Nonconvex/nonsmooth economic load dispatch using modified time‐varying particle swarm optimization

Abstract

In this paper, a modified time‐varying particle swarm optimization (MTVPSO) is proposed for solving nonconvex economic load dispatch problems. It is a variant of the traditional particle swarm optimization (PSO) algorithm. In an MTVPSO, novel acceleration coefficients for cognitive and social components are presented as linear time‐varying parameters in the velocity update equation of the PSO algorithm. In the early stages of the optimization process, it improves the global search capability of particles and directs the global optima at the end stage. Additionally, a linearly decreased inertia weight is introduced in an MTVPSO, instead of a fixed constant value, which helps improve the diversity of the population. Through this modification mechanism in PSO, the proposed algorithm has a higher probability of avoiding local optima, and it is likely to find global optima more quickly. Six complex benchmark functions have been used to validate the effectiveness of the proposed algorithm. Furthermore, to demonstrate its efficiency, feasibility, and fastness, six different cases (3‐, 6‐, 13‐, 15‐, and 40‐unit systems and one large‐scale Korean power 140‐unit system) of the economic load dispatch problem are solved by an MTVPSO. The results of the proposed algorithm have been compared with state‐of‐the‐art algorithms. It was found that the proposed MTVPSO can deliver better results in terms of solution quality, convergence characteristics, and robustness.

An advanced hybrid meta-heuristic algorithm for solving small- and large-scale engineering design optimization problems

“…The results produced by proposed algorithms on above considered different test systems of ELD problem are compared with other state-of-the-art algorithms. These compared algorithms are listed as follows: PSO [2], DE [9], GA [10], MTVPSO [28], IPSO [29], MPSO-TVAC [30], IPSO-TVAC [31], θ-PSO [32], MPSO [33], DEPSO [38], DPD [39], THS [57], MGSO [58], EHM [59], BCO [60], NCS [61], IABC [62] and c d e TSys-5 (140-unit) 0 1 00 200 3 00 400 5 00 600 7 00 800 9 00 1000 DHS [63]. In order to check the efficiency of the proposed algorithms aDE, aPSO and haDEPSO, least values of population size (30), maximum number of iterations (1000) and independent runs (30) have been considered among compared algorithms.…”

“…Therefore, accelerating convergence speed and avoiding local optimal solutions are two critical issues in PSO. To overcome such issues many modified PSO are proposed in the literature such as HEPSO [22], RPSOLF [23], CPSO [24], IPSO [25], QPSO [26], PSO-OPS [27], MTVPSO [28], IPSO [29], MPSO-TVAC [30], IPSO-TVAC [31], θ-PSO [32] and MPSO [33]. Furthermore, hybrid strategy is one of the main research directions to improve the performance of single algorithm.…”

An innovative hybrid algorithm to solve nonconvex economic load dispatch problem with or without valve point effects

“…The results produced by proposed algorithms on above considered different test systems of ELD problem are compared with other state‐of‐the‐art algorithms. These compared algorithms are listed as follows: PSO, 2 GA, 26 DE, 27 MTVPSO, 63 THS, 150 MGSO, 151 IPSO, 152 EHM, 153 BCO, 154 NCS, 155 MPSO‐TVAC, 156 IPSO‐TVAC, 157 𝜽‐PSO, 158 DEPSO, 159 DPD, 160 MPSO, 161 IABC, 162 and DHS 163 . In order to check the efficiency of the proposed nPSO, nDE, and i h PSODE algorithms, parameters such as population size (30), stopping criteria (maximum number of iterations 100), and independent run (30) are set the same or minimum of comparative algorithms, for fair comparison.…”

Non-convex Dynamic Economic Dispatch Using an Innovative Hybrid Algorithm

“…Therefore, accelerating the convergence speed and avoiding the local optimal solutions are two critical issues in PSO. To overcome such issues many different modifications of the PSO proposed in the recent-past literature [12][13][14][15][16][17][18][19][20][21][22][23]. The characteristics, advantages, disadvantages with application of these techniques are presented below in brief.…”