arXiv subjects

Mai Peng

Publications and source records attributed to Mai Peng.

3 recordsLinked to original sources

arXiv2025

PORTAL: Controllable Landscape Generator for Continuous Optimization-Part I: Framework

Benchmarking is central to optimization research, yet existing test suites for continuous optimization remain limited: classical collections are fixed and rigid, while previous generators cover only narrow families of landscapes with restricted variability and control over details. This paper introduces PORTAL (Platform for Optimization Research, Testing, Analysis, and Learning), a general benchmark generator that provides fine-grained, independent control over basin curvature, conditioning, variable interactions, and surface ruggedness. PORTAL's layered design spans from individual components to block-wise compositions of multi-component landscapes with controllable partial separability and imbalanced block contributions. It offers precise control over the shape of each component in every dimension and direction, and supports diverse transformation patterns through both element-wise and coupling operators with compositional sequencing. All transformations preserve component centers and local quadratic structure, ensuring stability and interpretability. A principled neutralization mechanism prevents unintended component domination caused by exponent or scale disparities, which addresses a key limitation of prior landscape generators. On this foundation, transformations introduce complex landscape characteristics, such as multimodality, asymmetry, and heterogeneous ruggedness, in a controlled and systematic way. PORTAL enables systematic algorithm analysis by supporting both isolation of specific challenges and progressive difficulty scaling. It also facilitates the creation of diverse datasets for meta-algorithmic research, tailored benchmark suite design, and interactive educational use. The complete Python and MATLAB source code for PORTAL is publicly available at [https://github.com/EvoMindLab/PORTAL].

cs.NE↗

arXiv2024

Extending the trapping theorem to provide local stability guarantees for quadratically nonlinear models

The Navier Stokes equations (NSEs) are partial differential equations (PDEs) to describe the nonlinear convective motion of fluids and they are computationally expensive to simulate because of their high nonlinearity and variables being fully coupled. Reduced-order models (ROMs) are simpler models for evolving the flows by capturing only the dominant behaviors of a system and can be used to design controllers for high-dimensional systems. However it is challenging to guarantee the stability of these models either globally or locally. Ensuring the stability of ROMs can improve the interpretability of the behavior of the dynamics and help develop effective system control strategies. For quadratically nonlinear systems that represent many fluid flows, the Schlegel and Noack trapping theorem (JFM, 2015) can be used to check if ROMs are globally stable (long-term bounded). This theorem was subsequently incorporated into system identification techniques that determine models directly from data. In this work, we relax the quadratically energy-preserving constraints in this theorem, and then promote local stability in data-driven models of quadratically nonlinear dynamics. First, we prove a theorem outlining sufficient conditions to ensure local stability in linear-quadratic systems and provide an estimate of the stability radius. Second, we incorporate this theorem into system identification methods and produce a-priori locally stable data-driven models. Several examples are presented to demonstrate the effectiveness and accuracy of the proposed algorithm.

physics.comp-ph↗

arXiv2023

EDOLAB: An Open-Source Platform for Education and Experimentation with Evolutionary Dynamic Optimization Algorithms

Many real-world optimization problems exhibit dynamic characteristics, posing significant challenges for traditional optimization techniques. Evolutionary Dynamic Optimization Algorithms (EDOAs) are designed to address these challenges effectively. However, in existing literature, the reported results for a given EDOA can vary significantly. This inconsistency often arises because the source codes for many EDOAs, which are typically complex, have not been made publicly available, leading to error-prone re-implementations. To support researchers in conducting experiments and comparing their algorithms with various EDOAs, we have developed an open-source MATLAB platform called the Evolutionary Dynamic Optimization LABoratory (EDOLAB). This platform not only facilitates research but also includes an educational module designed for instructional purposes. The education module allows users to observe: a) a 2-dimensional problem space and its morphological changes following each environmental change, b) the behaviors of individuals over time, and c) how the EDOA responds to environmental changes and tracks the moving optimum. The current version of EDOLAB features 25 EDOAs and four fully parametric benchmark generators. The MATLAB source code for EDOLAB is publicly available and can be accessed from [https://github.com/Danial-Yazdani/EDOLAB-MATLAB].

cs.NE↗