Probable Event Constrained Optimization and A Data-embedded Solution Paradigm

TL;DR

This paper introduces Probable Event Constrained Optimization (PECO), a new optimization framework under uncertainty that guarantees feasibility for high-probability uncertain events using a data-driven solution paradigm.

Contribution

It proposes PECO as an alternative to chance constraints and develops a novel data-embedded method with data reduction for efficient solutions.

Findings

PECO guarantees feasibility for all high-probability uncertain events.

The data-embedded solution paradigm effectively reduces computational complexity.

The approach maintains high accuracy despite data reduction.

Abstract

This paper solves a new class of optimization problems under uncertainty, called Probable Event Constrained Optimization (PECO), which optimizes an objective function of decision variables and subjects to a set of Probable Event Constraints (PEC). This new type of constraint guarantees that optimal solutions are feasible for all uncertain events whose joint probabilities are greater than a user-defined threshold. The PEC can be used as an alternative to the conventional chance constraint, while the latter cannot guarantee the solution's feasibility to high-probability uncertain events. Given that the existing solution methods of optimization problems under uncertainty are not suitable for solving PECO problems, we develop a novel data-embedded solution paradigm that uses historical measurements/data of the uncertain parameters as input samples. This solution paradigm is conceptually simple and allows us to develop effective data-reduction schemes which reduce computational burden while preserving high accuracy.