Designing Landscape-Aware Benchmarks with Explicit Local Optima for Single- and Multi-Objective Optimization

Abstract

The number and arrangement of local optima are crucial for evaluating the exploration-exploitation balance and the ability to discover promising local optima. However, existing benchmark suites rarely provide explicitly defined multi-modal landscapes, especially in multi-objective optimization. To bridge this gap, we propose a framework for designing both single- and multi-objective benchmark problems with identifiable local optima and controllable landscape features. Our approach builds on Max-Set of Gaussians (MSG) landscapes and extends them to the multi-objective domain. To match target landscape features, we optimize Gaussian heights and variances. Empirical results demonstrate that the framework can emulate several function classes from the Black-Box Optimization Benchmarking (BBOB) suite, including separable, multimodal, and ill-conditioned functions. Furthermore, we confirm that the framework can generate problems with Exploratory Landscape Analysis (ELA) feature patterns that are not present in the BBOB suite. Our results also imply that the landscape features of single-objective MSG landscapes are inherited in multi-objective extensions.