Mixed-Integer Optimal Control with Early Branch Pruning
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Mixed-integer programming problems, particularly in hybrid systems with both continuous and discrete variables, are challenging due to their non-convex nature, leading to computationally expensive optimization processes in model predictive control, as existing methods lack efficient early termination strategies for convex relaxations.
Innovation Solution
A tailored projection step is introduced to compute a dual feasible solution estimate using a primal-dual solution estimate within the interior point method, allowing for early termination of the convex solver in the branch-and-bound method by evaluating the dual objective against a global upper bound, reducing computational effort.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If interior point method is used to solve convex relaxations in branch-and-bound, then computational reliability is improved, but computational cost increases due to lack of dual feasible solution estimate for early termination
Solution Approach 1:
The patent introduces a projection step as an intermediary mechanism that transforms a sub-optimal dual solution estimate into a dual feasible solution estimate. This projection step acts as a mediator between the interior point method iterations and the early termination criterion, enabling the use of interior point method while recovering the ability to perform early termination checks that would otherwise require dual active-set methods.
2Productivity
If dual active-set solver is used, then early termination is enabled through dual feasible solution estimate, but device complexity increases compared to interior point methods
Solution Approach 1:
The patent segments the solution process into distinct phases: interior point method iterations to generate sub-optimal dual solutions, followed by a projection step to obtain dual feasible estimates, and finally early termination checks. This segmentation allows the use of the more reliable interior point method while recovering the early termination capability through a modular projection step.
Solution Approach 2:
The projection step performs a preliminary transformation of the dual solution estimate before it is used for early termination evaluation. By pre-processing the sub-optimal dual solution through projection onto the dual feasible space, the method enables early termination checks to be performed on reliable dual feasible estimates rather than sub-optimal infeasible ones.
Data Source
AI summary
A system is controlled by solving a mixed-integer optimal control optimization problem using branch-and-bound (B&B) optimization that searches for a global optimal solution within a search space. The B&B optimization iteratively partitions the search space into a nested tree of regions, and prunes at least one region from the nested tree of regions before finding a local optimal solution for each region when a dual objective value of a projection of a sub-optimal dual solution estimate for each region into a dual feasible space is greater than an upper bound or lesser than a lower bound of the global optimal solution maintained by the B&B optimization.