Multiple Response Optimization for Higher Dimensions in Factors and Responses

Abstract

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.

The experimental design approach to the optimization of a simple quick easy cheap effective rugged and safe method for the analysis of phytoestrogens in complex soy‐based food

“…This assumption is even more important when multiple responses have to be considered for the optimum localization. To find the best compromise among the optimal conditions identified for each response, the “multi‐criteria decision making” approach of Pareto fronts was used . A list of candidate predicted responses were plotted against one another, and the non‐dominated point, which corresponded to acceptable values for all responses, was selected as the optimal set of conditions.…”

Is designed data collection still relevant in the big data era?

“…This generally involves trade‐offs in performance across the various responses of interest. Pareto front optimization can allow for identifying combinations of results that provide the balance desired 40–41 . Finally, once desirable operation conditions have been identified, a confirmation phase is recommended to validate that the target input region yields the anticipated results 42 .…”

Understanding the merits of winning data competition solutions for varied sets of objectives

“…Lu et al [14] adapted the Pareto front approach for design selection based on considering multiple competing criteria and proposed graphical summaries for comparing solutions on the Pareto front and understand their trade-offs to match user priorities. Additional numerical and graphical tools to support informed decision-making are available in Lu and Anderson-Cook [19,20], Lu et al [21,22].…”