Table 1
The brief descriptions about employed metaheuristic algorithms
| Algorithm/population type | First proposer(s) | Operators or control parameters | Example reference | Employed technique, assigned value or formula | |
|---|---|---|---|---|---|
| GA (real-coded)/chromosomes |  | Holland (1975), Goldberg (1989) | Selection | Peltokangas & Sorsa (2008) | Tournament |
| Crossover | arithmetical crossover (Pc = 0.5) | ||||
| Mutation | Equations (3) and (4) (μ = 0.05; Pm = 0.1) | ||||
| PSO/particles |  | Kennedy & Eberhart (1995) | Acceleration coefficient | Rathore & Sharma (2017) | c1 = c2 = 2 |
| Velocity updating | Equation (5) | ||||
| Inertia weight RW | ω = 0.5 + 0.5*rand | ||||
| LDW | ω = [(itermax − t) (ωmax–ωmin)/itermax] + ωmin, t = 1,2,..,itermax | ||||
| NLDW | ωt = (ωmax − ωmin)(itermaxt)3 /itermax3 + ωmin, t = 1,2,..,itermax | ||||
| CRW | Zi = 4zi−1 (1 − zi−1), ωt = 0.5*rand + 0.5 Zi, t = 1,2,..,itermax | ||||
| DEA/chromosomes |  | Storn & Price (1997) | Mutation | Xu et al. (2012) | Equation (6) in which F = 0.5 |
| Crossover | Non-uniform crossover in which Cr = 0.5 | ||||
| Selection | Greedy criterion | ||||
| IWA/weed colony |  | Mehrabian & Lucas (2006) | Initial population | Asgari et al. (2016) | Npop, 0 = 5 |
| Production of seeds | Equation (7) in which Seedmin = 1, and Seed max = 5 | ||||
| Spread of seeds | NLDW (same as in PSO) | ||||
| Selection | Competitive exclusion (weed population size ≤ Npop) | ||||
| ABC/bee colony |  | Karaboga (2005) | Function of employed bees | Karaboga & Basturk (2008) | xneighbor = xold + Δx (similar to the use of Equations (3) and (4)) |
| Function of onlooker bees | Equation (8) | ||||
| Function of scout bees | Limit = 0.5*SN *Npar | ||||
| Algorithm/population type | First proposer(s) | Operators or control parameters | Example reference | Employed technique, assigned value or formula | |
|---|---|---|---|---|---|
| GA (real-coded)/chromosomes | | Holland (1975), Goldberg (1989) | Selection | Peltokangas & Sorsa (2008) | Tournament |
| Crossover | arithmetical crossover (Pc = 0.5) | ||||
| Mutation | Equations (3) and (4) (μ = 0.05; Pm = 0.1) | ||||
| PSO/particles | | Kennedy & Eberhart (1995) | Acceleration coefficient | Rathore & Sharma (2017) | c1 = c2 = 2 |
| Velocity updating | Equation (5) | ||||
| Inertia weight RW | ω = 0.5 + 0.5*rand | ||||
| LDW | ω = [(itermax − t) (ωmax–ωmin)/itermax] + ωmin, t = 1,2,..,itermax | ||||
| NLDW | ωt = (ωmax − ωmin)(itermaxt)3 /itermax3 + ωmin, t = 1,2,..,itermax | ||||
| CRW | Zi = 4zi−1 (1 − zi−1), ωt = 0.5*rand + 0.5 Zi, t = 1,2,..,itermax | ||||
| DEA/chromosomes | | Storn & Price (1997) | Mutation | Xu et al. (2012) | Equation (6) in which F = 0.5 |
| Crossover | Non-uniform crossover in which Cr = 0.5 | ||||
| Selection | Greedy criterion | ||||
| IWA/weed colony | | Mehrabian & Lucas (2006) | Initial population | Asgari et al. (2016) | Npop, 0 = 5 |
| Production of seeds | Equation (7) in which Seedmin = 1, and Seed max = 5 | ||||
| Spread of seeds | NLDW (same as in PSO) | ||||
| Selection | Competitive exclusion (weed population size ≤ Npop) | ||||
| ABC/bee colony | | Karaboga (2005) | Function of employed bees | Karaboga & Basturk (2008) | xneighbor = xold + Δx (similar to the use of Equations (3) and (4)) |
| Function of onlooker bees | Equation (8) | ||||
| Function of scout bees | Limit = 0.5*SN *Npar | ||||
Npop, population size; Npar, number of parameters to be calibrated; itermax, number of generation; rand, uniform random variable between [0, 1]; Pc, crossover probability; Pm, mutation probability; c, acceleration coefficient; ω, inertia weight; RW, random inertia weight; LDW, linear decreasing inertia weight; NLDW, nonlinear decreasing inertia weight; CRW, chaotic random inertia weight; CR, crossover constant in DEA; F, mutation factor in DEA; Npop 0, initial weed colony size in IWA; Seedmin, minimum number of seeds produced; Seedmin, maximum number of seeds produced; SN, number of food sources in ABC; limit, a limit value used in scout bee step of ABC.