Mixed-Integer Optimal Control With Recurrent Prediction Correction
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Solution Overview
Problem
Current mixed-integer programming (MIP) solvers for optimal control of hybrid systems are insufficiently fast for real-time applications and suffer from high probabilities of infeasibility and scalability issues with more than 100 decision variables, limiting the applicability of MIP-based controller design.
Innovation Solution
A recurrent architecture combined with an iterative presolve-based correction method is used to predict and correct mixed-integer convex programming solutions, transforming the problem into a convex programming format to ensure feasibility and optimality, leveraging machine learning to predict discrete variables and update them to satisfy constraints efficiently.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If mixed-integer programming solvers are used to solve MIP problems to optimality, then solution accuracy is improved, but computation time increases exponentially
Solution Approach 1:
The patent applies preliminary action by using a machine learning predictor to generate initial discrete variable values before the optimization process begins. This predictor is trained offline to provide warm-start solutions that guide the branch-and-bound algorithm, reducing the search space and computation time required to reach optimal solutions in real-time control applications
Solution Approach 2:
The patent segments the solution process into two distinct phases: an offline training phase where the machine learning model is trained on historical MIP solutions, and an online execution phase where the pre-trained model provides rapid predictions. This segmentation allows computationally intensive training to be performed beforehand, enabling fast real-time solving without sacrificing solution accuracy
2Adaptability or versatility
If the number of discrete decision variables increases, then the problem modeling capability is improved, but the computational complexity increases exponentially
Solution Approach 1:
The patent replaces the traditional mechanical branch-and-bound tree search mechanism with a machine learning-based prediction system. The neural network learns patterns from historical solutions and directly predicts discrete variable values, substituting the exponential-time combinatorial search with a polynomial-time prediction process that scales better with problem size
3Productivity
If supervised learning techniques are used to predict discrete variable solutions, then solution speed is improved, but solution feasibility probability decreases
Solution Approach 1:
The patent implements feedback by using the machine learning predictor within an iterative optimization framework where predictions are evaluated against constraints and objectives. Infeasible predictions trigger corrections through the branch-and-bound algorithm, and successful solutions feed back into the training data, continuously improving the predictor's feasibility while maintaining speed advantages
Solution Approach 2:
The patent introduces the machine learning predictor as an intermediary between the problem formulation and the optimization solver. Rather than directly solving MIP or relying on pure heuristics, the predictor provides informed initial guesses that guide the optimization process, acting as a bridge that combines the speed of learning-based methods with the reliability of exact optimization
Data Source
AI summary
A controller uses a motion trajectory for controlling a motion of a device to perform a task subject to constraints. The controller evaluates a parametric function to output predicted values for a set of discrete variables in a mixed-integer convex programming (MICP) problem for performing the task defined by the parameters. The controller fixes a first subset of discrete variables in the MICP to the predicted values outputted by the trained parametric function and updates at least some of the predicted values of a remaining subset of discrete variables to values are uniquely defined by the fixed values for the first subset of discrete variables and the constraints. Hence, the controller transforms the MICP into a convex programming (CP) problem, solves the CP problem subject to the constraints to produce a feasible motion trajectory, and controls the device according to the motion trajectory.