Optimization Solver Using Dynamic Penalty Terms for Constraints
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Solution Overview
Problem
Existing optimization solvers, such as Ising machines, struggle to efficiently calculate high-quality solutions while satisfying constraint conditions and handling non-quadratic objective functions, leading to suboptimal results due to limitations in setting constraint conditions and handling function types.
Innovation Solution
An information processing device that converts optimization problems into approximate problems using penalty terms and iterative simulated bifurcation algorithms to update intermediate states, allowing for the calculation of high-quality solutions by iteratively updating intermediate states and evaluating solutions based on evaluation values.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If a strong coupling coefficient is used in the penalty term, then the probability of outputting a solution that satisfies constraint conditions increases, but the probability of outputting a high-quality solution decreases
Solution Approach 1:
The patent applies dynamics by making the coupling coefficient time-dependent rather than fixed. The coupling coefficient is dynamically adjusted during the optimization process: initially set to a large value to ensure constraint satisfaction, then gradually reduced to allow exploration of high-quality solutions. This temporal variation resolves the contradiction between constraint satisfaction and solution quality.
Solution Approach 2:
The patent changes the parameter of the coupling coefficient from a static value to a dynamic one that evolves during optimization. By transitioning the coupling coefficient from large to small over time, the system first ensures constraint satisfaction and then optimizes solution quality, resolving the trade-off between these two objectives.
2Manufacturing precision
If a weak coupling coefficient is used in the penalty term, then the probability of outputting a high-quality solution increases, but the probability of outputting a solution that satisfies constraint conditions decreases
Solution Approach 1:
The patent resolves this contradiction by dynamically adjusting the coupling coefficient. Initially, a large value ensures constraint satisfaction; as optimization progresses, the coefficient is reduced to enable discovery of high-quality solutions. This temporal dynamics allows the system to prioritize different objectives at different stages.
Solution Approach 2:
The patent applies preliminary action by first establishing strong constraint satisfaction with a large coupling coefficient before transitioning to quality optimization. This preliminary phase ensures that feasible solutions are found before the system attempts to optimize among them, preventing the loss of constraint satisfaction.
3Productivity
If an Ising machine is used to solve combinatorial optimization problems, then high-speed solution search is achieved, but the capability to set constraint conditions is limited
Solution Approach 1:
The patent introduces an intermediary approach by formulating constraint conditions as penalty terms that are integrated into the objective function. This allows the Ising machine, which natively handles quadratic objective functions, to indirectly incorporate constraints through the penalty mechanism, maintaining high-speed performance while gaining constraint capability.
Solution Approach 2:
The patent changes the approach by transforming constraint satisfaction from a direct capability into a parameter-adjustment strategy. By modifying the objective function through penalty terms with adjustable coupling coefficients, the system enables constraint handling without changing the fundamental hardware architecture, preserving speed while enhancing versatility.
4Adaptability or versatility
If an approximate problem with penalty term is formulated, then constraint conditions can be handled, but higher-order objective functions cannot be directly solved
Solution Approach 1:
The patent applies parameter changes by reducing the order of the objective function through approximation. Higher-order terms are replaced with lower-order approximations that preserve the essential optimization characteristics while being compatible with the Ising machine's quadratic form, enabling both constraint handling and higher-order function support.
Solution Approach 2:
The patent uses a disposable approximation approach where the objective function is temporarily transformed into an approximate lower-order form suitable for the Ising machine. After obtaining solutions, the approximation is discarded and the original higher-order function is evaluated to assess solution quality, allowing flexible handling of complex functions.
Data Source
AI summary
According to an embodiment, an information processing device is configured to output a solution in a target optimization problem for minimizing or maximizing a target objective function, and includes one or more hardware processors configured to: provide a solver device configured to execute a solution-finding process while iteratively updating intermediate states of a solution, with an approximate problem for minimizing or maximizing an approximate function based on the target objective function; acquire a plurality of intermediate solutions based on the intermediate states and a final solution calculated after the plurality of intermediate solutions; calculate, for each of the plurality of intermediate solutions and the final solution, an evaluation value as a solution to the target optimization problem; and output, as the solution to the target optimization problem, any selected solution selected from among the plurality of intermediate solutions and the final solution based on the evaluation value.