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

Abstract: 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].