The Weighted Sum Ranking Algorithm

For the weighted sum algorithm to be valid, Performance Trade-off normalizes the objectives to bring them into the same range; otherwise, the effect of each objective function is not represented equally.

The weighted sum ranking algorithm does the following to calculate the overall score for each data point:

1. The thresholds for each parameter are evaluated. If the priority of a parameter is MH (Must Have), but its value falls outside the thresholds, the data point is given a score of 0.0, regardless of the objective values.
2. Performance Trade-off calculates the raw object value for each parameter with an objective, using the "higher" = "better" formulation:
   • If the objective is to minimize a parameter, $\text{raw}\_\text{object}\_\text{value }=-\text{1}*\text{parameter}\_\text{value}$
   • If the objective is to maximize a parameter, $\text{raw\_object\_value = parameter\_value}$
   • If the objective is a target value of a parameter, $\text{raw\_object\_value}=-1*\text{Abs}(\text{target}-\text{parameter\_value})$
3. For each parameter that was chosen as an objective, the raw object values are scaled to fall between 1 and 100. This is the scaled parameter objective value.
4. The scaled parameter objective values are multiplied by the final weight factor. This is the scaled and weighted parameter objective value.
5. For each data point, Performance Trade-off calculates the sum of the scaled and weighted objective values to get the weighted sum. This is the raw score for the data point.
6. Performance Trade-off calculates the score by scaling the raw scores for all the data points to fall between 1 and 100.