Correction to "Combining of Chaotic Differential Evolution and Quadratic Programming for Economic Dispatch Optimization with Valve-Point Effect"
TL;DR: The proposed combined method outperforms other state-of-the-art algorithms in solving load dispatch problems with the valve-point effect.
Abstract: Evolutionary algorithms are heuristic methods that have yielded promising results for solving nonlinear, nondifferentiable, and multi-modal optimization problems in the power systems area. The differential evolution (DE) algorithm is an evolutionary algorithm that uses a rather greedy and less stochastic approach to problem solving than do classical evolutionary algorithms, such as genetic algorithms, evolutionary programming, and evolution strategies. DE also incorporates an efficient way of self-adapting mutation using small populations. The potentialities of DE are its simple structure, easy use, convergence property, quality of solution, and robustness. This paper proposes a new approach for solving economic load dispatch problems with valve-point effect. The proposed method combines the DE algorithm with the generator of chaos sequences and sequential quadratic programming (SQP) technique to optimize the performance of economic dispatch problems. The DE with chaos sequences is the global optimizer, and the SQP is used to fine-tune the DE run in a sequential manner. The combined methodology and its variants are validated for two test systems consisting of 13 and 40 thermal units whose incremental fuel cost function takes into account the valve-point loading effects. The proposed combined method outperforms other state-of-the-art algorithms in solving load dispatch problems with the valve-point effect.
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TL;DR: A detailed review of the basic concepts of DE and a survey of its major variants, its application to multiobjective, constrained, large scale, and uncertain optimization problems, and the theoretical studies conducted on DE so far are presented.
Abstract: Differential evolution (DE) is arguably one of the most powerful stochastic real-parameter optimization algorithms in current use. DE operates through similar computational steps as employed by a standard evolutionary algorithm (EA). However, unlike traditional EAs, the DE-variants perturb the current-generation population members with the scaled differences of randomly selected and distinct population members. Therefore, no separate probability distribution has to be used for generating the offspring. Since its inception in 1995, DE has drawn the attention of many researchers all over the world resulting in a lot of variants of the basic algorithm with improved performance. This paper presents a detailed review of the basic concepts of DE and a survey of its major variants, its application to multiobjective, constrained, large scale, and uncertain optimization problems, and the theoretical studies conducted on DE so far. Also, it provides an overview of the significant engineering applications that have benefited from the powerful nature of DE.
4,321 citations
01 Mar 2012
TL;DR: This paper presents a novel approach to determining the feasible optimal solution of the ED problems using the recently developed Firefly Algorithm, and shows that the proposed FA is able to find more economical loads than those determined by other methods.
Abstract: The growing costs of fuel and operation of power generating units warrant improvement of optimization methodologies for economic dispatch (ED) problems. The practical ED problems have non-convex objective functions with equality and inequality constraints that make it much harder to find the global optimum using any mathematical algorithms. Modern optimization algorithms are often meta-heuristic, and they are very promising in solving nonlinear programming problems. This paper presents a novel approach to determining the feasible optimal solution of the ED problems using the recently developed Firefly Algorithm (FA). Many nonlinear characteristics of power generators, and their operational constraints, such as generation limitations, prohibited operating zones, ramp rate limits, transmission loss, and nonlinear cost functions, were all contemplated for practical operation. To demonstrate the efficiency and applicability of the proposed method, we study four ED test systems having non-convex solution spaces and compared with some of the most recently published ED solution methods. The results of this study show that the proposed FA is able to find more economical loads than those determined by other methods. This algorithm is considered to be a promising alternative algorithm for solving the ED problems in practical power systems.
578 citations
TL;DR: An improved PSO framework employing chaotic sequences combined with the conventional linearly decreasing inertia weights and adopting a crossover operation scheme to increase both exploration and exploitation capability of the PSO is proposed.
Abstract: This paper presents an efficient approach for solving economic dispatch (ED) problems with nonconvex cost functions using an improved particle swarm optimization (IPSO). Although the particle swarm optimization (PSO) approaches have several advantages suitable to heavily constrained nonconvex optimization problems, they still can have the drawbacks such as local optimal trapping due to premature convergence (i.e., exploration problem), insufficient capability to find nearby extreme points (i.e., exploitation problem), and lack of efficient mechanism to treat the constraints (i.e., constraint handling problem). This paper proposes an improved PSO framework employing chaotic sequences combined with the conventional linearly decreasing inertia weights and adopting a crossover operation scheme to increase both exploration and exploitation capability of the PSO. In addition, an effective constraint handling framework is employed for considering equality and inequality constraints. The proposed IPSO is applied to three different nonconvex ED problems with valve-point effects, prohibited operating zones with ramp rate limits as well as transmission network losses, and multi-fuels with valve-point effects. Additionally, it is applied to the large-scale power system of Korea. Also, the results are compared with those of the state-of-the-art methods.
516 citations
TL;DR: In this work, differential evolution (DE) algorithm was studied for solving economic load dispatch (ELD) problems in power systems and the current proposal was found better than, or at least comparable to, them considering the quality of the solution obtained.
470 citations
Book•
30 Sep 2004
TL;DR: In this article, a review of evolutionary method has been presented to solve the problem of allocating customers' load demands among the available thermal power generating units in an economic, secure and reliable way.
Abstract: Electric power systems have experienced continuous growth in all the three major sectors of the power system namely, generation, transmission and distribution. Electricity cannot be stored economically, but there has to be continuous balance between demand and supply. The increase in load sizes and operational complexity such as generation allocation, non-utility generation planning, and pricing brought about by the widespread interconnection of transmission systems and inter-utility power transaction contracts, has introduced major difficulties into the operation of power system. Allocation of customers' load demands among the available thermal power generating units in an economic, secure and reliable way has been a subject of interest since 1920 or even earlier. However practically, the generating units have non-convex input-output characteristics due to prohibited operating zones, valve-point loadings and multi-fuel effects considered as heavy equality and inequality constraints, which cannot be directly solved by mathematical programming methods. Dynamic programming can treat such types of problems, but it suffers from the curse of dimensionality. Over the past decade, many prominent methods have been developed to solve these problems, such as the hierarchical numerical methods, tabu search, neural network approaches, genetic algorithm, evolutionary programming, swarm optimisation, differential evolution and hybrid search methods. Review of evolutionary method has been presented.
384 citations
References
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TL;DR: A method is described for the minimization of a function of n variables, which depends on the comparison of function values at the (n 41) vertices of a general simplex, followed by the replacement of the vertex with the highest value by another point.
Abstract: A method is described for the minimization of a function of n variables, which depends on the comparison of function values at the (n 41) vertices of a general simplex, followed by the replacement of the vertex with the highest value by another point. The simplex adapts itself to the local landscape, and contracts on to the final minimum. The method is shown to be effective and computationally compact. A procedure is given for the estimation of the Hessian matrix in the neighbourhood of the minimum, needed in statistical estimation problems.
27,271 citations
"Correction to "Combining of Chaotic..." refers methods in this paper
...DE differs from conventional genetic algorithms in its use of perturbing vectors, which are the difference between two randomly chosen parameter vectors, a concept borrowed from the operators of Nelder and Mead’s simplex optimization technique [23]....
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TL;DR: In this article, a new heuristic approach for minimizing possibly nonlinear and non-differentiable continuous space functions is presented, which requires few control variables, is robust, easy to use, and lends itself very well to parallel computation.
Abstract: A new heuristic approach for minimizing possibly nonlinear and non-differentiable continuous space functions is presented. By means of an extensive testbed it is demonstrated that the new method converges faster and with more certainty than many other acclaimed global optimization methods. The new method requires few control variables, is robust, easy to use, and lends itself very well to parallel computation.
24,053 citations
9,153 citations
Book•
01 Jan 2009
TL;DR: The aim of this book is to provide a Discussion of Constrained Optimization and its Applications to Linear Programming and Other Optimization Problems.
Abstract: Preface Table of Notation Part 1: Unconstrained Optimization Introduction Structure of Methods Newton-like Methods Conjugate Direction Methods Restricted Step Methods Sums of Squares and Nonlinear Equations Part 2: Constrained Optimization Introduction Linear Programming The Theory of Constrained Optimization Quadratic Programming General Linearly Constrained Optimization Nonlinear Programming Other Optimization Problems Non-Smooth Optimization References Subject Index.
7,278 citations
"Correction to "Combining of Chaotic..." refers background or methods in this paper
...Therefore, (4) can be modified [15], [16] as...
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...Details of the SQP procedure are presented by Fletcher in [16]....
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Book•
01 Jan 1984
TL;DR: In this paper, the authors present a graduate-level text in electric power engineering as regards to planning, operating, and controlling large scale power generation and transmission systems, including characteristics of power generation units, transmission losses, generation with limited energy supply, control of generation, and power system security.
Abstract: Topics considered include characteristics of power generation units, transmission losses, generation with limited energy supply, control of generation, and power system security. This book is a graduate-level text in electric power engineering as regards to planning, operating, and controlling large scale power generation and transmission systems. Material used was generated in the post-1966 period. Many (if not most) of the chapter problems require a digital computer. A background in steady-state power circuit analysis is required.
6,344 citations
"Correction to "Combining of Chaotic..." refers background in this paper
...linear programming, and nonlinear programming techniques [ 2 ], [3]‐[7]....
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