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Pareto sampling: choosing the right weights by derivative pursuit

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Published:13 June 2010Publication History

ABSTRACT

The convex weighted-sum method for multi-objective optimization has the desirable property of not worsening the difficulty of the optimization problem, but can lead to very nonuniform sampling. This paper explains the relationship between the weights and the partial derivatives of the tradeoff surface, and shows how to use it to choose the right weights and uniformly sample largely convex tradeoff surfaces. It proposes a novel method, Derivative Pursuit (DP), that iteratively refines a simplicial approximation of the tradeoff surface by using partial derivative information to guide the weights generation. We demonstrate the improvements offered by DP on both synthetic and circuit test cases, including a 22 nm SRAM bitcell design problem with strict read and write yield constraints, and power and performance objectives.

References

  1. I. Das et al, "Normal-boundary intersection: a new method for generating the Pareto surface in nonlinear multicriteria optimization problems," SIAM J. Optim., 8(3), 1998. Google ScholarGoogle ScholarDigital LibraryDigital Library
  2. G. Stehr et al, "Performance trade-off analysis of analog circuits by normal-boundary intersection," IEEE/ACM DAC, 2003. Google ScholarGoogle ScholarDigital LibraryDigital Library
  3. A. Messac et al, "The normalized normal constraint method for generating the Pareto frontier," Struct. Multidisc. Optim., 25, 2003.Google ScholarGoogle Scholar
  4. I. Y. Kim et al, "Adaptive weighted sum method for multiobjective optimization: a new method for Pareto front generation," Struct. Multidisc. Optim., 31, 2006.Google ScholarGoogle Scholar
  5. N. Srinivas, "Multiobjective optimization using nondominated sorting in genetic algorithms," Evol. Comput., 2(3), 1994. Google ScholarGoogle ScholarDigital LibraryDigital Library
  6. T. McConaghy et al, "Variation-aware structural syntehsis of analog circuits via hierarchical building blocks and structural homotopy," IEEE Trans. CAD 28(9), 2009. Google ScholarGoogle ScholarDigital LibraryDigital Library
  7. E. Zitzler et al, "Multiobjective evolutionary algorithms: A comparative case study and the strength pareto approach," IEEE Trans. Evol. Comput., 3(4), 1999. Google ScholarGoogle ScholarDigital LibraryDigital Library
  8. I. Das et al, "A closer look at drawbacks of minimizing weighted sums of objectives for Pareto set generation in multicriteria optimization problems," Struct. Optim., 14, 1997.Google ScholarGoogle Scholar
  9. B. Fruhwirth et al, "Approximation of convex curves with application to bicriterial minimum cost flow problem," Euro. J. Oper. Res., 42, 1989.Google ScholarGoogle Scholar
  10. R. V. Efremov et al, "Properties of a method for polyhedral approximation of the feasible criterion set in convex multiobjective problems," Ann. Oper. Res., 166, 2009.Google ScholarGoogle Scholar
  11. G. H. Golub and C. F. Van Loan, "Matrix Computations," JHU Press, 3 ed., 1996.Google ScholarGoogle Scholar
  12. C. Wann et al, "SRAM cell design for stability methodology," Int. Symp. VLSI Tech., 2005.Google ScholarGoogle Scholar
  13. A. Singhee et al, "Statistical blockade: very fast statistical simulation and modeling of rare circuit events and its application to SRAM circuit design," IEEE Trans. CAD, 28(8), 2009. Google ScholarGoogle ScholarDigital LibraryDigital Library
  14. A. Conn et al, "A derivative-free optimization algorithm in practice," Symp. Multidisc. Anal. Optim., 1998.Google ScholarGoogle Scholar

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  1. Pareto sampling: choosing the right weights by derivative pursuit

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          cover image ACM Conferences
          DAC '10: Proceedings of the 47th Design Automation Conference
          June 2010
          1036 pages
          ISBN:9781450300025
          DOI:10.1145/1837274

          Copyright © 2010 ACM

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          Publication History

          • Published: 13 June 2010

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