CausalBench: A Comprehensive Benchmark for Causal Learning Capability of Large Language Models

Causality reveals fundamental principles behind data distributions in real-world scenarios, and the capability of large language models (LLMs) to understand causality directly impacts their efficacy across explaining outputs, adapting to new evidence, and generating counterfactuals. With the proliferation of LLMs, the evaluation of this capacity is increasingly garnering attention. However, the absence of a comprehensive benchmark has rendered existing evaluation studies being straightforward, undiversified, and homogeneous. To address these challenges, this paper proposes a comprehensive benchmark, namely CausalBench, to evaluate the causality understanding capabilities of LLMs. Originating from the causal research community, CausalBench encompasses three causal learning-related tasks, which facilitate a convenient comparison of LLMs' performance with classic causal learning algorithms. Meanwhile, causal networks of varying scales and densities are integrated in CausalBench, to explore the upper limits of LLMs' capabilities across task scenarios of varying difficulty. Notably, background knowledge and structured data are also incorporated into CausalBench to thoroughly unlock the underlying potential of LLMs for long-text comprehension and prior information utilization. Based on CausalBench, this paper evaluates nineteen leading LLMs and unveils insightful conclusions in diverse aspects. Firstly, we present the strengths and weaknesses of LLMs and quantitatively explore the upper limits of their capabilities across various scenarios. Meanwhile, we further discern the adaptability and abilities of LLMs to specific structural networks and complex chain of thought structures. Moreover, this paper quantitatively presents the differences across diverse information sources and uncovers the gap between LLMs' capabilities in causal understanding within textual contexts and numerical domains.

Exploring the True Potential: Evaluating the Black-box Optimization Capability of Large Language Models

Large language models (LLMs) have gained widespread popularity and demonstrated exceptional performance not only in natural language processing (NLP) tasks but also in non-linguistic domains. Their potential as artificial general intelligence extends beyond NLP, showcasing promising capabilities in diverse optimization scenarios. Despite this rising trend, whether the integration of LLMs into these black-box optimization problems is genuinely beneficial remains unexplored. This paper endeavors to tackle this issue by offering deeper insights into the potential of LLMs in optimization tasks through a comprehensive investigation. Our approach involves a comprehensive evaluation, covering both discrete and continuous optimization problems, aiming to assess the efficacy and distinctive characteristics that LLMs bring to the realm of optimization. Our findings reveal both the limitations and advantages of LLMs in optimization. On one hand, despite consuming the significant power required to run the model, LLMs exhibit subpar performance and lack desirable properties in pure numerical tasks, primarily due to a mismatch between the problem domain and their processing capabilities. On the other hand, although LLMs may not be ideal for traditional numerical optimization, their potential in broader optimization contexts remains promising. LLMs exhibit the ability to solve problems in non-numerical domains and can leverage heuristics from the prompt to enhance their performance. To the best of our knowledge, this work presents the first systematic evaluation of LLMs for numerical optimization, offering a progressive, wide-coverage, and behavioral analysis. Our findings pave the way for a deeper understanding of LLMs' role in optimization and guide future application in diverse scenarios for LLMs.

How Multimodal Integration Boost the Performance of LLM for Optimization: Case Study on Capacitated Vehicle Routing Problems

Recently, large language models (LLMs) have notably positioned them as capable tools for addressing complex optimization challenges. Despite this recognition, a predominant limitation of existing LLM-based optimization methods is their struggle to capture the relationships among decision variables when relying exclusively on numerical text prompts, especially in high-dimensional problems. Keeping this in mind, we first propose to enhance the optimization performance using multimodal LLM capable of processing both textual and visual prompts for deeper insights of the processed optimization problem. This integration allows for a more comprehensive understanding of optimization problems, akin to human cognitive processes. We have developed a multimodal LLM-based optimization framework that simulates human problem-solving workflows, thereby offering a more nuanced and effective analysis. The efficacy of this method is evaluated through extensive empirical studies focused on a well-known combinatorial optimization problem, i.e., capacitated vehicle routing problem. The results are compared against those obtained from the LLM-based optimization algorithms that rely solely on textual prompts, demonstrating the significant advantages of our multimodal approach.

Evolutionary Computation in the Era of Large Language Model: Survey and Roadmap

Large Language Models (LLMs), built upon Transformer-based architectures with massive pretraining on diverse data, have not only revolutionized natural language processing but also extended their prowess to various domains, marking a significant stride towards artificial general intelligence. The interplay between LLMs and Evolutionary Algorithms (EAs), despite differing in objectives and methodologies, reveals intriguing parallels, especially in their shared optimization nature, black-box characteristics, and proficiency in handling complex problems. Meanwhile, EA can not only provide an optimization framework for LLM's further enhancement under black-box settings but also empower LLM with flexible global search and iterative mechanism in applications. On the other hand, LLM's abundant domain knowledge enables EA to perform smarter searches, while its text processing capability assist in deploying EA across various tasks. Based on their complementary advantages, this paper presents a comprehensive review and forward-looking roadmap, categorizing their mutual inspiration into LLM-enhanced evolutionary optimization and EA-enhanced LLM. Some integrated synergy methods are further introduced to exemplify the amalgamation of LLMs and EAs in various application scenarios, including neural architecture search, code generation, software engineering, and text generation. As the first comprehensive review specifically focused on the EA research in the era of LLMs, this paper provides a foundational stepping stone for understanding and harnessing the collaborative potential of LLMs and EAs. By presenting a comprehensive review, categorization, and critical analysis, we contribute to the ongoing discourse on the cross-disciplinary study of these two powerful paradigms. The identified challenges and future directions offer guidance to unlock the full potential of this innovative collaboration.

Towards Multi-Objective High-Dimensional Feature Selection via Evolutionary Multitasking

Evolutionary Multitasking (EMT) paradigm, an emerging research topic in evolutionary computation, has been successfully applied in solving high-dimensional feature selection (FS) problems recently. However, existing EMT-based FS methods suffer from several limitations, such as a single mode of multitask generation, conducting the same generic evolutionary search for all tasks, relying on implicit transfer mechanisms through sole solution encodings, and employing single-objective transformation, which result in inadequate knowledge acquisition, exploitation, and transfer. To this end, this paper develops a novel EMT framework for multiobjective high-dimensional feature selection problems, namely MO-FSEMT. In particular, multiple auxiliary tasks are constructed by distinct formulation methods to provide diverse search spaces and information representations and then simultaneously addressed with the original task through a multi-slover-based multitask optimization scheme. Each task has an independent population with task-specific representations and is solved using separate evolutionary solvers with different biases and search preferences. A task-specific knowledge transfer mechanism is designed to leverage the advantage information of each task, enabling the discovery and effective transmission of high-quality solutions during the search process. Comprehensive experimental results demonstrate that our MO-FSEMT framework can achieve overall superior performance compared to the state-of-the-art FS methods on 26 datasets. Moreover, the ablation studies verify the contributions of different components of the proposed MO-FSEMT.

Solving Expensive Optimization Problems in Dynamic Environments with Meta-learning

Dynamic environments pose great challenges for expensive optimization problems, as the objective functions of these problems change over time and thus require remarkable computational resources to track the optimal solutions. Although data-driven evolutionary optimization and Bayesian optimization (BO) approaches have shown promise in solving expensive optimization problems in static environments, the attempts to develop such approaches in dynamic environments remain rarely unexplored. In this paper, we propose a simple yet effective meta-learning-based optimization framework for solving expensive dynamic optimization problems. This framework is flexible, allowing any off-the-shelf continuously differentiable surrogate model to be used in a plug-in manner, either in data-driven evolutionary optimization or BO approaches. In particular, the framework consists of two unique components: 1) the meta-learning component, in which a gradient-based meta-learning approach is adopted to learn experience (effective model parameters) across different dynamics along the optimization process. 2) the adaptation component, where the learned experience (model parameters) is used as the initial parameters for fast adaptation in the dynamic environment based on few shot samples. By doing so, the optimization process is able to quickly initiate the search in a new environment within a strictly restricted computational budget. Experiments demonstrate the effectiveness of the proposed algorithm framework compared to several state-of-the-art algorithms on common benchmark test problems under different dynamic characteristics.

A Scalable Test Problem Generator for Sequential Transfer Optimization

Sequential transfer optimization (STO), which aims to improve optimization performance by exploiting knowledge captured from previously-solved optimization tasks stored in a database, has been gaining increasing research attention in recent years. However, despite significant advancements in algorithm design, the test problems in STO are not well designed. Oftentimes, they are either randomly assembled by other benchmark functions that have identical optima or are generated from practical problems that exhibit limited variations. The relationships between the optimal solutions of source and target tasks in these problems are manually configured and thus monotonous, limiting their ability to represent the diverse relationships of real-world problems. Consequently, the promising results achieved by many algorithms on these problems are highly biased and difficult to be generalized to other problems. In light of this, we first introduce a few rudimentary concepts for characterizing STO problems (STOPs) and present an important problem feature overlooked in previous studies, namely similarity distribution, which quantitatively delineates the relationship between the optima of source and target tasks. Then, we propose general design guidelines and a problem generator with superior extendibility. Specifically, the similarity distribution of a problem can be systematically customized by modifying a parameterized density function, enabling a broad spectrum of representation for the diverse similarity relationships of real-world problems. Lastly, a benchmark suite with 12 individual STOPs is developed using the proposed generator, which can serve as an arena for comparing different STO algorithms. The source code of the benchmark suite is available at https://github.com/XmingHsueh/STOP.

Balancing Exploration and Exploitation for Solving Large-scale Multiobjective Optimization via Attention Mechanism

Large-scale multiobjective optimization problems (LSMOPs) refer to optimization problems with multiple conflicting optimization objectives and hundreds or even thousands of decision variables. A key point in solving LSMOPs is how to balance exploration and exploitation so that the algorithm can search in a huge decision space efficiently. Large-scale multiobjective evolutionary algorithms consider the balance between exploration and exploitation from the individual's perspective. However, these algorithms ignore the significance of tackling this issue from the perspective of decision variables, which makes the algorithm lack the ability to search from different dimensions and limits the performance of the algorithm. In this paper, we propose a large-scale multiobjective optimization algorithm based on the attention mechanism, called (LMOAM). The attention mechanism will assign a unique weight to each decision variable, and LMOAM will use this weight to strike a balance between exploration and exploitation from the decision variable level. Nine different sets of LSMOP benchmarks are conducted to verify the algorithm proposed in this paper, and the experimental results validate the effectiveness of our design.

Multi-Space Evolutionary Search for Large-Scale Optimization

In recent years, to improve the evolutionary algorithms used to solve optimization problems involving a large number of decision variables, many attempts have been made to simplify the problem solution space of a given problem for the evolutionary search. In the literature, the existing approaches can generally be categorized as decomposition-based methods and dimension-reduction-based methods. The former decomposes a large-scale problem into several smaller subproblems, while the latter transforms the original high-dimensional solution space into a low-dimensional space. However, it is worth noting that a given large-scale optimization problem may not always be decomposable, and it is also difficult to guarantee that the global optimum of the original problem is preserved in the reduced low-dimensional problem space. This paper thus proposes a new search paradigm, namely the multi-space evolutionary search, to enhance the existing evolutionary search methods for solving large-scale optimization problems. In contrast to existing approaches that perform an evolutionary search in a single search space, the proposed paradigm is designed to conduct a search in multiple solution spaces that are derived from the given problem, each possessing a unique landscape. The proposed paradigm makes no assumptions about the large-scale optimization problem of interest, such as that the problem is decomposable or that a certain relationship exists among the decision variables. To verify the efficacy of the proposed paradigm, comprehensive empirical studies in comparison to four state-of-the-art algorithms were conducted using the CEC2013 large-scale benchmark problems.