Hit-And-Run enables efficient weight generation for simulation-based multiple criteria decision analysis
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.
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Volume (Year): 224 (2013)
Issue (Month): 3 ()
|Contact details of provider:|| Web page: http://www.elsevier.com/locate/eor|
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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.
- Amit, Y. & Grenander, U., 1991. "Comparing sweep strategies for stochastic relaxation," Journal of Multivariate Analysis, Elsevier, vol. 37(2), pages 197-222, May.
- Tervonen, Tommi & Lahdelma, Risto, 2007. "Implementing stochastic multicriteria acceptability analysis," European Journal of Operational Research, Elsevier, vol. 178(2), pages 500-513, April.
- 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.
- 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.
- 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.
- 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.
When requesting a correction, please mention this item's handle: RePEc:eee:ejores:v:224:y:2013:i:3:p:552-559. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.