The integration of Large Language Models (LLMs) into optimization has created a powerful synergy, opening exciting research opportunities.This paper investigates how LLMs can enhance existing optimization algorithms.Using their pre-trained knowledge, we demonstrate their ability to propose innovative heuristic variations based on a semantic understanding of the algorithm's components.To evaluate this, we applied a nontrivial optimization algorithm, Construct, Merge, Solve & Adapt (CMSA)-a hybrid metaheuristic for combinatorial optimization problems that incorporates a heuristic in the solution construction phase.Our results show that an alternative heuristic proposed by GPT-4o outperforms the expert-designed heuristic of CMSA, with the performance gap widening on larger and denser graphs.

Search Trajectory Networks (STNs) serve as a tool for visualizing algorithm behavior within the realm of optimization problems. Despite their user-friendly nature, challenges arise in obtaining interpretable plots, for example, in the case of optimization problems with large solutions or many dimensions. To address this, we have introduced a new search space partitioning strategy utilizing hierarchical agglomerative clustering. This enhanced strategy, now available in STNWeb, the web version of STNs, produces plots that are easier to interpret than those produced by existing search space partitioning strategies. This facilitates an improved understanding of algorithm performance in complex scenarios.

The ability of Large Language Models (LLMs) to generate high-quality text and code has fuelled their rise in popularity. In this paper, we aim to demonstrate the potential of LLMs within the realm of optimization algorithms by integrating them into STNWeb. This is a web-based tool for the generation of Search Trajectory Networks (STNs), which are visualizations of optimization algorithm behavior. Although visualizations produced by STNWeb can be very informative for algorithm designers, they often require a certain level of prior knowledge to be interpreted. In an attempt to bridge this knowledge gap, we have incorporated LLMs, specifically GPT-4, into STNWeb to produce extensive written reports, complemented by automatically generated plots, thereby enhancing the user experience and reducing the barriers to the adoption of this tool by the research community. Moreover, our approach can be expanded to other tools from the optimization community, showcasing the versatility and potential of LLMs in this field.

The use of machine learning techniques within metaheuristics is a rapidly growing field of research. In this paper, we show how a deep learning framework can be beneficially used to improve an ant colony optimization algorithm. In particular, problem information obtained via deep learning is combined in our algorithm by means of Q-learning with the usual pheromone and greedy information. Our algorithm is applied to the Target Set Selection (TSS) problem, which is an NP-hard combinatorial optimization problem with applications, for example, in social networks. The specific problem variant considered in this paper asks for finding a smallest subset of the nodes of a given graph such that their influence can be spread to all other nodes of the graph via a diffusion process. The experimental results show, first, that the pure ant colony optimization approach can already compete with the state of the art. Second, the obtained results indicate that the hybrid algorithm variant outperforms the pure ant colony optimization approach especially in the context of large problem instances.

In this paper we solve a variant of the multi-hop influence maximization problem in social networks by means of a hybrid algorithm that combines a biased random key genetic algorithm with a graph neural network.Hereby, the predictions of the graph neural network are used with the biased random key genetic algorithm for a more accurate translation of individuals into valid solutions to the tackled problem.The obtained results show that the hybrid algorithm is able to outperform both the biased random key genetic algorithm and the graph neural network when used as standalone techniques.In other words, we were able to show that an integration of both techniques leads to a better algorithm.