Heuristic Method for Identifying Concave Pareto Frontiers in Multi-Objective Dynamic Programming Problems

摘要

Aerospace engineers and analysts tasked with informing system-level decisions commonly seek to identify the frontier of Pareto-optimal solutions with respect to objectives of interest. For problems in which decisions are made over multiple stages or periods, dynamic programming can be an efficient and effective method for identifying such a Pareto frontier. To employ traditional dynamic programming, however, a single objective function must be defined. Aggregation of multiple objectives into a single objective using traditional simple additive weighting has the limitation of permitting identification of only points on convex portions of the Pareto frontier. This can translate into detection of a frontier with significant and misleading gaps. This paper proposes a theory-motivated aggregation function modification and method to improve the ability of dynamic programming procedures to detect concave portions of Pareto frontiers in multi-objective, multistage problems. Following a theoretical motivation and method definition, a military aircraft route planning example is provided to illustrate the method's accuracy and efficiency.