This paper presents a particle swarm optimization (PSO) to solve hard combinatorial constrained optimization problems such as nonconvex and discontinuous economic dispatch (ED) problem of large thermal power plants. Several measures have been suggested in the control equation of the classical PSO by modifying its operators for better exploration and exploitation. The inertia operator of the PSO is modulated by introducing a new truncated sinusoidal function. The cognitive and social behaviors are dynamically controlled by suggesting new exponential constriction functions. The overall methodology effectively regulates the velocity of particles during their flight and results in substantial improvement in the classical PSO. The effectiveness of the proposed method has been tested for economic load dispatch of three standard test systems considering various operational constraints like valve-point loading effect, prohibited operating zones (POZs), network power loss, and so forth. The application results show that the proposed PSO method is very promising. 1. Introduction The economic dispatch (ED) aims at determining the optimal scheduling of thermal generating units so as to minimize the fuel cost while satisfying several operational and power system network constraints. The generator fuel cost functions are invariably nonlinear and also exhibit discontinuities due to prohibited operating zones (POZs). In addition, the valve-point loading effect causes nonconvex characteristic with multiple minima in the generator fuel cost functions and thus imposes challenges of obtaining the global optima for high dimensional ED problems. Thus, ED is a highly nonlinear, complex combinatorial, nonconvex, and multiconstraint optimization problem with continuous decision variables. The classical mathematical methods like gradient, Lagrange relaxation methods, and so forth, except dynamic programming, are not suitable for such complex optimization problems. The modern metaheuristic search techniques such as particle swarm optimization (PSO), genetic algorithms (GAs), biogeography-based optimization (BBO), differential evolution (DE), ant colony optimization (ACO), artificial bee colony (ABC), and hybrid swarm intelligent based harmony search algorithm (HHS) [1, 2] have shown potential to solve such complex ED problems due to their ability to obtain global or near global solution but are computationally demanding especially for modern power systems which are large and complex. The PSO has several advantages over other metaheuristic techniques in terms of simplicity,
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