High-dimensional Bayesian Optimization (BO) has attracted significant attention in recent research. However, existing methods have mainly focused on optimizing in continuous domains, while combinatorial (ordinal and categorical) and mixed domains still remain challenging. In this paper, we first propose MOCA-HESP, a novel high-dimensional BO method for combinatorial and mixed variables. The key idea is to leverage the hyper-ellipsoid space partitioning (HESP) technique with different categorical encoders to work with high-dimensional, combinatorial and mixed spaces, while adaptively selecting the optimal encoders for HESP using a multi-armed bandit technique. Our method, MOCA-HESP, is designed as a \textit{meta-algorithm} such that it can incorporate other combinatorial and mixed BO optimizers to further enhance the optimizers' performance. Finally, we develop three practical BO methods by integrating MOCA-HESP with state-of-the-art BO optimizers for combinatorial and mixed variables: standard BO, CASMOPOLITAN, and Bounce. Our experimental results on various synthetic and real-world benchmarks show that our methods outperform existing baselines. Our code implementation can be found at https://github.com/LamNgo1/moca-hesp

Reliable and efficient validation technologies are critical for the recent development of multi-vehicle cooperation and vehicle-road-cloud integration. In this paper, we introduce our miniature experimental platform, Mixed Cloud Control Testbed (MCCT), developed based on a new notion of Mixed Digital Twin (mixedDT). Combining Mixed Reality with Digital Twin, mixedDT integrates the virtual and physical spaces into a mixed one, where physical entities coexist and interact with virtual entities via their digital counterparts. Under the framework of mixedDT, MCCT contains three major experimental platforms in the physical, virtual and mixed spaces respectively, and provides a unified access for various human-machine interfaces and external devices such as driving simulators. A cloud unit, where the mixed experimental platform is deployed, is responsible for fusing multi-platform information and assigning control instructions, contributing to synchronous operation and real-time cross-platform interaction. Particularly, MCCT allows for multi-vehicle coordination composed of different multi-source vehicles (\eg, physical vehicles, virtual vehicles and human-driven vehicles). Validations on vehicle platooning demonstrate the flexibility and scalability of MCCT.

The Chirikov standard map and the 2D Froeschlé map are investigated. A few thousand values of the Hurst exponent (HE) and the maximal Lyapunov exponent (mLE) are plotted in a mixed space of the nonlinear parameter versus the initial condition. Both characteristic exponents reveal remarkably similar structures in this space. A tight correlation between the HEs and mLEs is found, with the Spearman rank ρ 0.83 and ρ 0.75 for the Chirikov and 2D Froeschlé maps, respectively. Based on this relation, a machine learning (ML) procedure, using the nearest neighbor algorithm, is performed to reproduce the HE distribution based on the mLE distribution alone. A few thousand HE and mLE values from the mixed spaces were used for training, and then using 2 2.4 10 The ML procedure allowed to reproduce the structure of the mixed spaces in great detail.