Model-based Evolutionary Parametric Optimization

Description

Many real-world applications involve repeatedly solving optimization problems with different patterns, such as engineering design, chemical process control, production planning, and intelligent agent design. These different patterns can be represented by problem parameters that describe the characteristics of each problem instance, and the task to solve all such instances is called parametric optimization. In the past few decades, many algorithms have been proposed to tackle parametric optimization. However, these algorithms have two major drawbacks: (1) They need to solve each individual optimization problem separately, which could lead to a very high computational overhead, especially when the cardinality of possible parameter values is large, and (2) many applications could require a real-time solution for a new problem instance, which is not supported by these algorithms.  In this project, we will develop novel and efficient model-based evolutionary algorithms for parametric optimization. By leveraging the information obtained from solving problem instances with different problem parameter values, we propose to build a math model, such as a Gaussian process or neural network model, for approximating the whole solution set for a given parametric optimization problem conditioned on the problem parameter value. In this way, approximate optimal solutions to new problem instances with different patterns can be obtained in a zero-shot manner. Viewing widely-used homotopy and smooth optimization methodologies from the point of view of parameter optimization, we will generalize our methods to homotopy and smooth optimization, and develop novel model-based algorithms for solving nonconvex and nonsmooth optimization problems. We will test our proposed algorithms on parametric optimization for electronic design automation.