COCO: A Platform for Comparing Continuous Optimizers in a Black-Box Setting (1603.08785v4)

Abstract: We introduce COCO, an open source platform for Comparing Continuous Optimizers in a black-box setting. COCO aims at automatizing the tedious and repetitive task of benchmarking numerical optimization algorithms to the greatest possible extent. The platform and the underlying methodology allow to benchmark in the same framework deterministic and stochastic solvers for both single and multiobjective optimization. We present the rationales behind the (decade-long) development of the platform as a general proposition for guidelines towards better benchmarking. We detail underlying fundamental concepts of COCO such as the definition of a problem as a function instance, the underlying idea of instances, the use of target values, and runtime defined by the number of function calls as the central performance measure. Finally, we give a quick overview of the basic code structure and the currently available test suites.

• The paper introduces COCO as a robust platform for comparing continuous optimization algorithms using automated, budget-free runtime performance metrics.
• It integrates multiple programming languages and employs runtime distribution plots (ECDFs) to visually assess algorithm efficiency across varied problem dimensions.
• Its extensible design and reproducible benchmarking approach enable detailed cross-dimensional analyses that advance both deterministic and stochastic solver evaluations.

COCO: A Platform for Comparing Continuous Optimizers in a Black-Box Setting

The paper introduces COCO (Comparing Continuous Optimizers) as an open-source platform designed to benchmark continuous optimization algorithms in a black-box setting. The platform tackles the arduous task of algorithm performance assessment by automating the benchmarking process for deterministic and stochastic solvers across both single and multi-objective optimization problems. Here, we delve into the pivotal features, methodological innovations, and prospective impacts of COCO.

Key Features and Methodology

COCO is distinguished by its ability to integrate various languages—C/C++, Java, Matlab/Octave, and Python—into the benchmarking framework, thus making it accessible and flexible for diverse user bases. The platform’s robustness arises from its compatibility with multiple test suites, which embody different function sets and problem dimensions to thoroughly evaluate algorithm performance across varied scenarios.

Key aspects of the COCO methodology include:

1. Instances and Problem Formulation: Each function has multiple instances differentiated by pseudo-random parameters. This setup ensures a non-trivial comparison between deterministic and stochastic solvers, thereby enhancing objectivity in benchmarking through increased variability and reducing overfitting risk.
2. Runtime as a Performance Measure: The primary measure of performance is the runtime, quantified by the number of function evaluations before meeting a predefined target accuracy. This approach facilitates consistent comparisons across various computational environments and provides a quantitative metric that is relevant and interpretable.
3. Aggregation and Visualization: The aggregation of performance data is achieved through runtime distribution plots (ECDFs), offering intuitive insights into the performance of algorithms over a range of target precision values, enabling comprehensive visual analytics of algorithm efficiency.
4. Budget-Free Evaluation: Unlike traditional methods with fixed computational budgets, COCO’s evaluation framework is budget-independent, allowing algorithms to be assessed based on their actual performance capabilities rather than arbitrary constraints.
5. Cross-Dimensional Analysis: While detailed results are provided for individual dimensions, COCO emphasizes comparisons within each dimension, as dimensionality is a fundamental aspect of the optimization landscape that directly influences solver applicability and efficiency.

Implications and Future Directions

COCO’s framework promises significant contributions to the field of numerical optimization. By standardizing the benchmarking process, it not only generates a wealth of reproducible data but also fosters a collaborative environment for researchers and practitioners to share insights and validate results. Its open-access data repositories enhance transparency and reproducibility in research, which is crucial in advancing the state of knowledge in optimization.

The platform's extensibility positions it for future enhancements, such as incorporating benchmark suites for constrained and multi-objective optimization with more than two objectives, thereby broadening the horizon for application-specific optimization research.

Speculations on the Trajectory of AI Developments

With the ongoing developments in COCO, the projected expansions to interface with real-world optimization problems signal a shift towards more application-driven AI research. The coupling of black-box optimization algorithms with COCO’s interactive benchmarking ethos could lead to more adaptive and resilient AI solutions capable of tackling real-world challenges characterized by dynamic and complex landscapes.

In summary, COCO provides a rigorous, flexible platform for benchmarking continuous optimization algorithms. Its innovative approach to performance assessment and commitment to open science establish it as a pivotal tool in the advancement of both theoretical and practical optimization endeavors.