Automatic Design of Efficient Guided Local Search Algorithms Using Evolutionary Computation and Large Language Models

Belangrijkste concepten

The proposed AEL framework combines the power of evolutionary computation and large language models to automatically design highly competitive guided local search algorithms for solving the traveling salesman problem, outperforming human-designed algorithms.

Samenvatting

The paper presents a novel framework called Algorithm Evolution using Large Language Model (AEL) that combines evolutionary computation and large language models to enable automatic algorithm design. The authors demonstrate the effectiveness of this approach by using AEL to design an efficient guided local search (GLS) algorithm for solving the traveling salesman problem (TSP).
The key highlights are:

The AEL framework maintains a population of algorithms and utilizes evolutionary operations like crossover and mutation, facilitated by large language models, to automatically evolve new algorithms.

The evolved GLS algorithm, named AEL-GLS, is evaluated on 1,000 randomly generated TSP instances of sizes 20, 50, and 100, as well as 29 instances from the TSPLib benchmark.

The results show that AEL-GLS outperforms state-of-the-art human-designed GLS algorithms, achieving a 0% gap on TSP20 and TSP50 instances, and a 0.032% gap on TSP100 instances, all within 1,000 iterations.

Compared to recent deep learning-based solvers, AEL-GLS demonstrates superior generalization, as the algorithm evolved on TSP100 instances can be directly applied to smaller problem sizes without retraining.

The entire algorithm evolution process takes only two days, with minimal human effort and no model training required, highlighting the potential of the AEL framework to usher in a new era of automatic algorithm design.

Statistieken

The average gap (%) to the optimal solution obtained by the Concorde solver on the test instances:

TSP20: 0.0%
TSP50: 0.0%
TSP100: 0.032%

Citaten

"In just two days, the GLS algorithm evolved by AEL achieved superior performance compared to human-designed GLS algorithms and many other algorithms developed over the past decades."
"The results demonstrate that the algorithm generated through AEL surpasses the manually crafted ones, achieving a 0% gap on TSP20 and TSP50, and a 0.032% gap on TSP100 in 1,000 iterations."

Belangrijkste Inzichten Gedestilleerd Uit

Evolution of Heuristics: Towards Efficient Automatic Algorithm Design Using Large Language Mode

by Fei Liu,Xial... om arxiv.org 05-02-2024

https://arxiv.org/pdf/2401.02051.pdf

Diepere vragen

How can the AEL framework be extended to design algorithms for other combinatorial optimization problems beyond the traveling salesman problem?

The AEL framework can be extended to design algorithms for other combinatorial optimization problems by following a similar workflow but tailoring it to the specific characteristics of each problem. Here are some steps to extend the AEL framework:

Problem Understanding: Understand the specific requirements and constraints of the new optimization problem. Define the objective function and the search space.

Algorithm Representation: Define how the algorithms will be represented in the AEL framework. This includes the algorithm description, code block, and fitness value specific to the new problem.

Prompt Engineering: Create prompts that guide the large language model in generating new algorithms for the specific optimization problem. These prompts should be tailored to the problem's characteristics and requirements.

Algorithm Evolution: Implement the evolutionary computation process within the AEL framework, incorporating the large language model to evolve algorithms automatically. Ensure that the evolution process is optimized for the new problem domain.

Evaluation and Validation: Evaluate the evolved algorithms on a diverse set of instances for the new optimization problem. Compare the performance of the AEL-designed algorithms with existing algorithms and benchmarks.

Iterative Improvement: Continuously refine the AEL framework based on the performance feedback from different optimization problems. Incorporate learnings from each problem domain to enhance the algorithm design process for future problems.

By following these steps and customizing the AEL framework for each specific combinatorial optimization problem, researchers can effectively extend the framework to design algorithms for a wide range of optimization problems beyond the traveling salesman problem.

How can the insights from the automatic algorithm design process be used to inspire new human-designed heuristics or guide further research in optimization algorithms?

The insights gained from the automatic algorithm design process using the AEL framework can be valuable in inspiring new human-designed heuristics and guiding further research in optimization algorithms in the following ways:

Algorithmic Innovations: Analyzing the evolved algorithms from the AEL framework can provide novel insights into algorithmic structures and strategies that may not have been considered by human designers. These insights can inspire the development of new heuristic approaches and optimization techniques.

Feature Extraction: By studying the features and patterns present in the evolved algorithms, researchers can identify key elements that contribute to algorithm performance. These features can be used to enhance existing heuristics or develop new algorithmic components.

Hybrid Approaches: The AEL-designed algorithms can serve as a foundation for hybrid approaches that combine the strengths of automated design and human expertise. Researchers can integrate elements of the evolved algorithms with human-designed heuristics to create more robust and efficient optimization algorithms.

Benchmarking and Comparison: The performance comparison between AEL-designed algorithms and human-designed algorithms can highlight areas where automated approaches excel or fall short. This information can guide researchers in focusing their efforts on improving specific aspects of optimization algorithms.

Interdisciplinary Collaboration: Insights from the automatic algorithm design process can facilitate interdisciplinary collaboration between experts in optimization, machine learning, and algorithm design. By sharing knowledge and expertise, researchers can develop innovative solutions that leverage the strengths of different domains.

Overall, the insights derived from the automatic algorithm design process can catalyze innovation in optimization algorithms, leading to the development of more effective and efficient heuristics for a wide range of combinatorial optimization problems.

What are the potential limitations or challenges in scaling the AEL framework to more complex algorithms or larger problem instances?

Scaling the AEL framework to more complex algorithms or larger problem instances may pose several challenges and limitations, including:

Computational Resources: As the complexity of the algorithms and problem instances increases, the computational resources required for the evolutionary computation process and language model training also escalate. Scaling up may necessitate high-performance computing infrastructure and substantial computational power.

Algorithm Representation: Designing a suitable representation for complex algorithms that captures their intricate structures and functionalities can be challenging. Ensuring that the language model can effectively generate and evaluate such representations is crucial for scalability.

Search Space Exploration: In more complex problem domains, the search space for potential algorithms becomes larger and more diverse. Efficiently exploring this vast search space to discover optimal solutions while avoiding local optima becomes increasingly challenging.

Evaluation and Validation: Evaluating the performance of evolved algorithms on larger problem instances requires extensive testing and validation. Ensuring the scalability of the evaluation process and the reliability of the results can be demanding.

Interpretability and Explainability: As algorithms become more complex, understanding and interpreting the evolved solutions may become more challenging. Ensuring the interpretability and explainability of the generated algorithms is essential for their practical applicability.

Generalization: Scaling the AEL framework to larger problem instances and diverse problem domains requires robust generalization capabilities. Ensuring that the evolved algorithms perform well across a wide range of instances and problem types is a key challenge.

Human Intervention: Balancing the level of human intervention in the algorithm design process as the complexity increases is crucial. Determining the optimal degree of human guidance and intervention to steer the evolution effectively is a critical consideration.

Addressing these limitations and challenges will be essential for successfully scaling the AEL framework to tackle more complex algorithms and larger optimization problem instances effectively.