Often optimization problems involve multiple objectives such as maximizing performance while minimizing risk. These types of problems require you to analyze the performance gains against the risk involved. OptQuest's multi-objective support gives you the information you need to make that analysis.
OptQuest supports three types of multi-objective:
A weighted multi-objective where each sub-objective is assigned a weight. When calculating the value of the multi-objective, each sub-objective is multiplied by its weight.
A goal multi-objective where you specify a range of acceptable values for the each sub-objective. OptQuest searches for solutions that give sub-objective values within the specified range. When the sub-objectives are combined as the multi-objective, solutions that are closest to all the sub-objective ranges are the best solutions. Weights can also be added to the sub-objectives to indicate the relative importance of each objective.
A pattern frontier multi-objective finds the set of solutions that are optimal, rather than a single "optimal" solution. When the solutions are plotted in a graph, the points on the pattern frontier points are the solutions for which there is no other solution in this set of solutions in which a trade-off would be considered better by giving up something to gain something else. The pattern frontier provides decision points similar to the efficient frontier but the user doesn't need to define the decision points. Rather the OptQuest Engine searches for the points. The chart below shows results of a pattern frontier multi-objective optimization that minimized investment and maximized NPV.
