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Research Questions

  1. How can conducting optimization under conditions of uncertainty be done with less-severe limitations to restrict how uncertainties can be factored in?
  2. How can one find the optimal solution to a problem that has a large number of decision variables, uncertain parameters, and uncertain scenarios?

This paper describes a new approach to a very difficult process of optimization under uncertainty. This approach is to find the optimal solution to a problem by designing a number of search algorithms or schemes in a way that allows analysts to apply to a problem that contains a significantly larger number of decision variables, uncertain parameters, and uncertain scenarios than analysts have had to contend with until now. The specific purpose of this paper is to convert a provisional patent application entitled Portfolio Optimization by Means of a Ranking and Competing Search by the author into a published volume available for public use.

This approach and its associated search algorithms have a key feature — they generate typically 10,000 uncertain scenarios according to their uncertainty distribution functions. While each of these scenarios is a point in the larger uncertainty space, the originally uncertain parameters are specified for the scenario and are, thereby, "determined" or "certain." Thus, the solvable mixed-integer linear programming model can be used "under certainty" (i.e., deterministically) to find the optimal solution for that scenario. Doing this for numerous scenarios provides a great deal of knowledge and facilitates the search for the optimal solution — or one close to it — for the larger problem under uncertainty. Thus, this approach allows one to avoid the impossible task of performing millions or trillions of searches to find the optimal solution for each scenario, yet enables one to gain just as much knowledge as if one were doing so.

Key Findings

Transparent Reasoning Is Used to Design the Search Schemes

  • The approach is to use transparent reasoning, as opposed to mathematical formulas, to design search schemes or algorithms to find the global optimum and not get trapped at one of the local optima.
  • This approach relies on arguments from devil's advocates to uncover the shortcomings of an algorithm in terms of why under certain situations it will not lead to the global optimum.

These Reasonable Search Algorithms Are Easy to Understand

  • Implementing search algorithms amounts to creating a flow chart and does not require the use of complicated mathematics or formulas; as a result, the approach allows for adoption by analysts and organizations that possess different skill sets. This approach based on reasoning rather than mathematics can open a new way for drawing in talents from the nonmathematical world to devise search schemes to tackle this very difficult task of optimization under uncertainty. Experience with this approach has been good.
  • Each of the algorithms developed in this paper takes minutes or hours to find the optimal solution.
  • The research behind this new search approach and the multiple algorithms that go with it was conducted as part of a series of previously released RAND studies by Brian G. Chow, Richard Silberglitt, Scott Hiromoto, Caroline Reilly and Christina Panis: Toward Affordable Systems II: Portfolio Management for Army Science and Technology Programs Under Uncertainties (2011) and Toward Affordable Systems III: Portfolio Management for Army Engineering and Manufacturing Development Programs (2012).

Table of Contents

  • Chapter One

    Introduction

  • Chapter Two

    Technical Description

  • Chapter Three

    Applications of the Approach in Past Studies

  • Chapter Four

    Overview of the Approach and Suggestions for Expanding Its Use

  • Appendix

    Embodiments of Computer Resources Used in Portfolio Optimization by Means of Multiple Certainty-Uncertainty Searches

The research described in this report was conducted as part of a series of previously released RAND studies carried out in RAND Arroyo Center and the RAND National Defense Research Institute (NDRI).

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