Table 6: Summary of continuous-binary operator transformation.

Binarization techniques Metaheuristic Problem Reference

Boolean approachParticle swarmAntenna design problem[98, 99]
Binary problems[97]
Binary artificial bee colonyBinary problems[100]

Set-based approachParticle swarmTraveling salesman problem[103]
Multidimensional knapsack problem
Vehicle routing problem[101]
Feature selection[144]
Jumping frogsCombinatorial problems[145]
Water cycleTruss structure[146]
Mine blastTruss structure[146]
GravitationalTraveling Salesman[147]
Imperialist competitionTransmission expansion Planning[148]
Invasive weedTypical benchmark functions (Sphere, Rosenbrock, Rastrigin, Griewank)[149]
Social impact theoryPattern recognition[150]

Quantum binary approachParticle swarmCompetitive facility[151]
Location problems
Knapsack problem[108]
Power quality monitor placement method[111]
Differential evolutionKnapsack problem[151]
Combinatorial problems[113]
Image thresholding[114]
Cuckoo search0-1 knapsack problem[115]
Bin packing problem[116]
Ant colony optimizationImage thresholding[114]
Harmony search0-1 knapsack problem[117]
Monkey0-1 knapsack problem[118]

Binary method based on estimation of distributionParticle swarmKnapsack problem[120]
Differential EvolutionOptimization problems[121, 122]
GeneticEconomic dispatch problem[106]
Local searchProbabilistic traveling salesman problem[123]
MemeticProbabilistic traveling salesman problem[123]