QuIP: Experimental design for expensive simulators with many Qualitative factors via Integer Programming

TL;DR

This paper introduces QuIP, a novel integer programming-based framework for designing experiments involving expensive simulators with many qualitative factors, significantly improving efficiency in path planning applications.

Contribution

The paper develops a new integer programming approach for experimental design with qualitative factors, enabling efficient and optimal sequential design for complex high-dimensional problems.

Findings

QuIP outperforms existing methods in path planning experiments.

Efficient global optimization achieved via integer programming formulations.

Demonstrated effectiveness in rover trajectory optimization.

Abstract

The need to explore and/or optimize expensive simulators with many qualitative factors arises in broad scientific and engineering problems. Our motivating application lies in path planning - the exploration of feasible paths for navigation, which plays an important role in robotics, surgical planning and assembly planning. Here, the feasibility of a path is evaluated via expensive virtual experiments, and its parameter space is typically discrete and high-dimensional. A carefully selected experimental design is thus essential for timely decision-making. We propose here a novel framework, called QuIP, for experimental design of Qualitative factors via Integer Programming under a Gaussian process surrogate model with an exchangeable covariance function. For initial design, we show that its asymptotic D-optimal design can be formulated as a variant of the well-known assignment problem in operations research, which can be efficiently solved to global optimality using state-of-the-art integer programming solvers. For sequential design (specifically, for active learning or black-box optimization), we show that its design criterion can similarly be formulated as an assignment problem, thus enabling efficient and reliable optimization with existing solvers. We then demonstrate the effectiveness of QuIP over existing methods in a suite of path planning experiments and an application to rover trajectory optimization.