Mathematical programming formulations for non-smooth and non-convex electricity dispatch problems

CFA optimizer: A new and powerful algorithm inspired by Franklin's and Coulomb's laws theory for solving the economic load dispatch problems

“…29 This case like case B is composed of 2 typical nonconvex ELD problems: type 1, an ELD problem considering only POZ constraint, and type 2, an ELD problem with considering both POZ and ramp rate limits. The results obtained for this case using CFA algorithm and also other reported algorithms in the literature such as CSO (civilized swarm optimization), 63 HBMO, 59 CIHBMO, 59 KHA-IV, 122 TL-QCP, 6 FAPSO, 41 CSA, 95 and NAPSO 41 for type 1, and PSO, 30 SOH-PSO, 30 GA, 30 MsEBBO/mut, 93 MsEBBO, 93 PSO-SIF, 38 MDE, 31 GAAPI, 25 FA, 88 CCPSO, 39 BFO, 61 NCS, 20 APSO, 47 CPSO, 36 ABC, 84 EPSO, 49 IA_EDP, 138 GABC, 82 EMA, 128 SGA, 14 and TLBO 118 for type 2 are listed in the Tables 13 and 14. It is clear from Tables 13 and 14 that the obtained results of min cost, mean cost, max cost, and SD values via the CFA algorithm are lower and more efficient compared with all the other algorithms.…”

“…[1][2][3][4] The ELD problem is a nonlinear, nonconvex, and nonsmooth optimization problem because of the characteristics of valve-point loading (VPL) effect as a result of the multivalve steam turbine, the network transmission power losses, the ramp rate limits, and the prohibited operating zones (POZ) of power generation units. [4][5][6][7][8][9][10][11][12][13][14] Classical mathematical programming techniques, such as evolutionary programming method, 15 the Hopfield artificial neural network method, 16 adaptive Hopfield neural network, 17 are used to solve the different ELD problems. These methods obtained solutions that are still far from reliable, fast, and optimum solutions.…”

An energy systems engineering approach for the design and operation of microgrids in residential applications

“…Recently, Yang et al, (2013) proposed mathematical programming-based models for the Electricity dispatch problem including detailed issue for valve point effects, multiple fuel options and transmission loss problems respectively. Their approach leads to robust and rigorous optimisation methods for these problems.…”

Opposition-based krill herd algorithm applied to economic load dispatch problem

“…Some of the classical optimization techniques such as gradient method [3], linear programming (LP) [4], nonlinear programming (NLP) [5], quadratic programming (QP) [6], base point (BP) method [7] and interior point (IP) method [8] have been applied for solving ELD problem. Very recently, Yang et al [9] presented an analytical method named quadratically constrained programming (QCP). In classical approach ELD problem is assumed to be a smooth and monotonically increasing continuous quadratic function.…”