TABLE OF CONTENTS - The Professional Green Building Council

Theme B: Creating a livable, healthy and environmentally viable citiesfinding local minima in the feasible region but identifying global minima on theboundary of the feasible region.Figure 1: Multi-criteria optimization [6]In order to find global minima, the approach for multi-criteria problems must befirst determined. As explained earlier, the a priori preference articulation (decide→search) method involves the DM first determining the weights and then finding anoptimal solution. Methods for determining weights include WSM (Weighted SumModel) [7], WPM (Weight Product Model) [8], AHP (Analytic Hierarchy Process)[9], ELECTRE (Elimination and Choice Translating Reality) [10] and TOPSIS(Technique for Order Preference by Similarity to Ideal Solution) [11]. Thesemethods find a design alternative for minimizing the objective function (F(X)) byapplying the weights to Eq. (1).MINF ( X ) = w1× f1+ w2× f2LLL+ wi×fiwhere, w = weights, f = objective function elements.ii(1)However, the weights are usually determined based on the DM's subjective andqualitative decision, which is not an absolute solution for multiple non-comparableobjectives. For example, weights of apples, bananas, oranges and watermelons willvary according to personal taste.The progressive preference articulation (decide↔search) method is laborious andtime-consuming since it requires changing the weights until a satisfactory solution396