A Comparative Theoretical and Computational Study on Robust Counterpart Optimization: III. Improving the Quality of...

Area of Science:

• Operations Research
• Optimization Theory
• Decision Science

Background:

• Robust optimization (RO) is often used to approximate probabilistic constraints.
• Traditional RO with a priori probability bounds is computationally efficient but yields conservative solutions.
• Approximation methods using a posteriori probability bounds offer less conservative results but are computationally intensive due to non-convex problems.

Purpose of the Study:

• To investigate the solution quality of robust optimization for probabilistic constraints.
• To propose a novel iterative method that improves solution quality.
• To combine the advantages of a priori and a posteriori probability bounds in robust optimization.

Main Methods:

• Comparative analysis of traditional RO (a priori bounds) and approximation RO (a posteriori bounds).
• Development of a novel iterative solution framework.
• Application and validation through numerical examples and planning/scheduling problems.

Main Results:

• Traditional RO is computationally efficient but conservative.
• A posteriori bound methods are less conservative but computationally demanding.
• The proposed iterative method improves solution quality without significant computational overhead.

Conclusions:

• The novel iterative framework effectively enhances the solution quality of robust optimization for probabilistic constraints.
• The method balances computational efficiency with solution conservatism.
• Demonstrated effectiveness in practical planning and scheduling applications.