Integrating LP Multi Criteria Optimisation and Preference Modelling

In optimisation models for multiple objective problems, we can distinguish non-preference and preference methods, as was discussed in Open Design, a Collaborative Approach to Architecture. With the non-preference approach, we limit the model to the production of information on non-dominated (Pareto) performances. A non-dominated (Pareto optimal) solution is one for which no other solution exists that is capable of providing a better performance in one criterion and no worse performance in all other criteria. Given criteria that completely express the goals of a decision problem and a complete Pareto set of solutions for those criteria, the best solution must lie within the Pareto set. In the preference approach, the model designer's trade-off preferences are incorporated in the model. For instance, he can reduce the multi criteria problem to a single-criterion problem by assigning weight factors to the criteria and optimise the weighted sum. The choice of the weight factors remains rather arbitrary however. Even if there were a rationale for a certain choice, it would be extremely difficult for the designer to explain why the interests of some crucial stakeholders are given less weight than those of others.

The non-preference Pareto optimisation generally used in Open Design is the Constraint method. This method retains one objective as primary, that means as variable to be optimised, while treating the remaining objectives as constraints. By doing this in turn for the various objectives, the relevant part of the Pareto set is found. Which member of that set is finally chosen, is determined in an iterative procedure in which crucial stakeholders in turn make concessions until a solution is found or the conclusion is drawn that their interests are irreconcilable.

An advantage of this procedure is that stakeholder's negotiations are limited to feasible solutions. A disadvantage is that stakeholders cannot express their preferences a priori, because their willingness to make concessions depends on how much their concessions influence the feasibility of the project in combination with concessions from other stakeholders. Preference modelling does allow stakeholders to express their preferences a priori, but does not take into account feasibility due to constraints imposed by other stakeholders.

This limitation is removed by integrating the preference and non-preference methods. In its simplest form, this can be done by incorporating the preferences and their associated weights as decision variables into the LP model. Since the weight factors are not manipulated by the modeller this procedure is still a non-preference method. This procedure is explained in the next section with the Project Developer's problem from Section 1.2

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Figure 6.1 Model structure after adding restrictions

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