Evolving Benchmark Functions to Compare Evolutionary Algorithms via Genetic Programming

Konsep Inti

Using Genetic Programming to automate the creation of benchmark functions for comparing evolutionary algorithms.

Abstrak

The study focuses on using Genetic Programming (GP) to generate benchmark functions that can differentiate between evolutionary algorithms. The research aims to automate the design of benchmark functions and compare the performance of different optimizers. By utilizing Wasserstein distance and MAP-Elites, the study showcases how these generated benchmarks outperform human-made benchmarks in distinguishing between algorithm configurations. The paper includes two case studies: one focusing on Differential Evolution configurations and another on comparing SHADE and CMA-ES optimizers. Results show that the GP-generated benchmark functions excel in differentiating algorithms based on decision variables and fitness values.
I. Introduction

Optimization benchmarks are crucial for evaluating evolutionary algorithms.
Good benchmark functions represent real-world problem characteristics.
Automatic generation of benchmark functions is challenging but essential.
II. Preliminaries

Optimization benchmarks are vital for comparing algorithm performance.
Existing benchmarks may not effectively differentiate between powerful algorithms.
Previous studies have explored evolving problem instances using GP.
III. Proposed Method

Using GP to evolve benchmark functions highlighting differences in optimizer performances.
Evaluation metrics include Wasserstein distance and MAP-Elites with landscape metrics.
IV. Experiments
A. Case Study on Differential Evolution Parametrization

Generated benchmark functions effectively differentiate between DE configurations.
Comparison with CEC2005 benchmarks shows superior performance in training phase.
B. Case Study on Different Algorithms (SHADE vs. CMA-ES)

Functions successfully differentiate between SHADE and CMA-ES optimizers.
V. Discussion on Generated Benchmarks

Detailed analysis of top-performing benchmark functions from both case studies.
VI. Conclusions

The study demonstrates the effectiveness of GP-generated benchmark functions in differentiating evolutionary algorithms.

Statistik

"The fitness measure of the GP is the Wasserstein distance of the solutions found by a pair of optimizers."
"We use multidimensional Wasserstein distance to compute the distance between parameter distributions."
"Our approach provides a novel way to automate the design of benchmark functions."

Kutipan

"Good benchmark functions represent characteristics of different families of real-world problems."
"Our method is promising to compose new optimization functions to compare evolutionary algorithms."

Wawasan Utama Disaring Dari

Evolving Benchmark Functions to Compare Evolutionary Algorithms via Genetic Programming

by Yifan He,Cla... pada arxiv.org 03-22-2024

https://arxiv.org/pdf/2403.14146.pdf

Pertanyaan yang Lebih Dalam

How can evolving benchmark functions impact future algorithm development

Evolving benchmark functions can significantly impact future algorithm development by providing a more tailored and effective way to compare the performance of different evolutionary algorithms. By automating the creation of benchmark functions using techniques like Genetic Programming (GP) and MAP-Elites, researchers can generate functions that specifically highlight the strengths and weaknesses of various algorithms. This targeted approach allows for a more nuanced analysis of algorithm behavior, enabling developers to identify areas for improvement and optimization.
Furthermore, evolving benchmark functions can serve as a valuable tool for evaluating new algorithmic components or modifications. By creating benchmarks that challenge specific aspects of algorithms, such as their ability to handle certain landscape features or problem characteristics, researchers can gain insights into how these changes impact overall performance. This iterative process of testing against evolving benchmarks can drive innovation in algorithm design by encouraging the development of more robust and adaptable solutions.

What potential limitations or biases could arise from automating the creation of benchmark functions

Automating the creation of benchmark functions may introduce potential limitations or biases that need to be carefully considered. One limitation is the risk of overfitting the benchmarks to specific algorithms or problem types during the evolution process. If not properly controlled, this could lead to biased results that favor certain algorithms over others unfairly.
Another limitation is related to the selection criteria used in GP and MAP-Elites when generating benchmarks. Depending on how these criteria are defined, there is a possibility of introducing unintentional biases into the generated functions. For example, if only specific landscape features are emphasized during evolution, it may overlook other important characteristics that could affect algorithm performance in real-world scenarios.
Additionally, automating benchmark function creation might result in an overly complex set of functions that are challenging to interpret or generalize across different problems. Ensuring transparency and interpretability in how benchmarks are evolved is crucial to avoid introducing unnecessary complexity or ambiguity into the evaluation process.

How might exploring other phenotypic descriptors enhance the diversity and quality of generated benchmarks

Exploring other phenotypic descriptors beyond Fitness Distance Correlation (FDC) and neutrality has the potential to enhance both diversity and quality in generated benchmarks significantly:

Diversity Enhancement: Introducing additional phenotypic descriptors can help capture a broader range of landscape features relevant for evaluating evolutionary algorithms' performance accurately.

Quality Improvement: By incorporating diverse phenotypic descriptors such as ruggedness measures or multimodality indicators alongside FDC and neutrality metrics, researchers can create richer benchmark sets with varied challenges reflecting real-world optimization problems better.

Robust Benchmark Selection: Utilizing multiple phenotypic descriptors ensures a comprehensive assessment framework for selecting high-quality benchmarks based on various dimensions like deception level, neutrality extent, modality distribution patterns effectively guiding algorithm comparison studies.

Generalizability Boost: Including diverse phenotypic descriptors enables researchers to develop benchmarks with broader applicability across different domains while maintaining specificity towards highlighting distinct aspects critical for assessing evolutionary algorithm behavior comprehensively.

By leveraging multiple phenotypic descriptors intelligently within automated benchmark generation frameworks like GP coupled with MAP-Elites selection strategies will likely lead to more robust evaluations fostering advancements in evolutionary computation research effectively capturing nuances essential for future algorithm developments efficiently.