| Summary: | 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 feature⁰́₄they 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 solution⁰́₄or one close to it⁰́₄for 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.
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 feature⁰́₄they 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 solutionС⁰́₄or one close to iтС⁰́₄for 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
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