A Biologically Inspired Modified Flower Pollination Algorithm for Solving Economic Dispatch Problems in Modern Power Systems Hari Mohan Dubey • Manjaree Pandit • B. K. Panigrahi Received: 30 September 2014 / Accepted: 23 February 2015 Ó Springer Science+Business Media New York 2015 Abstract Gradient-based traditional algorithms fail to locate optimal solutions for real-world problems with non-differentiable/discontinuous objective functions. But biologically inspired optimization algorithms, due to their unconventional random search capability, provide good solutions within finite time to multimodal and non-convex problems. The search capability of these methods largely depends on their exploration and exploitation potential. This paper presents a modified flower pollination algorithm (MFPA) in which (1) the local pollination of FPA is con- trolled by a scaling factor and (2) an intensive exploitation phase is added to tune the best solution. The effectiveness of MFPA is tested on some mathematical benchmarks and four large practical power system test cases. Keywords Modified flower pollination algorithm (MFPA)  Intensive exploitation phase  Biologically inspired (BI) techniques  Le ´vy flight  Ramp rate limits (RRL)  Prohibited operating zones (POZ)  Valve point loading (VPL) effects Introduction During the last two decades, researchers have focussed their attention toward developing biologically inspired optimization algorithms for solving complex real-world problems. As a result, many new algorithms have come into existence taking inspiration from birds, insects, fish bacteria, ants, and some natural phenomenon such as evolution, gravity. The performance of these population- based random search algorithms depends on their ability to maintain population diversity during the search. The first generation of these methods suffered from premature convergence problems which were later corrected by im- proved algorithms designed to maintain a good balance between exploration and exploitation during the iterative search. The new research in this area addresses these issues by providing two separate phases for carrying out these tasks. Economic dispatch (ED) is one of the key optimization issues of modern power system operation [1]. The objec- tive is to adjust the power output of all committed gener- ating units such that the total fuel cost is minimized and load demand and other operational constraints are met. The ED problem is very complex to solve due to its massive dimension, a nonlinear objective function, and a large number of equality and inequality constraints. Significant cost saving can be achieved if the scheduling of committed generating units is carried out optimally. Over the years, the ED problem has received immense research focus due to its practical relevance and simple implementation. The conventional methods fail to solve this problem with practical constraints such as ramp rate limits (RRL), prohibited operating zones (POZ), valve point loading (VPL) effects. Therefore, a large number of bio-inspired techniques starting with improved evolution- ary programming (EP) [2] and particle swarm optimization (PSO) [3–6] were proposed. Recently, many new biologically inspired (BI) optimization algorithms are de- veloped; simultaneously, many improved variants of ex- isting BI algorithms are also being proposed. Prominent H. M. Dubey  M. Pandit (&) Department of Electrical Engineering, Madhav Institute of Technology and Science, Gwalior, M.P., India e-mail: manjaree_p@hotmail.com B. K. Panigrahi Department of Electrical Engineering, Indian Institute of Technology, Hauz Khas, New Delhi, India 123 Cogn Comput DOI 10.1007/s12559-015-9324-1