Yes, VSD can be extended to handle continuous or mixed discrete-continuous design spaces, which would significantly enhance its applicability in various optimization scenarios. The extension would involve adapting the variational distribution to accommodate continuous variables, which can be achieved through the use of mixture models or hybrid generative models that can represent both discrete and continuous components.
In continuous design spaces, the optimization procedure would need to incorporate techniques such as gradient-based optimization methods, which can efficiently navigate the continuous landscape. This could involve using Gaussian processes or neural networks to model the fitness function, allowing for the estimation of gradients and facilitating the optimization of continuous variables.
For mixed design spaces, the sampling procedure would require a more sophisticated approach to ensure that both discrete and continuous candidates are generated effectively. One potential method is to use rejection sampling or importance sampling, where candidates are drawn from a joint distribution that accounts for both types of variables. This would ensure that the generated candidates are representative of the entire design space.
Additionally, the optimization objective may need to be reformulated to account for the different types of variables. For instance, one could use a multi-objective optimization framework that simultaneously optimizes for both discrete and continuous objectives, allowing for a more holistic approach to the design problem.
Overall, extending VSD to handle continuous or mixed discrete-continuous design spaces would enhance its flexibility and effectiveness, enabling it to tackle a broader range of optimization challenges in fields such as bioinformatics, materials science, and engineering design.