Neural Evolution Strategy for Black-box Pareto Set Learning

From Pareto to Neural: A Mathematical Survey of Multi-Objective Optimization Algorithms—With Applications to Software Testing

A systematic mapping study of multi-objective optimization algorithms, tracing their evolution from classical Pareto-based methods toward AI-driven and hybrid approaches, with software testing as the primary application domain, and outlining a research roadmap for the next generation of multi-objective optimization systems that combine the complementary mathematical strengths of neural function approximation and evolutionary diversity preservation.

RLDMGO: a reinforcement learning-driven hybrid framework for complex optimization problems

LLM-Enhanced Adaptive MOEA/D for Solving Multiobjective Problems with Complex Pareto Fronts

Adaptively adjusting the components or parameters of decomposition-based multiobjective evolutionary algorithms (MOEA/Ds) is crucial for enhancing its performance in handling multiobjective optimization problems with complex Pareto fronts. However, component design strategies and parameter tuning mechanisms based on domain knowledge remain the primary bottleneck limiting performance improvement. This paper proposes a large language model (LLM)-enhanced MOEA/D algorithm. The algorithm leverages LLM’s domain priors and prompt engineering techniques to automatically generate modular code, replacing manually designed search operators. Furthermore, by reasoning about the algorithm’s iterative process information, it achieves adaptive dynamic adjustments of the aggregation function, weight strategy, and parameter rules. Experimental results on 12 benchmark test instances with complex Pareto fronts demonstrate that the proposed LLM-driven MOEA/D variant exhibits significant advantages over traditional methods in the HV performance metric.

Common Pitfalls to Avoid While Using Multiobjective Optimization in Machine Learning

Abstract. Recently, there has been increasing interest in the application of multiobjective optimization (MOO) in machine learning (ML). This interest is driven by the numerous real-life situations in which multiple objectives must be optimized simultaneously. A key aspect of MOO is the existence of a Pareto set, rather than a single optimal solution, which represents the optimal trade-offs between different objectives. Despite its potential, there is a noticeable lack of satisfactory literature serving as an entry-level guide for ML practitioners aiming to apply MOO effectively. In this paper, our goal is to provide such a resource and highlight pitfalls to avoid. We begin by establishing the groundwork for MOO, focusing on well-known approaches such as the weighted sum (WS) method alongside more advanced techniques like the multiobjective gradient descent algorithm (MGDA). We critically review existing studies across various ML fields in which MOO has been applied and identify challenges that can lead to incorrect interpretations. One of these fields is physics informed neural networks (PINNs), which we use as a guiding example to carefully construct experiments illustrating these pitfalls. By comparing WS and MGDA with one of the most common evolutionary algorithms, NSGA-II, we demonstrate that difficulties can arise regardless of the specific MOO method used. We emphasize the importance of understanding the specific problem, the objective space, and the selected MOO method, while also noting that the neglect of factors such as convergence criteria can result in misleading experiments.

A general hybrid framework for many-objective optimization: integrating local search into reference-vector-based evolutionary algorithms

Results show that integrating local search significantly enhances performance, while a principled method for setting hybrid parameters ensures robustness and reproducibility, highlighting the potential of combining mathematical programming techniques with evolutionary algorithms for high-dimensional many-objective optimization problems.

LLMDE: A Large Language Model-Driven Differential Evolution Algorithm for Portfolio Optimization

This study proposes a Large Language Model-Driven Differential Evolution (LLMDE) algorithm to reduce the reliance on handcrafted hyperparameter design. The proposed algorithm leverages a prompt engineering strategy, allowing large language models (LLMs) to dynamically select mutation strategies and configure control parameters guided by optimization feedback, thus enhancing the performance of the DE algorithm. We evaluate the performance of LLMDE on the CEC2022 benchmark suite, comparing it with standard DE and representative metaheuristics. Furthermore, we employ factor analysis and K-means clustering for stock selection, and then apply LLMDE to solve the Conditional Value at Risk (CVaR) portfolio optimization problem using the selected stocks, subject to budget and minimum expected return constraints. Experimental results demonstrate that LLMDE achieves competitive performance on the benchmark suite while continuously generating high-quality solutions for complex constrained optimization tasks. These outcomes successfully demonstrate the viability of embedding LLMs within metaheuristics, paving a promising path toward the design of advanced LLM-assisted optimization techniques.