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Anti-optimization

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This page is open for visitors but is still under construction.

The usual Disclaimer

The objective of this page is not to give the visitor a crash course on you “Anti-optimization”. Rather, this page provide you with a rather broad description of the concept, and links to easily accessible material that you can use to study this subject on your own. This page is just a general preface to the conversations I have had with ChatGPT and Bart about this concept.

What is Anti-optimization?

This is a very relevant question because the term “Anti-optimization” has different meanings. Let us invite ChatGPT and Bard to help us sort this difficulty, recalling that in our discussion we are interested in the meaning of “Anti-optimization” in the context of decision-making under severe uncertainty.

So consider this:


Would the meaning of Anti-optimization” be the same in the context of decision-making under severe uncertainty? Let us see:


This is surprising, because it seems that our friends the chatbots are not aware of the fact that in decision-making under severe uncertainty, the term “Anti-optimization” has a different meaning, a much simpler one. That is, in decision-making under severe uncertainty,

Anti-optimization = Pessimization = antonym of optimization.

In the context of decision-making under uncertainty, the term “anti-optimization” was coined by Elishakoff and Colombi (1993, p. 187):

For the first time in the literature the system uncertainty in the random vibrations is dealt with as an ‘anti-optimization’ problem of finding the least favorable values of the mean-square response. The approach developed here opens a new avenue for tackling parameter uncertainty which is often encountered in various branches of engineering.

More explicitly, as has been emphasized in many publications since then, for example in the book “Optimization and Anti-Optimization of Structures Under Uncertainty” (Elishakoff and Oshaki 2010) , practically speaking

Anti-optimization = worst-case analysis.

Therefore, in our discussion we view this term as equivalent to Worst-case analysis and treat it as such.

Our interest in the term “Anti-optimization” is solely then in connection with the theory that Elishakoff et al (1994) called Optimization with Anti-optimization which is discussed in detail in Elishakoff and Oshaki 2010). As we shall see Optimization with Anti-optimization is a reinvention of Wald’s maximin paradigm.

Bibliography

  • Elishakoff, I., Haftka, R.T., and Fang, J. (1994) Structural design under bounded uncertainty—Optimization with anti-optimization. Computers & Structure
    53(6):1401-1405.
  • Elishakoff, I., and Oshaki, M. (2010) Optimization and Anti-Optimization of Structures Under Uncertainty. World Scientific.
  • Sniedovich, M. (2011) A classical decision theoretic perspective on worst-case analysis. Applications of Mathematics 56(5):499-509. Download.

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