensate for the unknown dynamics online. Lyapunov theory is used to prove the ultimate boundedness of the synchronization tracking error. The correctness and effectiveness of the presented control scheme are demonstrated by two simulations in SISO and MIMO cases, respectively.

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Evolutionary Many‐objective Optimization: Difficulties, Approaches, and Discussions

Satō

Ishibuchi

2023

IEEJ Transactions Elec Engng

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Population‐based evolutionary algorithms are suitable for solving multi‐objective optimization problems involving multiple conflicting objectives. This is because a set of well‐distributed solutions can be obtained by a single run, which approximate the optimal tradeoff among the objectives. Over the past three decades, evolutionary multi‐objective optimization has been intensively studied and used in various real‐world applications. However, evolutionary multi‐objective optimization faces various difficulties as the number of objectives increases. The simultaneous optimization of more than three objectives, which is called many‐objective optimization, has attracted considerable research attention. This paper explains various difficulties in evolutionary many‐objective optimization, reviews representative approaches, and discusses their effects and limitations. © 2023 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC.

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A Controlled Strengthened Dominance Relation for Evolutionary Many-Objective Optimization

Cited by 35 publications

References 53 publications

A Mating Selection Based on Modified Strengthened Dominance Relation for NSGA-III

A Mating Selection Based on Modified Strengthened Dominance Relation for NSGA-III

Distributed cooperative neural control of a class of nonlinear multi‐agent systems with unknown time‐varying control coefficient

Evolutionary Many‐objective Optimization: Difficulties, Approaches, and Discussions

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