Multiple Response Optimization for Higher Dimensions in Factors and Responses

When optimizing a product or process with multiple responses, a two‐stage Pareto front approach is a useful strategy to evaluate and balance trade‐offs between different estimated responses to seek optimum input locations for achieving the best outcomes. After objectively eliminating non‐contenders in the first stage by looking for a Pareto front of superior solutions, graphical tools can be used to identify a final solution in the second subjective stage to compare options and match with user priorities. Until now, there have been limitations on the number of response variables and input factors that could effectively be visualized with existing graphical summaries. We present novel graphical tools that can be more easily scaled to higher dimensions, in both the input and response spaces, to facilitate informed decision making when simultaneously optimizing multiple responses. A key aspect of these graphics is that the potential solutions can be flexibly sorted to investigate specific queries, and that multiple aspects of the solutions can be simultaneously considered. Recommendations are made about how to evaluate the impact of the uncertainty associated with the estimated response surfaces on decision making with higher dimensions.