Multilevel Optimization with Bounded Rationality
Abstract
Multilevel optimization is a framework for modeling optimization problems in which multiple decision-makers (DMs) with possibly competing objectives make a sequence of decisions, each of which affects the options available for decisions later in the sequence. Such optimization models have found wide application, particularly in military contexts, but the traditional frameworkhas been developed based on an underlying assumption of rationality and complete information. Computationally, this means that each DM~s action is assumed to be the result of solving an optimization model. While this assumption may seem natural, it has two major drawbacks. The first derives from the well-known notion that human beings, while often intending to be rational in their decision-making, have limited cognitive abilities, and do not always make ~optimal~ decisions, even in the face of complete information. The second and equally important drawback is that the rationality assumption often leads to intractable models, even in very simple cases, e.g., when possible actions involve discrete decisions. The framework of bounded rationality explicitly recognizes that human decision-makers use heuristics rather than exact optimization in determining courses of action. We propose to develop aframework for incorporating bounded rationality into the analysis of multilevel optimization problems. The goal is both to improve the tractability of the resulting models and to take a more realistic view of the decision-making process, which may be limited either by a lack of complete information or by an inability to perform an exact optimization. Our focus is primarily on bilevel optimization problems in which a leader acts first and a follower reacts. From a computationalstandpoint, the goal is to determine the leader~s course of action, given her knowledge of the follower~s decision making process. We also propose to study several applications of such models in a range of areas, including applications of future naval interest, such as defender-attacker, interdiction, and decentralized resource allocation. The overall goal of this work is to develop and implement algorithms for solving multilevel optimization problems with bounded rationality and to deploy the resulting software in real-world applications. We propose to develop a formal framework for studying multilevel models in which the decision-makers employ inexact decision-making processes (e.g., heuristics). This approach requires a much more formal notion of ~heuristic~ than is usually required in practice since the heuristic decision-making process must be modeled precisely using either a mathematical programming approach or a well-defined black box algorithm.The outcomes of this project will be (1) a conceptual framework for modeling these competitive decision-making processes, (2) a computational framework for determining their outcome under a variety of assumptions, (3) in-depth studies of applications in which these models are necessary for obtaining realistic and tractable models, (4) the testing of the methodology against alternatives, such as exact optimization, and (5) the publishing of the results in the open literature with accompanying open-source software. The optimization software we develop will be made available to the OR community through the open-source COIN-OR repository.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- May 23, 2019
- Source ID
- N000141912330
Entities
People
- Theodore Ralphs
Organizations
- Lehigh University
- Office of Naval Research
- United States Navy