QGA (Quantum Genetic Algorithm) R package
This package allows the application of the Quantum Genetic Algorithm that was first proposed by Han and Kim in 2000.
In this package, each optimization problem is represented as a maximization one, where each solution is a sequence of (qu)bits. Following the quantum paradigm, these qubits are in a superposition state: when measuring them, they collapse in a 0 or 1 state. After measurement, the fitness of the solution is calculated as in usual genetic algorithms.
The evolution at each iteration is oriented by the application of two quantum gates to the amplitudes of the qubits:
- a rotation gate (always);
- a Pauli-X gate (optionally).
The rotation is based on the theta angle values: higher values allow a quicker evolution, and lower values avoid local maxima.
The Pauli-X gate is equivalent to the classical mutation operator and determines the swap between alfa and beta amplitudes of a given qubit.
The package has been developed in such a way as to permit a complete separation between the “engine”, and the particular problem subject to combinatorial optimization. So far, three specific problems have been implemented, namely:
- best stratification of a sampling frame;
- traveler salesman problem;
- knapsack problem.
In the “inst/docs” folder, the corresponding examples of applications are contained:
- BestStratificationExample.R
- TravelerSalesmanExample.R
- KnapsackProblemExample.R
Once installed the package, after executing
devtools::install_github("barcaroli/QGA")they can be run, and their results analyzed.
In particular, QGA can be compared with the traditional genetic algorithm.
In the case of the best stratification, QGA is compared with the GA implemented in the package “SamplingStrata”. It can be verified that QGA converges to a convenient solution more rapidly than SamplingStrata.
In the other cases, QGA is compared with the GA implemented in the “genalg” package. QGA is more rapidly converging to a good solution in the knapsack problem, while the opposite is in the case of the traveler salesman.
Reference
Kuk-Hyun Han and Jong-Hwan Kim, “Genetic quantum algorithm and its application to combinatorial optimization problem,” Proceedings of the 2000 Congress on Evolutionary Computation. CEC00 (Cat. No.00TH8512), 2000, pp.1354-1360 vol.2, doi: 10.1109/CEC.2000.870809.