2023/03/08 by Lucy L. Gao, Jane J. Ye, Gao, Lucy L. +5
Computer Science · Decision Sciences · Engineering · #Advanced Multi-Objective Optimization Algorithms #FOS: Computer and information sciences #Manufacturing Process and Optimization #Methodology (stat.ME) #Optimal Experimental Design Methods
paper · pdf · doi:10.48550/arxiv.2303.04746
openalex publication_date 2023/03/08 · openalex created_date 2023/03/10 · openalex updated_date 2026/07/28
We typically construct optimal designs based on a single objective function. To better capture the breadth of an experiment's goals, we could instead construct a multiple objective optimal design based on multiple objective functions. While algorithms have been developed to find multi-objective optimal designs (e.g. efficiency-constrained and maximin optimal designs), it is far less clear how to verify the optimality of a solution obtained from an algorithm. In this paper, we provide theoretical results characterizing optimality for efficiency-constrained and maximin optimal designs on a discrete design space. We demonstrate how to use our results in conjunction with linear programming algorithms to verify optimality.