Evolutionary Computing: Constraints, Surrogate Models, and Noisy Gradients

Black-box optimization is the task of solving optimization problems where querying the value of the objective function is the only way of learning about the problem. Black-box problems occur in many areas, as for example in cases where simulations need to be run or prototypes be built in order to assess the quality of a solution. The objective function cannot be specified analytically, no assumptions regarding continuity or smoothness can be made, and observations of function values may be noisy. Gradient approximations can sometimes be obtained through finite differencing, but may not justify the cost incurred in obtaining them. Evolutionary algorithms (EAs) are stochastic algorithms for black-box optimization. The objective of this program of research is to contribute to the development of EAs in three areas: constrained optimization, surrogate model assisted optimization, and evolutionary search based on noisy gradients. In all cases, designs will be informed by systematically studying algorithm behaviour on scalable unit test problems. A primary concern in the development will be the preservation of desirable invariance properties. The proposed work will benefit users of EAs in that it will result in more capable algorithms for black-box optimization. It will significantly expand the range of problems that EAs can beneficially be applied to. Evolutionary search strategies based on noisy gradients have potentially wide ranging applications in machine learning, where variants of stochastic gradient descent that are commonly used for training neural networks do not possess desirable invariance properties and often require the careful tuning of parameters in order to be successful. The work will also result in several HQP with superior problem solving skills and unique expertise in the development and application of modern stochastic black-box optimization techniques as well as in aspects of machine learning and the design and analysis of experiments.