Ising Model Formulation of Outlier Rejection, with Application in WiFi Based Positioning

Quantum annealing is an emerging new platform for combinatorial optimization, requiring an Ising model formulation for optimization problems. The formulation can be an essential obstacle to the permeation of this innovation into broad areas of everyday life. Our research is aimed at the proposal of a Petri net modeling approach for an Ising model formulation. Although the proposed method requires users to model their optimization problems with Petri nets, this process can be carried out in a relatively straightforward manner if we know the target problem and the simple Petri net modeling rules. With our method, the constraints and objective functions in the target optimization problems are represented as fundamental characteristics of Petri net models, extracted systematically from Petri net models, and then converted into binary quadratic nets, equivalent to Ising models. The proposed method can drastically reduce the difficulty of the Ising model formulation.

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Ising Model Formulation for Job-Shop Scheduling Problems Based on Colored Timed Petri Nets

Intelligent Computing & Optimization - Lecture Notes in Networks and Systems ◽

10.1007/978-3-030-93247-3_54 ◽

2022 ◽

pp. 546-554

Author(s):

Kohei Kaneshima ◽

Morikazu Nakamura

Keyword(s):

Ising Model ◽

Petri Nets ◽

Job Shop ◽

Job Shop Scheduling ◽

Scheduling Problems ◽

Model Formulation ◽

Timed Petri Nets ◽

Shop Scheduling

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Maximizing gerrymandering through ising model optimization

Scientific Reports ◽

10.1038/s41598-021-03050-z ◽

2021 ◽

Vol 11 (1) ◽

Author(s):

Yasuharu Okamoto

Keyword(s):

Combinatorial Optimization ◽

Ising Model ◽

Model Optimization ◽

Model Formulation ◽

Binary Variables ◽

Electoral District

AbstractBy using the Ising model formulation for combinatorial optimization with 0–1 binary variables, we investigated the extent to which partisan gerrymandering is possible from a random but even distribution of supporters. Assuming that an electoral district consists of square subareas and that each subarea shares at least one edge with other subareas in the district, it was possible to find the most tilted assignment of seats in most cases. However, in cases where supporters' distribution included many enclaves, the maximum tilted assignment was usually found to fail. We also discussed the proposed algorithm is applicable to other fields such as the redistribution of delivery destinations.

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