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<p>Derivative-free optimization (DFO) algorithms are critical for solving complex black-box problems where gradient information is unavailable or impractical to obtain. However, DFO methods often struggle with mixed-integer problems, especially those with high dimensionality, due to the complexity of the search space. This paper presents an approach to enhance DFO algorithms for mixed-integer problems through an adaptive sampling procedure. The proposed methodology integrates surrogate modeling with DFO algorithms, directing the search towards promising regions within the solution space by leveraging the error maximization strategy (EMS). We specifically focus on enhancing two state-of-the-art DFO implementations, SNOBFIT and MISO, resulting in the development of ADASNOBFIT and ADAMISO methods. Our work includes a comprehensive evaluation of the proposed ADASNOBFIT and ADAMISO algorithms against existing DFO methods, across a diverse set of 594 mixed-integer benchmark problems, highlighting notable increases in optimal solutions and improved execution times, particularly in large-sized problem categories with 51 to 500 variables. Experimental results demonstrate the efficiency and robustness of these enhanced algorithms, showing significant improvements of 16.5% and 31% respectively in the percentage of solutions obtained over the DFO methods. Moreover, the methodology is further validated through a real-world application involving the optimization of the GCC compiler using the PolyBenchC-4.2.1 benchmark suite. In this scenario, the proposed methods outperform existing DFO solvers and the OpenTuner tuning tool, both in terms of optimal solutions and execution time, demonstrating their practical applicability and effectiveness. This adaptive sampling approach offers a promising solution for addressing the challenges posed by black-box systems across various fields, providing efficient and robust solutions for complex optimization tasks.</p>

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A surrogate-based adaptive sampling approach for mixed-integer black-box optimization problems

  • 期刊论文

  • 发表日期：

    2025年12月2日

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  • Emmanouil Karantoumanis,
  • Nikolaos Ploskas

摘要

Derivative-free optimization (DFO) algorithms are critical for solving complex black-box problems where gradient information is unavailable or impractical to obtain. However, DFO methods often struggle with mixed-integer problems, especially those with high dimensionality, due to the complexity of the search space. This paper presents an approach to enhance DFO algorithms for mixed-integer problems through an adaptive sampling procedure. The proposed methodology integrates surrogate modeling with DFO algorithms, directing the search towards promising regions within the solution space by leveraging the error maximization strategy (EMS). We specifically focus on enhancing two state-of-the-art DFO implementations, SNOBFIT and MISO, resulting in the development of ADASNOBFIT and ADAMISO methods. Our work includes a comprehensive evaluation of the proposed ADASNOBFIT and ADAMISO algorithms against existing DFO methods, across a diverse set of 594 mixed-integer benchmark problems, highlighting notable increases in optimal solutions and improved execution times, particularly in large-sized problem categories with 51 to 500 variables. Experimental results demonstrate the efficiency and robustness of these enhanced algorithms, showing significant improvements of 16.5% and 31% respectively in the percentage of solutions obtained over the DFO methods. Moreover, the methodology is further validated through a real-world application involving the optimization of the GCC compiler using the PolyBenchC-4.2.1 benchmark suite. In this scenario, the proposed methods outperform existing DFO solvers and the OpenTuner tuning tool, both in terms of optimal solutions and execution time, demonstrating their practical applicability and effectiveness. This adaptive sampling approach offers a promising solution for addressing the challenges posed by black-box systems across various fields, providing efficient and robust solutions for complex optimization tasks.