Late to the conversation, but interested in the topic. You are correct that the desirability function may prematurely converge to a local optimum. In addition to Robert’s recommendation to review the possible solutions, there are automated methods such as use random multi-start, or a global optimization method like a genetic algorithm. The latter tends to be slower than the former, but typically does a better job at finding a global optimum solution.
Note that neither method guarantees a global optimum but they definitely improve the likelihood of finding a global optimum!
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