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Hit-And-Run enables efficient weight generation for simulation-based multiple criteria decision analysis

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Author Info

  • Tervonen, Tommi
  • van Valkenhoef, Gert
  • Baştürk, Nalan
  • Postmus, Douwe

Abstract

Models for Multiple Criteria Decision Analysis (MCDA) often separate per-criterion attractiveness evaluation from weighted aggregation of these evaluations across the different criteria. In simulation-based MCDA methods, such as Stochastic Multicriteria Acceptability Analysis, uncertainty in the weights is modeled through a uniform distribution on the feasible weight space defined by a set of linear constraints. Efficient sampling methods have been proposed for special cases, such as the unconstrained weight space or complete ordering of the weights. However, no efficient methods are available for other constraints such as imprecise trade-off ratios, and specialized sampling methods do not allow for flexibility in combining the different constraint types. In this paper, we explore how the Hit-And-Run sampler can be applied as a general approach for sampling from the convex weight space that results from an arbitrary combination of linear weight constraints. We present a technique for transforming the weight space to enable application of Hit-And-Run, and evaluate the sampler’s efficiency through computational tests. Our results show that the thinning factor required to obtain uniform samples can be expressed as a function of the number of criteria n as φ(n)=(n−1)3. We also find that the technique is reasonably fast with problem sizes encountered in practice and that autocorrelation is an appropriate convergence metric.

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Bibliographic Info

Article provided by Elsevier in its journal European Journal of Operational Research.

Volume (Year): 224 (2013)
Issue (Month): 3 ()
Pages: 552-559

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Handle: RePEc:eee:ejores:v:224:y:2013:i:3:p:552-559

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Web page: http://www.elsevier.com/locate/eor

Related research

Keywords: Multiple criteria analysis; Simulation; Uncertainty modeling; Markov Chain Monte Carlo; Stochastic Multicriteria Acceptability Analysis (SMAA);

References

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  1. Vansnick, Jean-Claude, 1986. "On the problem of weights in multiple criteria decision making (the noncompensatory approach)," European Journal of Operational Research, Elsevier, vol. 24(2), pages 288-294, February.
  2. Tervonen, Tommi & Lahdelma, Risto, 2007. "Implementing stochastic multicriteria acceptability analysis," European Journal of Operational Research, Elsevier, vol. 178(2), pages 500-513, April.
  3. Butler, John & Jia, Jianmin & Dyer, James, 1997. "Simulation techniques for the sensitivity analysis of multi-criteria decision models," European Journal of Operational Research, Elsevier, vol. 103(3), pages 531-546, December.
  4. Greco, Salvatore & Mousseau, Vincent & Slowinski, Roman, 2008. "Ordinal regression revisited: Multiple criteria ranking using a set of additive value functions," European Journal of Operational Research, Elsevier, vol. 191(2), pages 416-436, December.
  5. Amit, Y. & Grenander, U., 1991. "Comparing sweep strategies for stochastic relaxation," Journal of Multivariate Analysis, Elsevier, vol. 37(2), pages 197-222, May.
  6. Tervonen, Tommi & Figueira, José Rui & Lahdelma, Risto & Dias, Juscelino Almeida & Salminen, Pekka, 2009. "A stochastic method for robustness analysis in sorting problems," European Journal of Operational Research, Elsevier, vol. 192(1), pages 236-242, January.
  7. Greco, Salvatore & Mousseau, Vincent & Slowinski, Roman, 2010. "Multiple criteria sorting with a set of additive value functions," European Journal of Operational Research, Elsevier, vol. 207(3), pages 1455-1470, December.
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Cited by:
  1. Kadziński, Miłosz & Tervonen, Tommi, 2013. "Robust multi-criteria ranking with additive value models and holistic pair-wise preference statements," European Journal of Operational Research, Elsevier, vol. 228(1), pages 169-180.
  2. Doumpos, Michael & Zopounidis, Constantin & Galariotis, Emilios, 2014. "Inferring robust decision models in multicriteria classification problems: An experimental analysis," European Journal of Operational Research, Elsevier, vol. 236(2), pages 601-611.

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