Multiobjective evolutionary algorithms (MOEAs) are major methods for solving
multiobjective optimization problems (MOPs). Many MOEAs have been proposed in
the past decades, of which the operators need carefully handcrafted design with
domain knowledge. Recently, some attempts have been made to replace the
manually designed operators in MOEAs with learning-based operators (e.g.,
neural network models). However, much effort is still required for designing
and training such models, and the learned operators might not generalize well
to solve new problems. To tackle the above challenges, this work investigates a
novel approach that leverages the powerful large language model (LLM) to design
MOEA operators. With proper prompt engineering, we successfully let a general
LLM serve as a black-box search operator for decomposition-based MOEA (MOEA/D)
in a zero-shot manner. In addition, by learning from the LLM behavior, we
further design an explicit white-box operator with randomness and propose a new
version of decomposition-based MOEA, termed MOEA/D-LO. Experimental studies on
different test benchmarks show that our proposed method can achieve competitive
performance with widely used MOEAs. It is also promising to see the operator
only learned from a few instances can have robust generalization performance on
unseen problems with quite different patterns and settings. The results reveal
the potential benefits of using pre-trained LLMs in the design of MOEAs.

使用预训练的大型语言模型（LLM）设计的多目标进化算法（MOEA）运算符显示出潜在的优势，并能在不同模式和设置下具有稳健的泛化性能。

大型语言模型用于多目标进化优化

Large Language Model for Multi-objective Evolutionary Optimization

The performance of multiobjective evolutionary algorithms (MOEAs) varies
across problems, making it hard to develop new algorithms or apply existing
ones to new problems. To simplify the development and application of new
multiobjective algorithms, there has been an increasing interest in their
automatic design from their components. These automatically designed
metaheuristics can outperform their human-developed counterparts. However, it
is still unknown what are the most influential components that lead to
performance improvements. This study specifies a new methodology to investigate
the effects of the final configuration of an automatically designed algorithm.
We apply this methodology to a tuned Multiobjective Evolutionary Algorithm
based on Decomposition (MOEA/D) designed by the iterated racing (irace)
configuration package on constrained problems of 3 groups: (1) analytical
real-world problems, (2) analytical artificial problems and (3) simulated
real-world. We then compare the impact of the algorithm components in terms of
their Search Trajectory Networks (STNs), the diversity of the population, and
the anytime hypervolume values. Looking at the objective space behavior, the
MOEAs studied converged before half of the search to generally good HV values
in the analytical artificial problems and the analytical real-world problems.
For the simulated problems, the HV values are still improving at the end of the
run. In terms of decision space behavior, we see a diverse set of the
trajectories of the STNs in the analytical artificial problems. These
trajectories are more similar and frequently reach optimal solutions in the
other problems.

研究使用自动设计的算法对多目标进化算法进行了效果评估，通过比较搜索轨迹网络、种群的多样性和任意时刻的超体积值，发现算法组件对于不同问题具有不同的影响。

多目标进化算法中组件效应对算法行为的影响

Multiobjective Evolutionary Component Effect on Algorithm behavior

Recent decades have witnessed great advancements in multiobjective
evolutionary algorithms (MOEAs) for multiobjective optimization problems
(MOPs). However, these progressively improved MOEAs have not necessarily been
equipped with scalable and learnable problem-solving strategies for new and
grand challenges brought by the scaling-up MOPs with continuously increasing
complexity from diverse aspects, mainly including expensive cost of function
evaluations, many objectives, large-scale search space, time-varying
environments, and multi-task. Under different scenarios, divergent thinking is
required in designing new powerful MOEAs for solving them effectively. In this
context, research studies on learnable MOEAs with machine learning techniques
have received extensive attention in the field of evolutionary computation.
This paper begins with a general taxonomy of scaling-up MOPs and learnable
MOEAs, followed by an analysis of the challenges that these MOPs pose to
traditional MOEAs. Then, we synthetically overview recent advances of learnable
MOEAs in solving various scaling-up MOPs, focusing primarily on four attractive
directions (i.e., learnable evolutionary discriminators for environmental
selection, learnable evolutionary generators for reproduction, learnable
evolutionary evaluators for function evaluations, and learnable evolutionary
transfer modules for sharing or reusing optimization experience). The insight
of learnable MOEAs is offered to readers as a reference to the general track of
the efforts in this field.

本研究论文总结了最近学习型多目标进化算法在解决不同尺度多目标优化问题中的进展和挑战，并提供了四个有吸引力的方向，即用于环境选择的可学习进化鉴别器，用于繁殖的可学习进化生成器，用于函数评估的可学习进化评估器，以及用于共享或重复使用优化经验的可学习进化传输模块，作为这一领域的努力的参考。

可学习演化算法在可扩展多目标优化中的调查

A Survey on Learnable Evolutionary Algorithms for Scalable Multiobjective Optimization

Understanding the search dynamics of multiobjective evolutionary algorithms
(MOEAs) is still an open problem. This paper extends a recent network-based
tool, search trajectory networks (STNs), to model the behavior of MOEAs. Our
approach uses the idea of decomposition, where a multiobjective problem is
transformed into several single-objective problems. We show that STNs can be
used to model and distinguish the search behavior of two popular multiobjective
algorithms, MOEA/D and NSGA-II, using 10 continuous benchmark problems with 2
and 3 objectives. Our findings suggest that we can improve our understanding of
MOEAs using STNs for algorithm analysis.

本文研究多目标进化算法（MOEAs）的搜索动态，并将 STN 模型应用于两种常用算法（MOEA/D 和 NSGA-II）的分析，结果表明我们可以通过 STNs 来提高 MOEA 的算法分析。