Pareto Optimization with PARODIS

Pareto Optimization with PARODIS

Pareto optimization is about finding compromises between a number of objectives, thus it is part of multi-objective optimization. The Pareto front is the set of all Pareto optimal points. A point is called Pareto optimal, if you cannot decrease any cost function value any further without increasing at least one other. PARODIS calculates parts of the Pareto front and presents them to the user or selects one point as a solution automatically. This is done in three steps: First, the extreme points, meaning the points minimizing exactly one objective, are calculated, using Extreme point functions. Second, the extreme points are used to calculate points on the Pareto front step-by-step. This is done using Front determination schemes, methods that scalarize the multi-objective problem to a singular objective problem and find a singular Pareto optimal point. Finally, the Pareto front is either presented to the user using the Interactivity Tool or automatically selected using metrics.

Pareto Front Determination Methods

PARODIS determines Pareto fronts using two types of methods. Weighted sum methods add the weighted cost functions and minimize the sum, the resulting point is Pareto-optimal point. Boundary intersection methods generate points in the k-dimensional space and project them onto the Pareto front.

Metrics

PARODIS provides two types of metrics, knee point metrics and compromise metrics. Knee point metrics aim to find knee points on the Pareto front, meaning points that satisfy multiple possible weightings. As they fulfill multiple weights the user could choose, the possibility of fulfilling the user's choice is higher than other points. Compromise metrics select a compromise solution, the Pareto optimal point that is "most similar" to the Utopia point regarding this metric.