Evolutionary simplex adaptive Hooke-Jeeves algorithm for economic load dispatch problem considering valve point loading effects

Abstract Economic load dispatch problems are most important in operation and management of the electric power systems which are formulated as optimization problems. Modern deterministic and stochastic optimization techniques are efficient in solving economic load dispatch problems without any limitation because of their capability to seek the global optimal solution. Economic load dispatch problems involve linear equality constraints which are difficult to handle along with discontinuous, non-differentiable and highly non-linear objective functions. The problem becomes challenging for optimization techniques, especially for deterministic methods. This study presents a new approach based on a hybrid algorithm consisting of Genetic algorithm and modified Hooke and Jeeves method to solve the economic load dispatch problems with equality constraints. The performance of proposed Algorithm is tested on five generating systems with valve-point effects. Test results of proposed technique are quite promising and effective, with good convergence property and generation cost to produce better quality solution compared with several state-of-the-art methods.

[1]  Provas Kumar Roy,et al.  Grey wolf optimization applied to economic load dispatch problems , 2016 .

[2]  Cheng-Chien Kuo,et al.  A novel string structure for economic dispatch problems with practical constraints , 2008 .

[3]  Abderrahim Belmadani,et al.  Hooke-Jeeves' Method Applied to a New Economic Dispatch Problem Formulation , 2008, J. Inf. Sci. Eng..

[4]  Hossein Nezamabadi-pour,et al.  A modified particle swarm optimization for economic dispatch with non-smooth cost functions , 2010, Eng. Appl. Artif. Intell..

[5]  Waree Kongprawechnon,et al.  Ant colony optimisation for economic dispatch problem with non-smooth cost functions , 2010 .

[6]  Alireza Lorestani,et al.  Optimization of single and multi-areas economic dispatch problems based on evolutionary particle swarm optimization algorithm , 2018, Energy.

[7]  M. Rafiee,et al.  Species-based Quantum Particle Swarm Optimization for economic load dispatch , 2014 .

[8]  Sishaj P. Simon,et al.  Maclaurin series-based Lagrangian method for economic dispatch with valve-point effect , 2009 .

[9]  Malabika Basu,et al.  Kinetic gas molecule optimization for nonconvex economic dispatch problem , 2016 .

[10]  Nima Amjady,et al.  Solution of non-convex economic dispatch problem considering valve loading effect by a new Modified Differential Evolution algorithm , 2010 .

[11]  Abu S. S. M. Barkat Ullah,et al.  Handling equality constraints in evolutionary optimization , 2012, Eur. J. Oper. Res..

[12]  Ajit Kumar Barisal,et al.  Comparative analysis of optimal load dispatch through evolutionary algorithms , 2015 .

[13]  Dinu Calin Secui,et al.  A modified Symbiotic Organisms Search algorithm for large scale economic dispatch problem with valve-point effects , 2016 .

[14]  A. Ebenezer Jeyakumar,et al.  Hybrid PSO–SQP for economic dispatch with valve-point effect , 2004 .

[15]  Hao Yin,et al.  An efficient crisscross optimization solution to large-scale non-convex economic load dispatch with multiple fuel types and valve-point effects , 2016 .

[16]  Mojtaba Ghasemi,et al.  A new solution to the non-convex economic load dispatch problems using phasor particle swarm optimization , 2019, Appl. Soft Comput..

[17]  Ismail H. Altas,et al.  A novel modified hybrid PSOGSA based on fuzzy logic for non-convex economic dispatch problem with valve-point effect , 2015 .

[18]  M. Madrigal,et al.  An analytical solution to the economic dispatch problem , 2000 .

[19]  Frank L. Lewis,et al.  Dynamic formulation and approximation methods to solve economic dispatch problems , 2013 .

[20]  Chandan Kumar Chanda,et al.  Teaching learning based optimization for economic load dispatch problem considering valve point loading effect , 2015 .

[21]  Yang Wang,et al.  Dynamic Economic Dispatch Considering Transmission Losses Using Quadratically Constrained Quadratic Program Method , 2013, IEEE Transactions on Power Systems.

[22]  Waree Kongprawechnon,et al.  Application of multiple tabu search algorithm to solve dynamic economic dispatch considering generator constraints , 2008 .

[23]  Sang-Bong Rhee,et al.  Jaya Algorithm With Self-Adaptive Multi-Population and Lévy Flights for Solving Economic Load Dispatch Problems , 2019, IEEE Access.

[24]  Sishaj P. Simon,et al.  Dynamic economic dispatch using Maclaurin series based Lagrangian method , 2010 .

[25]  S. Khamsawang,et al.  DSPSO–TSA for economic dispatch problem with nonsmooth and noncontinuous cost functions , 2010 .

[26]  Katya Scheinberg,et al.  Introduction to derivative-free optimization , 2010, Math. Comput..

[27]  Ajit Kumar Barisal,et al.  Large scale economic dispatch of power systems using oppositional invasive weed optimization , 2015, Appl. Soft Comput..

[28]  Zwe-Lee Gaing,et al.  Particle swarm optimization to solving the economic dispatch considering the generator constraints , 2003 .

[29]  P. K. Chattopadhyay,et al.  Evolutionary programming techniques for economic load dispatch , 2003, IEEE Trans. Evol. Comput..

[30]  Nazir Ahmad,et al.  SOLUTION OF WAR PLANNING PROBLEM USING DERIVATIVE FREE METHODS , 2015 .

[31]  G. Sheblé,et al.  Genetic algorithm solution of economic dispatch with valve point loading , 1993 .

[32]  Dinu Calin Secui,et al.  A new modified artificial bee colony algorithm for the economic dispatch problem , 2015 .

[33]  Ze Dong,et al.  A General Intelligent Optimization Algorithm Combination Framework with Application in Economic Load Dispatch Problems , 2019, Energies.

[34]  Ling Wang,et al.  An effective differential harmony search algorithm for the solving non-convex economic load dispatch problems , 2013 .

[35]  Jan K. Sykulski,et al.  A hybrid GA–PS–SQP method to solve power system valve-point economic dispatch problems , 2010 .

[36]  Robert Hooke,et al.  `` Direct Search'' Solution of Numerical and Statistical Problems , 1961, JACM.

[37]  T. Jayabarathi,et al.  Economic dispatch using hybrid grey wolf optimizer , 2016 .

[38]  A. Srinivasa Reddy,et al.  Shuffled differential evolution for economic dispatch with valve point loading effects , 2013 .

[39]  Ebrahim Babaei,et al.  ECONOMIC LOAD DISPATCH USING ?-PSO , 2013 .

[40]  P. Subbaraj,et al.  Parallel particle swarm optimization with modified stochastic acceleration factors for solving large scale economic dispatch problem , 2010 .

[41]  Bijaya K. Panigrahi,et al.  Economic load dispatch solution by improved harmony search with wavelet mutation , 2011, Int. J. Comput. Sci. Eng..

[42]  Whei-Min Lin,et al.  Combining of Direct Search and Signal-to-Noise Ratio for economic dispatch optimization , 2011 .

[43]  P. K. Chattopadhyay,et al.  Solving complex economic load dispatch problems using biogeography-based optimization , 2010, Expert Syst. Appl..

[44]  Mimoun Younes,et al.  Optimal Power Flow Based on Hybrid Genetic Algorithm , 2007, J. Inf. Sci. Eng..

[45]  Juan R. Velasco,et al.  Optimisation of control parameters for genetic algorithms to test computer networks under realistic traffic loads , 2011, Appl. Soft Comput..

[46]  Xin-She Yang,et al.  Economic dispatch using chaotic bat algorithm , 2016 .

[47]  Z. Dong,et al.  Quantum-Inspired Particle Swarm Optimization for Valve-Point Economic Load Dispatch , 2010, IEEE Transactions on Power Systems.

[48]  H. Barati,et al.  An efficient hybrid MPSO-GA algorithm for solving non-smooth/non-convex economic dispatch problem with practical constraints , 2016, Ain Shams Engineering Journal.

[49]  Leandro dos Santos Coelho,et al.  An efficient cultural self-organizing migrating strategy for economic dispatch optimization with valve-point effect , 2010 .

[50]  Anping Lin,et al.  Multi-Leader Comprehensive Learning Particle Swarm Optimization with Adaptive Mutation for Economic Load Dispatch Problems , 2018, Energies.

[51]  E. Kyriakides,et al.  A GA-API Solution for the Economic Dispatch of Generation in Power System Operation , 2012, IEEE Transactions on Power Systems.

[52]  P. K. Chattopadhyay,et al.  Hybrid Differential Evolution With Biogeography-Based Optimization for Solution of Economic Load Dispatch , 2010, IEEE Transactions on Power Systems.

[53]  J.G. Vlachogiannis,et al.  Economic Load Dispatch—A Comparative Study on Heuristic Optimization Techniques With an Improved Coordinated Aggregation-Based PSO , 2009, IEEE Transactions on Power Systems.

[54]  Joong-Rin Shin,et al.  A particle swarm optimization for economic dispatch with nonsmooth cost functions , 2005, IEEE Transactions on Power Systems.

[55]  Tomonobu Senjyu,et al.  Solving economic load dispatch problem with valve-point effects using a hybrid quantum mechanics inspired particle swarm optimisation , 2011 .

[56]  Bijaya Ketan Panigrahi,et al.  Adaptive particle swarm optimization approach for static and dynamic economic load dispatch , 2008 .

[57]  Taher Niknam,et al.  Probabilistic multiobjective wind-thermal economic emission dispatch based on point estimated method , 2012 .

[58]  Binod Shaw,et al.  Solution of economic dispatch problems by seeker optimization algorithm , 2012, Expert Syst. Appl..

[59]  Hany M. Hasanien,et al.  Single and Multi-objective Optimal Power Flow Using Grey Wolf Optimizer and Differential Evolution Algorithms , 2015 .

[60]  Hong-Tzer Yang,et al.  Evolutionary programming based economic dispatch for units with non-smooth fuel cost functions , 1996 .

[61]  Taher Niknam,et al.  A novel hybrid particle swarm optimization for economic dispatch with valve-point loading effects , 2011 .

[62]  Rahmat-Allah Hooshmand,et al.  Emission, reserve and economic load dispatch problem with non-smooth and non-convex cost functions using the hybrid bacterial foraging-Nelder–Mead algorithm , 2012 .

[63]  Chiem Trong Hien,et al.  A Novel Social Spider Optimization Algorithm for Large-Scale Economic Load Dispatch Problem , 2019, Energies.

[64]  Mohammed Azmi Al-Betar,et al.  A non-convex economic load dispatch problem with valve loading effect using a hybrid grey wolf optimizer , 2019, Neural Computing and Applications.

[65]  Kazem Zare,et al.  Solving non-convex economic dispatch problem with valve point effects using modified group search optimizer method , 2012 .

[66]  Muhammad Saeed,et al.  Adaptive Hooke-Jeeves-evolutionary algorithm for linear equality constrained problems , 2018, International Journal of ADVANCED AND APPLIED SCIENCES.

[67]  Talal M. Alkhamis,et al.  A modified Hooke and Jeeves algorithm with likelihood ratio performance extrapolation for simulation optimization , 2006, Eur. J. Oper. Res..

[68]  Lixiang Li,et al.  A hybrid FCASO-SQP method for solving the economic dispatch problems with valve-point effects , 2012 .

[69]  Whei-Min Lin,et al.  A novel stochastic search method for the solution of economic dispatch problems with non-convex fuel cost functions , 2011 .

[70]  Taher Niknam,et al.  A new honey bee mating optimization algorithm for non-smooth economic dispatch , 2011 .

[71]  Abbas Rabiee,et al.  Continuous quick group search optimizer for solving non-convex economic dispatch problems , 2012 .

[72]  Abhinav Sadu,et al.  A hybrid multi-agent based particle swarm optimization algorithm for economic power dispatch , 2011 .

[73]  David H. Wolpert,et al.  No free lunch theorems for optimization , 1997, IEEE Trans. Evol. Comput..

[74]  Provas Kumar Roy,et al.  Opposition-based krill herd algorithm applied to economic load dispatch problem , 2018, Ain Shams Engineering Journal.

[75]  A. Chowdhury,et al.  Cuckoo search algorithm for economic dispatch , 2013 .

[76]  M. Kenan Dosoglu,et al.  Symbiotic Organisms Search algorithm for economic load dispatch problem with valve-point effect , 2017 .

[77]  Md Samar Ahmad,et al.  Hybrid Harmony Search Algorithm and Interior Point Method for Economic Dispatch with Valve-Point Effect , 2014 .

[78]  Hamdi Abdi,et al.  A modified crow search algorithm (MCSA) for solving economic load dispatch problem , 2018, Appl. Soft Comput..

[79]  Jan K. Sykulski,et al.  Solution of Different Types of Economic Load Dispatch Problems Using a Pattern Search Method , 2008 .

[80]  Jida Huang,et al.  A novel algorithm for economic load dispatch of power systems , 2016, Neurocomputing.

[81]  Lixiang Li,et al.  A hybrid CPSO–SQP method for economic dispatch considering the valve-point effects , 2012 .

[82]  Bijaya K. Panigrahi,et al.  Neighborhood Search-Driven Accelerated Biogeography-Based Optimization for Optimal Load Dispatch , 2012, IEEE Transactions on Systems, Man, and Cybernetics, Part C (Applications and Reviews).

[83]  Manoj Kumar Tiwari,et al.  A clonal algorithm to solve economic load dispatch , 2007 .

[84]  M. Pandit,et al.  Self-Organizing Hierarchical Particle Swarm Optimization for Nonconvex Economic Dispatch , 2008, IEEE Transactions on Power Systems.

[85]  P. Subbaraj,et al.  Enhancement of Self-adaptive real-coded genetic algorithm using Taguchi method for Economic dispatch problem , 2011, Appl. Soft Comput..

[86]  Chih-Wen Liu,et al.  Non-smooth/non-convex economic dispatch by a novel hybrid differential evolution algorithm , 2007 .

[87]  Cheng-Chien Kuo,et al.  A Novel Coding Scheme for Practical Economic Dispatch by Modified Particle Swarm Approach , 2008, IEEE Transactions on Power Systems.

[88]  Carlos A. Coello Coello,et al.  An immune algorithm with power redistribution for solving economic dispatch problems , 2015, Inf. Sci..

[89]  Arifur Rahman,et al.  Three-phase induction motor design optimization using the modified Hooke-Jeeves method , 1990 .