Uncertainty Analysis of Trade-offs Between Multiple Responses Using Hypervolume

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global and instance-specific normalized hypervolumes, model parameter uncertainty, multiple response optimization, Pareto front, scaling choices

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When multiple responses are considered in process optimization, the degree to which they can be simultaneously optimized depends on the optimization objectives and the amount of trade-offs between the responses. The normalized hypervolume of the Pareto front is a useful summary to quantify the amount of trade-offs required to balance performance across the multiple responses. To quantify the impact of uncertainty of the estimated response surfaces and add realism to what future data to expect, 2 versions of the scaled normalized hypervolume of the Pareto front are presented. To demonstrate the variation of the hypervolume distributions, we explore a case study for a chemical process involving 3 responses, each with a different type of optimization goal. Results show that the global normalized hypervolume characterizes the proximity to the ideal results possible, while the instance-specific summary considers the richness of the front and the severity of trade-offs between alternatives. The 2 scaling schemes complement each other and highlight different features of the Pareto front and hence are useful to quantify what solutions are possible for simultaneous optimization of multiple responses.

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Citation / Publisher Attribution

Quality and Reliability Engineering International, v. 33, issue 8, p. 2343-2360