Different from single-objective evolutionary algorithms, where non-elitism is an established concept, multi-objective evolutionary algorithms almost always select the next population in a greedy fashion. In the only notable exception, Bian, Zhou, Li, and Qian (IJCAI 2023) proposed a stochastic selection mechanism for the SMS-EMOA and proved that it can speed up computing the Pareto front of the bi-objective jump benchmark with problem size $n$ and gap parameter $k$ by a factor of $\max\{1,2^{k/4}/n\}$. While this constitutes the first proven speed-up from non-elitist selection, suggesting a very interesting research direction, it has to be noted that a true speed-up only occurs for $k \ge 4\log_2(n)$, where the runtime is super-polynomial, and that the advantage reduces for larger numbers of objectives as shown in a later work. In this work, we propose a different non-elitist selection mechanism based on aging, which exempts individuals younger than a certain age from a possible removal. This remedies the two shortcomings of stochastic selection: We prove a speed-up by a factor of $\max\{1,Θ(k)^{k-1}\}$, regardless of the number of objectives. In particular, a positive speed-up can already be observed for constant $k$, the only setting for which polynomial runtimes can be witnessed. Overall, this result supports the use of non-elitist selection schemes, but suggests that aging-based mechanisms can be considerably more powerful than stochastic selection mechanisms.

The advent of large language models (LLMs) such as Chat-GPT has attracted considerable attention in various domains due to their remarkable performance and versatility. As the use of these models continues to grow, the importance of effective prompt engineering has come to the fore. Prompt optimization emerges as a crucial challenge, as it has a direct impact on model performance and the extraction of relevant information. Recently, evolutionary algorithms (EAs) have shown promise in addressing this issue, paving the way for novel optimization strategies. In this work, we propose a evolutionary multi-objective (EMO) approach specifically tailored for prompt optimization called EMO-Prompts, using sentiment analysis as a case study. We use sentiment analysis capabilities as our experimental targets. Our results demonstrate that EMO-Prompts effectively generates prompts capable of guiding the LLM to produce texts embodying two conflicting emotions simultaneously.

Optimizing multiple competing objectives is a common problem across science and industry. The inherent inextricable trade-off between those objectives leads one to the task of exploring their Pareto front. A meaningful quantity for the purpose of the latter is the hypervolume indicator, which is used in Bayesian Optimization (BO) and Evolutionary Algorithms (EAs). However, the computational complexity for the calculation of the hypervolume scales unfavorably with an increasing number of objectives and data points, which restricts its use in those common multiobjective optimization frameworks. To overcome these restrictions, previous work has focused on approximating the hypervolume using deep learning. In this work, we propose a novel deep learning architecture to approximate the hypervolume function, which we call DeepHV. For better sample efficiency and generalization, we exploit the fact that the hypervolume is scale equivariant in each of the objectives as well as permutation invariant w.r.t. We show through an ablation study that including these symmetries leads to significantly improved model accuracy. We evaluate our method against exact, and approximate hypervolume methods in terms of accuracy, computation time, and generalization. We also apply and compare our methods to state-of-theart multi-objective BO methods and EAs on a range of synthetic and real-world benchmark test cases. The results show that our methods are promising for such multi-objective optimization tasks. Imagine, while listening to a lecture you also quickly want to check out the latest news on your phone, so you can appear informed during lunch. As an experienced listener, who knows what lecture material is important, and an excellent reader, who knows how to scan over the headlines, you are confident in your abilities in each of those tasks.

Evolutionary algorithms (EAs) have been widely and successfully applied to solve multi-objective optimization problems, due to their nature of population-based search. Population update is a key component in multi-objective EAs (MOEAs), and it is performed in a greedy, deterministic manner. That is, the next-generation population is formed by selecting the first population-size ranked solutions (based on some selection criteria, e.g., non-dominated sorting, crowdedness and indicators) from the collections of the current population and newly-generated solutions. In this paper, we question this practice. We analytically present that introducing randomness into the population update procedure in MOEAs can be beneficial for the search. More specifically, we prove that the expected running time of a well-established MOEA (SMS-EMOA) for solving a commonly studied bi-objective problem, OneJumpZeroJump, can be exponentially decreased if replacing its deterministic population update mechanism by a stochastic one. Empirical studies also verify the effectiveness of the proposed stochastic population update method. This work is an attempt to challenge a common practice for the population update in MOEAs. Its positive results, which might hold more generally, should encourage the exploration of developing new MOEAs in the area.