Release Level	5.4
Release Date	2008 10
Revision Level	1.0

DMC: discrete multi-criteria optimization

The sets of alternatives to analyze can either be:

1. imported as a set from WRM optimization scenarios (use the button: DMC" after a successful optimization run at the optimization scenario overview level to export the feasible alternatives generated);
2. imported individually from WRM model runs;
3. imported from a CSV file (exported from a spreadsheet)
4. created (and edited) manually.

Basic Concepts

Every one of the criteria used is define in the Knowledge Base (KB) associated with the tool.

For each of the criteria, there is

• a (scalar) value defined
• an optimization strategy or direction (minimize, maximize, meet) defined; the latter case is a shortcut for minimizing the deviation in either direction from the reference, in this case, by default the median of the distribution for that criterion in the set.
• an (optional) contraint (upper or lower bound, or normalised distance depending on the strategy or direction of optimization) defined.

• feasible subset: the set of alternatives that meets all of the constraints;
• UTOPIA: a hypothetical point defined by the "best" value for each the criteria in the set.
• NADIR: a hypothetical point defined by the "worst" value for each of the critiera in the set;
• dominated subset: an alternative is considered dominated, if we can find another in the set that is better in at least one, and not worse in any other (i.e., at least equal), of the criteria. The dominated subset is identified and excluded from consideration.
• PARETO set: this consists of all non-dominated alternatives;
• Reference Point: a hypothetical point defined by the user who select his preferred value for each of the criteria. The default Reference Point is UTOPIA.
• Efficient Point: this is the feasible and non-dominated alternative "nearest" to the Reference Point. The distance is determined as the N (number of criteria) dimension Euclidean distance in the spce define by all (active) critiera normalized between NADIR and UTOPIA. The distance is described as a (normalized in %) level of achievement or (100% - distance): 100% would be UTOPIA itself, 50% halfway between UTOPIA and NADIR, and 0% would represent the position of NADIR.

  In addition to the achievement level of the efficient point, the tools also shows the (arithmetic) average achievement level of the PARETO set.

Basic functionality

1. define the set, add and delete alternatives; with every new alternative, NADIR and UTOPIA may change;
2. define the criteria, select or deselect from consideration; a good strategy is to start with two criteria only, and add critiera one by one towards a more complex problem.
3. introduce constraints on any of the criteria to limit the subset of feasible alternatives to be considered;
4. introduce a reference point different from its default (UTOPIA).

Auxiliary analysis

• a summary of the optimisation scenario with the import and configuration interface;
• a tabular summary and editor interface for an individual alternative selected from the main list of alternatives with the associated scattergram of all alternatives, the current alternative marked;
• a tabular summary of the set with the associated scattergram;
• an enlarge scattergram;
• the statistics for an individual criterion with a histogram, with the possibility to select a second criterion for a display of a scatergram and correlation (covariance) estimate.

Criteria