Maximizing gerrymandering through ising model optimization

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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Petri Net Modeling for Ising Model Formulation in Quantum Annealing

Applied Sciences ◽

10.3390/app11167574 ◽

2021 ◽

Vol 11 (16) ◽

pp. 7574

Author(s):

Morikazu Nakamura ◽

Kohei Kaneshima ◽

Takeo Yoshida

Keyword(s):

Combinatorial Optimization ◽

Ising Model ◽

Petri Net ◽

Optimization Problems ◽

Ising Models ◽

Objective Functions ◽

Quantum Annealing ◽

Model Formulation ◽

Target Problem ◽

Straightforward Manner

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 of Outlier Rejection, with Application in WiFi Based Positioning

ICASSP 2019 - 2019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) ◽

10.1109/icassp.2019.8683807 ◽

2019 ◽

Cited By ~ 3

Author(s):

Muhammed Tahsin Rahman ◽

Shuo Han ◽

Navid Tadayon ◽

Shahrokh Valaee

Keyword(s):

Ising Model ◽

Outlier Rejection ◽

Model Formulation

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Collective Equilibrium Behaviour of Ion Channel Gating in Cell Membranes: An Ising Model Formulation

Journal of Biological Physics ◽

10.1007/s10867-007-9034-3 ◽

2007 ◽

Vol 32 (6) ◽

pp. 523-529 ◽

Cited By ~ 2

Author(s):

Rıza Erdem

Keyword(s):

Ising Model ◽

Ion Channel ◽

Cell Membranes ◽

Channel Gating ◽

Model Formulation ◽

Ion Channel Gating

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Theorems Supporting r-flip Search for Pseudo-Boolean Optimization

Modeling, Analysis, and Applications in Metaheuristic Computing ◽

10.4018/978-1-4666-0270-0.ch016 ◽

2012 ◽

pp. 286-305

Author(s):

Bahram Alidaee ◽

Gary Kochenberger ◽

Haibo Wang

Keyword(s):

Combinatorial Optimization ◽

Optimization Problems ◽

Neighborhood Search ◽

Binary Variables ◽

Preliminary Results ◽

Combinatorial Optimization Problems ◽

Neighborhood Structures ◽

Heuristic Search Methods ◽

Boolean Optimization ◽

Simple Heuristics

Modern metaheuristic methodologies rely on well defined neighborhood structures and efficient means for evaluating potential moves within these structures. Move mechanisms range in complexity from simple 1-flip procedures where binary variables are “flipped” one at a time, to more expensive, but more powerful, r-flip approaches where “r” variables are simultaneously flipped. These multi-exchange neighborhood search strategies have proven to be effective approaches for solving a variety of combinatorial optimization problems. In this paper, we present a series of theorems based on partial derivatives that can be readily adopted to form the essential part of r-flip heuristic search methods for Pseudo-Boolean optimization. To illustrate the use of these results, we present preliminary results obtained from four simple heuristics designed to solve a set of Max 3-SAT problems.

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