**Multiobjective Real-Coded Genetic Algorithm for**

**Economic/Environmental Dispatch Problem**

**Ragab A. El-SEHIEMY ^{1}, Mostafa Abdelkhalik El-HOSSEINI^{2},**

Aboul Ella HASSANIEN^{3 }

**Electrical Engineering Department, Faculty of Engineering-Kafrelsheikh University**

^{1 }

elsehiemy@eng.kfs.edu.eg

**Computers and Systems Engineering Department, Faculty of Engineering – Mansoura**

^{2 }melhosseini@eng.mans.edu.eg

**Cairo University, Faculty of Computers & Information**

^{3 }aboitcairo@fci-cu.edu.eg

**Abstract**: This paper outlines the optimization problem of nonlinear constrained multi-objective economic/environmental dispatch (EED) problems of thermal generators in power systems and presents novel improved real-coded genetic optimization (MO-RCGA) algorithm for solving EED problems. The considered problem minimizes environmental emission and non-smooth fuel cost simultaneously while fulfilling the system operating constraints. The proposed MO-RCGA technique evolves a multi-objective version of GA by proposing redefinition of global best and local best individuals in multi-objective optimization domain. The performance of the proposed MO-RCGA enhanced with biased Initialization, dynamic parameter setting, and elitism is carried out. The validity and effectiveness of the proposed MO-RCGA is verified by means of several optimization runs accomplished at different population sizes on standard IEEE 30-bus test system. Simulation results demonstrated the capabilities of the proposed MO-RCGA algorithm to obtain feasible set of effective well-distributed solutions.

**Keywords**: Multiobjective real-coded genetic algorithm, economic environmental dispatch (EED), security.

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**CITE THIS PAPER AS**:

Ragab A. EL-SEHIEMY, Mostafa Abdelkhalik EL-HOSSEINI, Aboul Ella HASSANIEN, **Multiobjective Real-Coded Genetic Algorithm for Economic/Environmental Dispatch Problem**, *Studies in Informatics and Control*, ISSN 1220-1766, vol. 22 (2), pp. 113-122, 2013.

**Introduction**

The problem of Economic environmental dispatch (EED) is an important optimization task in fossil fuel fired power plant operation for allocating generation among the committed units. It aims at optimizing two conflicted objectives of fuel cost and emission level, simultaneously while satisfying all operational system constraints [1-3].

The EED problem is a large-scale highly non-linear constrained optimization problem characterized by complex and nonlinear with heavy equality and inequality constraints characteristics [4].

Traditionally, electric power systems aim at operating in such a way that the total fuel cost is minimized regardless of the emission produced in the system. An increased public awareness regarding the harmful effects of atmospheric pollutants on the environment has been noticed with concentrating on the importance of environmental protection and the passage of the Clean Air Act Amendments of 1990 has forced the utilities to adapt their design and operational strategies in order to reduce pollution and atmospheric emissions of the thermal power plants [5].

Many algorithms are developed to alleviate the effects of emission as installation of pollutant cleaning equipment, switching to low emission fuels, replacement of the aged fuel-burners with cleaner ones, and emission dispatching. The fourth option is the recent interested costless option compared to the first three options. That option is not any installing or modifying the exited pollution equipment. Then, the problem that has attracted much attention is pollution minimization due to the pressing public demand for clean air [4-6].

As the concern of environmental pollution has been increased in recent decades as well as the dramatic growing of fuel costs assure the continuous necessity of improvement of optimization methodologies for efficiently solving EED problems.

Classical methods such as the lambda iteration method and gradient method have been applied to solve the EED problems. But unfortunately, these methods are not feasible in practical power systems owing to the non-linear characteristics of the generators and non-smooth cost functions. Consequently, many powerful mathematical optimization techniques that are fast and reliable, such as non-linear programming and dynamic programming have been employed to solve the EED problems. But due to the non-differential and non-convex characteristics of the cost functions, these methods are also unable to locate the global optima [1, 3].

In recent years, modern search-based optimization techniques were developed as efficient alternative practical tools for non-linear optimization problems. A wide range of improved techniques is used to tackle both EED objectives simultaneously as competing objectives. The salient search based methods are [4-8], niched Pareto genetic algorithm [4], differential evolution [6] fuzzy model with adaptive genetic algorithm [7] and Real-Coded Genetic Algorithm [8].

Fuzzy sets can also be applied for decision making in multiple objectives including various constraints, therefore, an interactive fuzzy satisfying method is suggested to solve ED/EED problems [7, 9-10], particle swarm optimization technique [11-13], Biogeography-based algorithm for solving different economic load dispatch problems [14-15], differential evolution assisted by interior point algorithm [16] ant colony optimization (ACO) [17], seeker optimization algorithm [18] firefly algorithm [19], non-dominated sorting genetic algorithm (NSGA) [20], niched Pareto genetic algorithm (NPGA) [20], strength Pareto evolutionary algorithm (SPEA) [20] and multiobjective fuzzy based on particle swarm optimization algorithm [11], multiobjective bacteria foraging [21], Modified Shuffled Frog Leaping Algorithm (MSFLA) [22], and fuzzy ranking based real coded genetic algorithm (FR-RCGA) [42].

The binary GA solves many optimization problems that stump traditional techniques. When the variables are naturally quantized, the binary GA fits nicely. However, when the variables are continuous it is more logical to represent them by floating-point numbers [23-27].

A novel real-coded GA will be developed that has a lot of features that makes it improved algorithm; rarely stuck in local optima. These features include Biased Initialization, Elitism, and Dynamic parameter setting. It has been widely confirmed that real-number encoding performs better than binary or Gray encoding for function optimizations and constrained optimizations for many reasons include:

- Binary encoding for function optimization problems is known to have severe drawbacks due to the existence of
*Hamming cliffs*, pair of encodings having a large Hamming distance while belonging to points of minimal distance in phenotype space. For example, the pair 01111111111 and 10000000000 belongs to neighboring points in phenotype space (points of minimal Euclidean distance) but have maximum Hamming distance in genotype space [24] - As the topological structure of the genotype space for real-number encoding is identical to that of the phenotype space, it is easy to form effective genetic operators by borrowing useful techniques from conventional ones [23].
- Also, the binary GA has its precision limited by the binary representation of variables; using floating point numbers instead easily allows representation to the machine precision [25].
- Real-coded GA also has the advantage of requiring less storage than the binary GA because a single floating-point number represents the variable instead of
*Nbits*integers [23, 26].

This paper proposes Multiobjective real coded genetic algorithm (MO-RCGA) for simultaneously optimizing both economic and environmental objectives while achieving the operating system constraints. This EED problem is formulated as a nonlinear constrained optimization problem. In order to show the effectiveness of the proposed approach, problem solving is applied on standard IEEE 30 bus system.

**References**:

- WOOD, A. J., B. F. WOLLENBERGY,
**Power Generation, Operation, and Control**. New York: Wiley, 1984. - BASU, M.,
**Economic Environmental Dispatch using Multi-objective Differential Evolution**, Applied Soft Computing, vol. 11, 2011, pp. 2845-2853. - ZHU, J.,
**Optimization of Power System Operation**, IEEE Press Series on Power Engineering, 2009. - ABIDO, M. A.,
**A Niched Pareto Genetic Algorithm for Multiobjective Environmental/Economic Dispatch**, Electrical Power and Energy Systems, vol. 25, 2009, pp. 97-105. - GJORGIEV, B., M. CEPIN,
**A Multi-objective Optimization based Solution for the Combined Economic-Environmental Power Dispatch Problem**, Engineering Applications of Artificial Intelligence, vol. 26, 2013, pp. 417-429. - WU, L. H., Y. N. WANG, X. F. YUAN, S. W. ZHOU,
**Environmental/Economic Power Dispatch Problem using Multi-objective Differential Evolution Algorithm**, Electric Power Systems Research, vol. 80, 2010, pp. 1171-1181. - YANJUN, J., J. JIANG, Y. ZHANG,
**A Novel Fuzzy Multiobjective Model using Adaptive Genetic Algorithm Based on Cloud Theory for Service Restoration of Shipboard Power Systems**, IEEE Translations on Power Systems, vol. 20, 2012, pp. 612-620. - AMJADY, N., H. NASIRI-RED,
**Nonconvex Economic Dispatch with AC Constraints by a New Real Coded Genetic Algorithm**, IEEE Trans. on Power Systems, vol. 24, 2009, pp. 1489-1502. - ABOU EL-ELA, A. A., M. BISHR, S. ALLAM, R. EL-SEHIEMY,
**Optimal Preventive Control Actions in Power System using Multi-Objective****Fuzzy Linear Programming Technique**, Electric Power Systems Research, vol. 74, 2005, pp. 147-155. - AGRAWAL, S., B. K. PANIGRAHI, M. K. TIWARI,
**Multiobjective Particle Swarm Algorithm with Fuzzy Clustering for Electrical Power Dispatch**, IEEE Trans. on Evolutionary Computation, vol. 12, 2008, pp. 529-541. - CHATURVEDI, K. T., M. PANDIT, L. SRIVASTAVA,
**Self-Organization Hierarchical Particle Swarm Optimization for Nonconvex Economic Dispatch**, IEEE Trans. on Power Systems, vol. 23, 2008, pp. 1079-1087. - MENG, K., H. G. WANG, Z. Y. DONG, K. P. WONG,
**Quantum-Inspired Particle Swarm Optimization for Valve-Point Economic Load Dispatch**, IEEE Trans. on Power Systems, vol. 20, 2010, pp. 215-222. - VLACHOGIANNIS, J. G., K. Y. LEE,
**Economic Load Dispatch—A Comparative Study on Heuristic Optimization Techniques With an Improved Coordinated Aggregation-Based PSO**, IEEE Trans. on Power Systems, vol. 24, 2009, pp. 991-1001. - BHATTACHARYA, A., P. KUMAR CHATTOPADHYAY,
**Biogeography-based Optimization for Different****Economic Load Dispatch Problems**, IEEE Trans. on power systems, vol. 25, 2010, pp. 1064-1077. - BHATTACHARYA, A., P. KUMAR CHATTOPADHYAY,
**Hybrid Differential Evolution with Biogeography-based Optimization for Solution of Economic Load Dispatch**, IEEE Trans. on Power Systems, vol. 25, 2010, pp. 1955-1964. - DUVVURU, N., K. S. SWARUP,
**A Hybrid Interior Point Assisted Differential Evolution Algorithm for Economic Dispatch**, IEEE Trans. Power systems, vol. 26, 2011, pp. 542-549. - POTHIYA, S., I. NGAMROO, W. KONGPRAWECHNON,
**Ant Colony Optimization for Economic Dispatch Problem with Non-smooth Cost Functions**, International Journal of Electrical Power and Energy System, vol. 32, 2010, pp. 478–487. - SHAW, B., V. MUKHERJEE, S. P. GHOSHAL,
**Solution of Economic Dispatch Problems by Seeker Optimization Algorithm**, Expert Systems with Applications, vol. 39, 2012, pp. 508-519. - YANG, X., S. S. S. HOSSEINI, A. H. GANDOMI,
**Firefly Algorithm for Solving Non-convex Economic Dispatch Problems with Valve Loading Effect**, Applied Soft Computing, vol. 12, 2012, pp. 180-1186. - ABIDO, M. A.,
**Multiobjective Evolutionary Algorithms for Electric Power Dispatch Problem**. IEEE Trans. on Evolutionary Computation, vol. 10, 2006, pp. 315-329. - HOTA, P. K., A. K. BARISAL, R. CHAKRABARTI,
**Economic Emission Load Dispatch through based Bacterial Foraging Algorithm**, International Journal of Electrical Power & Energy Systems, vol. 32, 2010, pp. 794-803. - SRINIVASA REDDY, A., K. VAISAKH,
**Economic Emission Load Dispatch by Modified Shuffled Frog Leaping Algorithm**, International Journal of Computer Applications, vol. 31, 2011, pp. 58-65. - CHONG, E. K. P., S. H. ZAK,
**An Introduction to Optimization**, 2^{nd}Ed., Wiley Interscience Series In Discrete Mathematic and Optimization, 2001. - HAUPT, R. L., S. E. HAUPT,
**Practical Genetic Algorithms**, 2^{nd}Edition, Wiley Interscience, 2004. - EIBEN, A. E., R. HINTERDING, Z. MICHALEWICZ,
**Parameter Control in Evolutionary Algorithms**, IEEE Trans. on Evolutionary Computation, vol. 3(2), July 1999, pp. 124-141. - GEN, M., R. CHENG,
**Genetic Algorithms and Engineering Optimization**, A Wiley-Interscience Publication, 2000. - DREOET, J. Al.,
**Metaheuristics for Hard Optimization**, Springer-Verlag Berlin Heidelberg, 2006. - Washington University Website: www.ee.washington.edu/research/pstca/