QUBO Solver State Generation for Combinatorial Optimization
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Solution Overview
Problem
Existing combinatorial optimization problems, such as packing and scheduling, face difficulties in accurately expressing constraint conditions like item shapes and positions using Quadratic Unconstrained Binary Optimization (QUBO), leading to inefficient solution finding with Ising machines.
Innovation Solution
A data processing device generates states for items based on their positions and calculates evaluation functions for pairs, forming an Ising-type objective function with cost terms that sum evaluation values, allowing a QUBO solver to efficiently find solutions by focusing on item combinations and constraints.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If direct QUBO expression is used for complex combinatorial optimization problems, then the problem can be solved, but the formulation becomes difficult and processing time increases
Solution Approach 1:
The patent divides the complex combinatorial optimization problem into smaller sub-problems by considering only pairs of items at a time. The evaluation function is calculated for each pair of items based on their positions, and these pair-wise evaluations are summed to form the total cost term in the QUBO formulation. This segmentation makes the problem formulation easier and reduces processing complexity.
Solution Approach 2:
The patent introduces an intermediary evaluation function that serves as a mediator between the item positions and the QUBO objective function. Instead of directly formulating the complex problem in QUBO, the evaluation function first computes pairwise interaction costs, which then serve as coefficients in the QUBO Hamiltonian. This intermediary step simplifies the overall formulation process.
2Measurement precision
If detailed constraint conditions like item shapes and positions are accurately expressed in QUBO, then solution accuracy improves, but device complexity and formulation difficulty increase
Solution Approach 1:
The patent applies local quality by focusing on pairwise interactions between items rather than global constraints. The evaluation function calculates costs based on the positions of specific pairs of items, allowing different pairs to have different interaction strengths. This localized approach captures essential constraint information without requiring complex global formulations.
3Reliability
If comprehensive state combinations are considered in QUBO, then solution optimality improves, but processing cost and time increase
Solution Approach 1:
The patent uses partial action by considering only the necessary pairwise interactions to define the cost structure, rather than enumerating all possible state combinations explicitly. The QUBO formulation naturally handles the search through state space using the pairwise interaction terms, achieving good solutions without the computational burden of exhaustive search.
Data Source
AI summary
A recording medium storing a program for causing a computer to execute: acquiring information indicating a problem of arranging a plurality of items in a predetermined region; generating, for each of the plurality of items, a plurality of states according to a position at which the item is arranged in the area based on the information; specifying pairs of two items included in the plurality of items, and calculating an evaluation function indicating an evaluation value according to a combination of states of the two items in the specified pairs; generating, for combinations of the states of the plurality of items, an Ising-type objective function including a cost term indicating a sum of the evaluation values of each of the pairs indicated by the evaluation function; and acquiring a solution that corresponds to the problem by using a search unit that searches for the solution based on the objective function.