Adaptive Nonconvex Optimization for Real-Time System Control
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Solution Overview
Problem
Existing optimization methods struggle with nonconvex systems, which are nonlinear and have multiple extrema, saddle points, and require a priori problem structure knowledge, leading to challenges like premature termination and numerical instability.
Innovation Solution
A system and method that combines grid search and random search to optimize nonconvex functions without requiring a priori knowledge, using Monte Carlo methods to increase the likelihood of finding global extrema, and employs a gradient-free approach to handle non-differentiable systems.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If gradient-based optimization methods are used for nonconvex systems, then optimization speed may be improved, but numerical instability and premature termination occur due to multiple extrema and saddle points
Solution Approach 1:
The patent replaces gradient-based mechanical optimization methods with a probabilistic sampling approach (Monte Carlo method). Instead of using gradient descent that relies on continuous derivatives and can get trapped in local minima, the system uses random sampling to explore the solution space, evaluating the objective function at randomly generated points and selecting the best solution found. This substitution eliminates numerical instability from gradient calculations while maintaining optimization capability.
2Measurement precision
If a priori problem structure knowledge is required for optimization, then convergence to optimal solution may be improved, but adaptability to new systems is reduced
Solution Approach 1:
The optimization system performs self-service by automatically adapting to different nonconvex systems without requiring pre-configured problem structure knowledge. The Monte Carlo method inherently handles any objective function by simply evaluating it at random points and selecting the best result. The system self-adjusts to the specific characteristics of each problem through the random sampling process, eliminating the need for manual configuration or domain-specific optimization algorithms.
Solution Approach 2:
The patent creates a universal optimization framework that can handle any nonconvex system regardless of its specific structure or characteristics. The Monte Carlo approach is problem-agnostic, working with any objective function that can be evaluated, making the system versatile across different applications without requiring problem-specific knowledge or customization.
3Stability of the object's composition
If deterministic optimization methods are used, then reproducibility is improved, but ability to handle non-differentiable systems is reduced
Solution Approach 1:
The patent substitutes deterministic gradient-based methods with a probabilistic Monte Carlo approach that uses random sampling instead of derivative calculations. This replacement allows the system to handle non-differentiable objective functions while maintaining reproducibility through controlled random seed initialization. The probabilistic nature does not compromise reproducibility because the same random seed produces the same sequence of random numbers and thus the same optimization results.
Data Source
AI summary
Systems and methods for adaptively optimizing a performance function for a system. In one embodiment, an apparatus is configured to select an independent variable that determines an operating state of the system described by the performance function being discontinuous, establish a range of values for the independent variable from data from the system, select a set of random values within the range of values for the independent variable, and evaluate the performance function with the set of random values for the independent variable to provide extrema results for the performance function. The apparatus is further configured to optimize the performance function by selecting a value for the independent variable from the set of random values that provides an extremum result from the extrema results to produce an optimized performance function, and utilize the optimized performance function to control the system in response to real-time data from the system.