Symmetric Tensor Network for Constrained Optimization
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Conventional optimization methods, such as those using LaGrange multipliers, result in constrained cost functions that are computationally expensive and can lead to imperfect solutions, excessive resource consumption, and energy wastage, particularly in problems like logistics optimization, predictive maintenance, and portfolio optimization.
Innovation Solution
A system and method utilizing an optimal tensor network configuration with symmetries, employing a Time Evolution Block Decimation (TEBD) process to generate a tensor network that satisfies constraints, and an adaptive trotter delta scheduler to optimize the objective function, transforming constrained problems into unconstrained quadratic unconstrained binary optimization (QUBO) models.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If conventional optimization methods using LaGrange multipliers are applied, then constraints can be incorporated into the objective function, but the cost function becomes computationally expensive and resource-intensive
Solution Approach 1:
The patent extracts and removes the LaGrange multipliers from the optimization formulation, transforming the constrained optimization problem into an unconstrained one using tensor network methods. This eliminates the need for complex penalty terms while maintaining constraint satisfaction through the inherent structure of the tensor network representation.
Solution Approach 2:
The patent replaces the conventional mechanical approach of using LaGrange multipliers and penalty functions with a quantum-inspired tensor network approach. This substitution uses quantum state evolution and measurement to solve optimization problems, fundamentally changing how constraints are handled from algebraic penalties to structural representations.
2Measurement precision
If conventional optimization methods are used to ensure accuracy, then constraint satisfaction is achieved, but computer resources are drained and energy is wasted
Solution Approach 1:
The patent introduces dynamic evolution of quantum states through time evolution operators to optimize the tensor network configuration. This dynamic approach allows the system to adaptively search for optimal solutions through quantum evolution, improving accuracy while reducing energy consumption compared to static conventional optimization methods.
Solution Approach 2:
The patent changes the fundamental parameters of the optimization problem by representing it as a quantum state rather than a classical cost function. This parameter transformation enables more efficient search spaces and reduces the computational energy required to achieve accurate optimization results.
3Device complexity
If tensor network methods with symmetries are applied, then computational complexity is reduced and resource usage is minimized, but the method transforms constrained problems into unconstrained formulations
Solution Approach 1:
The patent creates a universal tensor network framework that can handle both constrained and unconstrained optimization problems through a single unified approach. The same tensor network machinery handles constraint satisfaction and objective optimization simultaneously, eliminating the need for separate handling of constraints and reducing overall formulation complexity.
Data Source
AI summary
A system and method for minimizing an objective function with constraints using an optimal tensor network configuration with symmetries are provided. The system comprises a non-transitory computer-readable memory and a processor in communication with the memory storing program instructions. The program instructions, when executed by a processor, causes the processor to: receive an objective function and one or more constraints for optimization; generate a time evolution block decimation (TEBD) process based on the objective function without the one or more constraints: generate a tensor network based on the objective function with symmetries to satisfy the one or more constraints; and find the optimal tensor network that optimizes the objective function using the TEBD process. Generating the tensor network may include applying the symmetries to transform the objective function into an unconstrained quadratic unconstrained binary optimization (QUBO) model.