Covariance matrix adapted evolution strategy algorithm-based solution to dynamic economic dispatch problems

Nonconvex Dynamic Economic Power Dispatch Problems Solution Using Hybrid Immune-Genetic Algorithm

“…It is evidently observed that the obtained results with IGA algorithm is less than those of reported in literature. [17] 1019786.000 NA NA 11.25 EP-SQP [12] 1031746.000 1035748.000 NA 20.51 PSO-SQP [37] 1027334.000 1028546.000 1033986.000 16.37 DGPSO [26] 1028835.000 1030183.000 NA 15.39 MHEP-SQP [35] 1028924.000 1031179.000 NA 21.23 IPSO [27] 1023807.000 1026863.000 NA 0.06 HDE [18] 1031077.000 NA NA NA IDE [19] 1026269.000 NA NA NA ABC [8] 1021576.000 1022686.000 1024316.000 2.6029 MDE [20] 1031612.000 1033630.000 NA 12.50 CMAES [49] 1023740.000 1026307.000 1032939.000 0.63 AIS [24] 1021980.000 1023156.000 1024973.000 19.01 HHS [4] 1019091.000 NA NA 12.233 ICPSO [28] 1019072.000 1020027.000 NA 0.467 AIS-SQP [34] 1029900.000 NA NA NA SOA-SQP [36] 1021460.010 NA NA NA CS-DE [15] 1023432.000 1026475.000 1027634.000 0.24 CDE [21] 1019123.000 1020870.000 1023115.000 0.32 AHDE [50] 1020082.000 1022474.000 NA NA ECE [30] 1022271 …”

“…The obtained optimal results are compared with results of previously developed algorithms such as differential evolution (DE) [17], hybrid EP and SQP [12], Hybrid PSO-SQP [37], deterministically guided PSO (DGPSO) [26], modified hybrid EP-SQP (MHEP-SQP) [35], improved PSO (IPSO) [27], Hybrid DE (HDE) [18], Improved DE (IDE) [19], artificial bee colony algorithm (ABC) [8], modified differential evolution (MDE) [20], covariance matrix adapted evolution strategy (CMAES) [49], artificial immune system (AIS) [24], hybrid swarm intelligence based harmony search algorithm (HHS) [4], improved chaotic particle swarm optimization algorithm (ICPSO) [28], hybrid artificial immune systems and sequential quadratic programming (AIS-SQP) [34], hybrid SOA-SQP algorithm [36], chaotic sequence based differential evolution algorithm (CS-DE) [15], chaotic differential evolution (CDE) method [21], adaptive hybrid differential evolution algorithm (AHDE) [50], and enhanced cross-entropy method (ECE) [30] in Table V. The maximum iteration number is selected to be 2000. The convergence characteristic of the proposed algorithm is depicted in Fig.…”

Imperialist competitive algorithm for solving non-convex dynamic economic power dispatch

“…Table 3 shows the obtained results for 10-unit system without considering transmission losses. The minimum cost, mean cost, and maximum cost of obtained optimal results are compared with results of previously developed algorithms such as differential evolution (DE) [14], hybrid EP and SQP [10], Hybrid PSO-SQP [32], deterministically guided PSO (DGPSO) [23], modified hybrid EP-SQP (MHEP-SQP) [40], improved PSO (IPSO) [16], Hybrid DE (HDE) [41], Improved DE (IDE) [15], artificial bee colony algorithm (ABC) [21], modified differential evolution (MDE) [17], covariance matrix adapted evolution strategy (CMAES) [42], artificial immune system (AIS) [20], hybrid swarm intelligence based harmony search algorithm (HHS) [3], improved chaotic particle swarm optimization algorithm (ICPSO) [43], hybrid artificial immune systems and sequential quadratic programming (AIS-SQP) [27], hybrid SOA-SQP algorithm [28], chaotic sequence based differential evolution algorithm (CS-DE) [12], chaotic differential evolution (CDE) method [18], adaptive hybrid differential evolution algorithm (AHDE) [31], and enhanced cross-entropy method (ECE) [25] in Table 4. The maximum iteration number and number of trails are selected to be 200 and 100, respectively.…”

Gravitational search algorithm-based dynamic economic dispatch by estimating transmission system losses using A-loss coefficients

“…This mechanical constraint is translated into limits on the rate of increase of the electrical output and is known as the ramp rate limit, which is vital in solving the dynamic economic dispatch (DED) problem [1]. Therefore, the DED is an extension of the conventional ED problem in which ramp rate limits of generating units are taken into account [2,3].…”

“…In the literature, various heuristic optimization algorithms are proposed to solve the DED problem with * Correspondence: malanisuryakumaran@gmail.com a nonsmooth cost function [3,4,[6][7][8][9][10][11][12][13][14][15][16][17]. Heuristic algorithms do not guarantee the global optima.…”