Pareto optimal maps in ArcGIS

[Deepa]

Hi all,

I am working with spatial multi-criteria analysis in ArcMap 10.8. I have 5 objectives or criteria maps with me. I need 2 criteria maps like solar energy, distance to residential  to be maximized and other 3 factors like distance to power line, distance to transformer station, distance to road to be minimized. Is there a way in ArcMap where i could create Pareto optimal maps based on the 5 objectives.

Thank you,

Deepa

[DavidPike]

MCA involving distance from certain features is commonly done with Euclidean Distance—Help | ArcGIS for Desktop.
Alterations to output cell values are then done through Raster Calculator Raster Calculator—Help | ArcGIS for Desktop or Raster Algebra (such as taking the inverse distance, negative distance or applying a non-linear gradient to the distance value).

As for Solar energy, I'm unsure on that one, other than looking for some remote sensing data or ground station observations.

[Deepa]

HI David,

Thanks for the reply 🙂

What i am trying is to take each pixel by pixel and compare one another to eliminate the pixels that clearly perform badly interms of all 5 objectives. 

I want to first take two objectives/factors that is maximise solar energy and maximise distance to residentials. for every pixels. Comparing pixel 1 and pixel 2, if pixel 1 dominates pixel 2 in terms of both factors, i want to eliminate pixel 2. Similarly the pixel 3 with pixel 4, pixel 5 with pixel 6 etc through out entire study area to eliminate the clearly bad pixels.  I want to finally have a set of pixels where it is hard to choose a pixel since every pixel dominate other one in terms of one objective. Then I want to check with this set of pixels with next set of objectives.

In other words, a non dominant sorting of pixels with my 5 objectives (2 maximising and 3 minimising). 

[DanPatterson]

When you say comparing pixel 1 to pixel 2, is that for 1 criteria on 1 map? 

If so it looks like you are looking for the dominant class in a moving window (eg. the mode ) to remove local outliers.

If it is through all layers (eg your 5 layers/criteria), you would have to deal with the local dominance per layer/attribute first as describe above.

At this stage, a visual showing what you are working with would help assess your inputs.

[Deepa]

No I have two criteria or criteria maps for a study area.  First criteria map shows the distance to powerline which i want to minimize and the other criteria map is distance to residential which i want to maximize.

I would like to compare each pixel with other pixel in the study area. If the pixel 1 doesn't perform well in both the objectives in comparison with any other pixel in the whole study area, i would like to eliminate it. I want to check this for all the pixels through comparisons with one another  in the study area . Finally i want to be left with those pixels where it is hard to choose since in every pixel only one objective is dominated (or one objective only wins) and the other objective objective is not dominated (other objective is lost).

I hope it is clear 🙂

[DanPatterson]

visuals?

But first thought is since you have two distance rasters, power and residential, did you try querying/comparing

residential dist. >= power dist.

or power dist. minus res dist  to see if there is an inflection point/line

[RandyBurton]

The Weighted Overlay tool might help with maximizing and minimizing the various objectives.

[Deepa]

Thanks Randy 🙂

I have worked with weighted overlay but this time i was looking for something different. I want to compare both objectives pixel by pixel and see if there are pixels that i can clearly eliminate since they dont perform good in both objectives in comparison to any other pixel,