Planning Macro-Energy Systems and Climatic Years, A Quadratic Trust-Region Approach for Benders

Описание: Hypothalamus Artificial Intelligence, HAI, and Research Center for Advanced Decision Technologies, RCADT, a division of HAI,

Present the conference

Planning Macro-Energy Systems With Multiple Climatic Years,
A Quadratic Trust-Region Approach for Benders Decomposition.

The Benders Trust region refers to a primal stabilization technique or heuristic used to speed up the Benders Decomposition algorithm. It addresses the problem of "oscillation," where solutions in early iterations jump sharply between different regions of the feasible set, leading to slow convergence.

Core Mechanism

The method restricts the search for new solutions to a neighborhood, the "region of trust" around the currently best-known solution.

Trust Region Constraint: A constraint is added to the Benders Master Problem that limits how much variables can change from the previous iteration.

Hamming Distance: For problems with binary variables, the confidence region is typically defined using the Hamming distance to measure the number of bits reversed relative to the current solution.

Dynamic Adjustment: The radius of the confidence region adjusts based on performance: it narrows if the actual improvement is low compared to the predicted one, and it widens if the algorithm progresses well.

This conference applies Bender’s decomposition, BD, to two-stage stochastic problems for energy planning with multiple climatic years, a key problem for the design of renewable energy systems.

A BD was first developed with a simple continuous master problem, and few, but large, subproblems. Next, a trust region method, BD-TR, was developed using a quadratic constraint that is continuously adapted to further improve the algorithm.

In a quantitative case study, BD-TR accelerates BD by a factor of four to six, slightly increasing the time to solve the master problem but greatly reducing the number of iterations.

With adequate computational resources, BD-TR outperforms closed optimization if the planning covers more than six climatic years, because, thanks to distributed computing, the execution time does not increase with the number of scenarios.

In addition, the results show that BD-TR benefits from an initial heuristic solution, but its performance does not depend on it

   • Planning Macro-Energy Systems and Climatic...