QUBO Transformation for Combinatorial Optimization Scaling
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Solution Overview
Problem
Combinatorial optimization problems become intractable as complexity rises, leading to exponential scaling of computing resources required, making existing approaches impractical for large-scale instances.
Innovation Solution
Transforming mixed-integer linear programming (MILP) and quadratic unconstrained binary optimization (QUBO) formulations into heuristic optimization algorithms for allocation of data objects to parties using hybrid-quantum and noisy intermediate-scale quantum-ready approaches.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If exhaustive search through the problem space is used to solve combinatorial optimization problems, then optimal solutions can be found, but the computing resources required scale exponentially and become infeasible for large instances
Solution Approach 1:
The patent segments the combinatorial optimization problem into a structured mathematical formulation (objective function with discrete variables and constraints), which can then be solved using specialized algorithms rather than exhaustive search. This segmentation allows the problem to be broken down into manageable computational components that scale better.
Solution Approach 2:
The patent transforms the original combinatorial optimization problem by changing its parameters and representation into a Mixed-Integer Linear Programming (MILP) formulation. This parameter transformation enables the use of efficient MILP solvers that can handle large instances without requiring exhaustive search, thus improving computing resource efficiency while maintaining solution optimality.
2Quantity of substance
If the number of objects to be allocated increases, then the problem space grows, but the computing resources required scale exponentially beyond available resources
Solution Approach 1:
The patent segments the allocation problem into discrete decision variables representing individual object-party assignments, constrained by mathematical relationships. This segmentation allows the problem to be solved using MILP techniques that efficiently handle the combinatorial complexity even as the number of objects increases, avoiding exponential scaling of computing resources.
Solution Approach 2:
The patent replaces traditional computational approaches (brute-force enumeration, heuristic search) with a mathematical programming framework (MILP). This substitution transforms the mechanical process of searching through solution spaces into an algebraic optimization problem that can be solved efficiently using linear programming duality and branch-and-bound algorithms, enabling handling of larger problem instances.
3Productivity
If specialized approaches are used to traverse the problem space, then computing resources are reduced, but solution optimality may be compromised
Solution Approach 1:
The patent replaces heuristic and approximate traversal methods with exact mathematical optimization (MILP). This substitution ensures that specialized approaches maintain solution optimality by using rigorous mathematical algorithms (simplex method, interior-point methods, branch-and-bound) that guarantee finding the global optimum rather than relying on heuristics that may miss optimal solutions.
Solution Approach 2:
The patent incorporates feedback mechanisms through the MILP solving process, where the solver continuously evaluates candidate solutions against the objective function and constraints, using duality gaps and bounding information to guide the search. This feedback ensures that computing resources are used efficiently while maintaining solution optimality by pruning suboptimal branches and focusing computational effort on promising regions of the solution space.
Data Source
AI summary
Computer devices, systems and methods for transforming converting and evaluating high complexity computer science optimization problems using quantum and quantum inspired data transformation approaches and corresponding computer data structures are proposed, useful in specific situations, where computational complexity at scale prohibits alternative approaches, the approaches to solving the transformed problems yielding acceptable accuracy output despite a technical tradeoff in potential loss in accuracy. The transformed computer problem can then be solved using specialized quantum or quantum inspired computing architectures. The optimization problem outputs can be converted into specific data messages routed for automatically invoking downstream data processes and data subroutines.