Multi-objective Economic Emission Load Dispatch Research Articles

Solution of the Multi-objective Economic and Emission Load Dispatch Problem Using Adaptive Real Quantum Inspired Evolutionary Algorithm

Economic load dispatch is a complex and significant problem in power generation. The inclusion of emission with economic operation makes it a Multi-objective economic emission load dispatch (MOEELD) problem. So it is a tough task to resolve a constrained MOEELD problem with antagonistic multiple objectives of emission and cost. Evolutionary Algorithms (EA) have been widely used for solving such complex multi-objective problems. However, the performance of EAs on such problems is dependent on the choice of the operators and their parameters, which becomes a complex issue to solve in itself. The present work is carried out to solve a Multi-objective economic emission load dispatch problem using a Multi-objective adaptive real coded quantum-inspired evolutionary algorithm (MO-ARQIEA) with gratifying all the constraints of unit and system. A repair-based constraint handling and adaptive quantum crossover operator (ACO) are used to satisfy the constraints and preserve the diversity of the suggested approach. The suggested approach is evaluated on the IEEE 30-Bus system consisting of six generating units. These results obtained for different test cases are compared with other reputed and well-known techniques.

Hybrid method for achieving Pareto front on economic emission dispatch

In this paper hybrid method, Modified Nondominated Sorted Genetic Algorithm (MNSGA-II) and Modified Population Variant Differential Evolution(MPVDE) have been placed in effect in achieving the best optimal solution of Multiobjective economic emission load dispatch optimization problem. In this technique latter, one is used to enforce the assigned percent of the population and the remaining with the former one. To overcome the premature convergence in an optimization problem diversity preserving operator is employed, from the tradeoff curve the best optimal solution is predicted using fuzzy set theory. This methodology validated on IEEE 30 bus test system with six generators, IEEE 118 bus test system with fourteen generators and with a forty generators test system. The solutions are dissimilitude with the existing metaheuristic methods like Strength Pareto Evolutionary Algorithm-II, Multiobjective differential evolution, Multi-objective Particle Swarm optimization, Fuzzy clustering particle swarm optimization, Nondominated sorting genetic algorithm-II.

Relaxed I-SHOT trust-region algorithm for solving multi-objective economic emission load dispatch problem

ABSTRACTIn this paper, a new algorithm for tackling nonlinear constrained multi-objective optimization problems is introduced. This algorithm, which we call relaxed the interactive sequential hybrid optimization technique (relaxed I-SHOT), is based on a hybrid method between the I-SHOT method and step method (STEM) to transform a multi-objective problem into a single-objective one. An active set strategy is used together with a suggested penalty method to transform a single-objective constrained optimization problem into unconstrained one. A trust-region globalization strategy is added to the algorithm to solve the obtained unconstrained problem to ensure global convergence. The suggested approach is utilized to solve the multi-objective economic emission load dispatch (EELD) problems to assert the effectiveness of the proposed algorithm. The proposed algorithm is tested on the standard IEEE 30-bus 6-generator test system. The results of the proposed approach are compared against those reported in the literature. The comparison asserts the potential of the proposed algorithm to solve the EELD problem.

Population variant differential evolution-based multiobjective economic emission load dispatch

Summary This paper presents a novel heuristic optimization approach using population variant differential evolution algorithm for solving the multiobjective economic emission load dispatch (EELD) problem. The EELD problem simultaneously takes into consideration the effect of gaseous pollutants like NOx, SOx, etc, including the cost of the fossil fuel used in the thermal power plants. A population refreshment mechanism, based on the concept of interquartile range, has been applied to the classical differential evolution method to compute the EELD problem successfully. The algorithm has been tested on IEEE-30 bus 6-generator test system and a standard 40-generator test system, taking valve point loading effects into consideration for effective solutions. The results have been compared with the standard existing techniques in the literature such as linear programming, multiobjective stochastic search technique, nondominated sorting genetic algorithm, fuzzy clustering particle swarm optimization, and modified bacterial foraging algorithm, which authenticate the capability of the proposed algorithm. A novel concept of applying the proposed methodology to a deregulated power market has also been presented in this paper, where successful results have been obtained. This method appears as an efficient and robust optimization algorithm in terms of minimizing the total cost, emission, and computational time.

Quadratic approximation-based hybrid Artificial Cooperative Search algorithm for economic emission load dispatch problems

Summary In this article, Artificial Cooperative Search (ACS) algorithm is incorporated with the quadratic approximation (QA) operator to solve the multi-objective economic emission load dispatch (EELD) problems with different generation units. ACS is a Swarm Intelligence–based metaheuristic algorithm, based on the interaction between prey and predator organisms in a habitat, which is effective at global search; however, it does not perform so well at exploring promising regions. The QA operator, on the other hand, is a non-derivative–based efficient local search method that finds the minimum of a quadratic hyperspace passing through three points in a D-dimensional space. Solving the EELD problems with the hybridized ACS-QA algorithm, as being proposed in the present article, leads to more accurate results with fewer function evaluations. Also, multi-objectivity of the problem is handled by transforming it into a single-objective problem by using the weighted sum method. The efficiency of the proposed ACS-QA algorithm is tested in comparison to the algorithms existing in literature by implementing it on six different benchmark optimization problems. Afterward, the proposed ACS-QA algorithm and the ACS algorithm are implemented on multi-objective EELD problems with different generation units. The results are compared with the solutions in literature utilizing different metaheuristic optimization algorithms. Both studies firmly showed that the ACS-QA algorithm is able to find more accurate results even though it uses fewer function evaluation calls.

I-SHOT line-search algorithm for solving multi-objective economic emission load dispatch problem

I-SHOT line-search algorithm for solving multi-objective economic emission load dispatch problem

Modified particle swarm optimization for economic-emission load dispatch of power system operation

This paper proposes a modified particle swarm optimization considering time-varying acceleration coefficients for the economic-emission load dispatch (EELD) problem. The new adaptive parameter is introduced to update the particle movements through the modification of the velocity equation of the classical particle swarm optimization (PSO) algorithm. The idea is to enhance the performance and robustness of classical PSO. The price penalty factor method is used to transform the multiobjective EELD problem into a single-objective problem. Then the weighted sum method is applied for finding the Pareto front solution. The best compromise solution for this problem is determined based on the fuzzy ranking approach. The IEEE 30-bus system has been used to validate the effectiveness of the proposed algorithm. It was found that the proposed algorithm can provide better results in terms of best fuel cost, best emissions, convergence characteristics, and robustness compared to the reported results using other optimization algorithms.

Multi-Objective Economic Emission Load Dispatch Solution Using Evolutionary Algorithm with and without Considering Wind Power Penetration and Valve Point Effect

The electrical power system is considered as the most complex man-made systems mainly due to their wide geographical coverage. Electrical energy industries contributes environmental pollution which rise questions concern environmental protection and methods of eliminating or reducing pollution from power plants either by design or by operational strategies. Electric power plants are mainly aimed to operate al low fuel cost strategies .In this paper a Multi –Objective Economic Emission Load Dispatch problem is solved to minimize the emission of nitrogen oxides (NOx) , oxides of other fuels that release during generation of electricity and fuel cost considering both Thermal generators and Wind turbines. A large number of iterations and oscillation are those of the major concern in solving the economic load dispatch problem by using the BFO(bacterial foraging optimization) method. By applying BFO method the economic dispatch problem is optimized to minimize the total generation cost of a power system while satisfying various equality and inequality constraints. The effect of Wind power on overall emission is also investigated here using Quadratic programming by wolf’s method. This method has better convergence characteristic. Wolf’s method is an extended simplex procedure which can be applied to Quadratic programming problems in which all the problem variables are non-negative.

Hybrid ant optimization system for multiobjective economic emission load dispatch problem under fuzziness

In this paper, a new hybrid optimization system is presented. Our approach integrates the merits of both ant colony optimization and steady state genetic algorithm and it has two characteristic features. Firstly, since there is instabilities in the global market and the rapid fluctuations of prices, a fuzzy representation of the economic emission load dispatch (EELD) problem has been defined, where the input data involve many parameters whose possible values may be assigned by the expert. Secondly, by enhancing ant colony optimization through steady state genetic algorithm, a strong robustness and more effectively algorithm was created. Also, stable Pareto set of solutions has been detected, where in a practical sense only Pareto optimal solutions that are stable are of interest since there are always uncertainties associated with efficiency data. Moreover to help the decision maker DM to extract the best compromise solution from a finite set of alternatives a Technique for Order Performance by Similarity to Ideal Solution (TOPSIS) method is adopted. It is based upon simultaneous minimization of distance from an ideal point (IP) and maximization of distance from a nadir point (NP). The results on the standard IEEE systems demonstrate the capabilities of the proposed approach to generate true and well-distributed Pareto optimal nondominated solutions of the multiobjective EELD.

Solution of Economic Emission Load Dispatch problems of power systems by Real Coded Chemical Reaction algorithm

This paper presents a Real Coded Chemical Reaction algorithm (RCCRO) approach to solve the Economic Emission Load Dispatch (EELD) problem of thermal generators of power systems. Emission substance like NOX, power demand equality constraint and operating limit constraint are considered here. EELD problem has been originated as a multi-objective problem by considering both economy and emission simultaneously. Chemical Reaction Optimization (CRO) mimics the interactions of molecules in a chemical reaction to reach a low energy stable state. Basically, the CRO is designed to work in the discrete domain optimization problems. A real coded version of it, known as Real-Coded Chemical Reaction Optimization (RCCRO) is applied here to solve multi-objective EELD problems, in order to show the advantages of proposed algorithm to solve complex continuous optimization problems. Different test systems having 10, 13 and 40 generators, addressing valve-point loading and NOX emission have been considered. The solutions obtained are quite encouraging and superior to different existing optimization techniques.

Multi-Objective Economic Emission Load Dispatch using Teacher-Learning-Based Optimization Technique

Abstract In this paper, a new parameter-less diversity preservation approach to solve the non-linear multi-objective economic emission load dispatch (EED) problem is envisaged using Teacher-Learning Based Optimization (TLBO) method. The TLBO technique is totally parameter less and takes less computation time as compared to other optimization techniques for the determination of solutions in the Pareto-optimal front. The TLBO method is tested for EED problem on 6-generator test system (IEEE 30- bus) and the results obtained are compared with those obtained from Non-dominated Sorting Genetic Algorithm (NSGA). The simulation results confirm the computational advantage of the TLBO method.

Multi-objective economic emission load dispatch problem with trust-region strategy

In this paper, we present a trust region algorithm for solving multi-objective economic emission load dispatch problem (EELD). The trust region algorithm has proven to be a very successful globalization technique for solving a single objective constrained optimization problems. The proposed approach is suitable for multi-objective problem (EELD) such that its objective functions may be ill- defined or having a non convex pareto-optimal front. Also, we identify the weight values which reflect the degree of satisfaction of each objective. The proposed approach is carried out on the standard IEEE 30-bus 6-generator test systems to confirm the effectiveness of the algorithm used to solve the multi-objective problem (EELD). Our results with the proposed approach have been compared to those reported in the literature. The comparison demonstrates the superiority of the proposed approach and confirm its potential to solve the multi-objective problem (EELD).A Matlab implementation of our algorithm was used in solving one case study and the results are reported.

Multi-objective economic emission load dispatch solution using gravitational search algorithm and considering wind power penetration

In this paper an economic emission load dispatch (EELD) problem is solved to minimize the emission of nitrogen oxides (NOX) and fuel cost, considering both thermal generators and wind turbines. The effects of wind power on overall NOX emission are also investigated here. To find the optimum emission dispatch, optimum fuel cost, best compromising emission and fuel cost, a newly developed optimization technique, called Gravitational Search Algorithm (GSA) has been applied. GSA is based on the Newton’s law of gravity and mass interactions. In GSA, the searcher agents are collection of masses which interact with each other using laws of gravity and motion of Newton. IEEE 30-bus system having six conventional thermal generators has been considered as test system. Two extra wind turbines are also placed at two weak load bus of the system. Two Weak load buses have been selected based on their L-index value. After placing the wind power sources, those buses have been considered as generator bus. Minimum fuel cost, minimum emission and best compromising solution obtained by GSA are compared with those of biogeography-based optimization (BBO). The results show that the GSA surpasses the other available techniques in terms of solution quality and computational efficiency.

Hybrid multiobjective evolutionary algorithm based technique for economic emission load dispatch optimization problem

In this paper, we present a hybrid approach combining two optimization techniques for solving economic emission load dispatch (EELD) optimization problem. The proposed approach integrates the merits of both genetic algorithm (GA) and local search (LS), where it employs the concept of co-evolution and repair algorithm for handling nonlinear constraints, also, it maintains a finite-sized archive of non-dominated solutions which gets iteratively updated in the presence of new solutions based on the concept of -dominance. The use of -dominance also makes the algorithms practical by allowing a decision maker to control the resolution of the Pareto set approximation. To improve the solution quality, local search technique was implemented as neighborhood search engine where it intends to explore the less-crowded area in the current archive to possibly obtain more nondominated solutions. Several optimization runs of the proposed approach are carried out on the standard IEEE 30-bus 6-genrator test system. Simulation results with the proposed approach have been compared to those reported in literature. The comparison demonstrates the superiority of the proposed approach and confirms its potential to solve the multiobjective EELD problem. Key words: Economic emission load dispatch, evolutionary algorithms, multiobjective optimization, local search.

Hybrid differential evolution with biogeography-based optimization algorithm for solution of economic emission load dispatch problems

This paper presents combination of differential evolution (DE) and biogeography-based optimization (BBO) algorithm to solve complex economic emission load dispatch (EELD) problems of thermal generators of power systems. Emission substances like NO X , SO X , CO X, Power demand equality constraint and operating limit constraint are considered here. Differential evolution (DE) is one of the very fast and robust, accurate evolutionary algorithms for global optimization and solution of EELD problems. Biogeography-based optimization (BBO) is another new biogeography inspired algorithm. Biogeography deals with the geographical distribution of different biological species. This algorithm searches for the global optimum mainly through two steps: migration and mutation. In this paper combination of DE and BBO (DE/BBO) is proposed to accelerate the convergence speed of both the algorithm and to improve solution quality. To show the advantages of the proposed algorithm, it has been applied for solving multi-objective EELD problems in a 3-generator system with NO X and SO X emission, in a 6-generators system considering NO X emission, in a 6-generator system addressing both valve-point loading and NO X emission. The current proposal is found better in terms of quality of the compromising and individual solution obtained.

Solving economic emission load dispatch problems using hybrid differential evolution

This paper presents the combination of differential evolution (DE) and Biogeography-based Optimization (BBO) algorithm to solve complex economic emission load dispatch (EELD) problems of thermal generators of power systems. Emission substances like NO X , SO X , CO X , power demand equality constraint and operating limit constraint are considered here. Differential evolution (DE) is one of the very fast and robust, accurate evolutionary algorithms for global optimization and solution of EELD problems. Biogeography-based Optimization (BBO) is another new biogeography inspired algorithm. Biogeography deals with the geographical distribution of different biological species. This algorithm searches for the global optimum mainly through two steps: migration and mutation. In this paper the combination of DE and BBO (DE/BBO) is proposed to accelerate the convergence speed of both the algorithm and to improve solution quality. To show the advantages of the proposed algorithm, it has been applied for solving multi-objective EELD problems in a 3 generator system with NO X and SO X emission, in a 6 generators system considering NO X emission, in a 6 generator system addressing both valve-point loading and NO X emission. The current proposal is found better in terms of quality of the compromising and individual solution obtained.

Multiobjective bacteria foraging algorithm for electrical load dispatch problem

In this paper the bacteria foraging meta-heuristic is extended into the domain of multiobjective optimization. In this multiobjective bacteria foraging (MOBF) optimization technique, during chemotaxis a set of intermediate bacteria positions are generated. Next, we use pareto non-dominance criterion to determine final set of bacteria positions, which constitute the superior solutions among current and intermediate solutions. To test the efficacy of our proposed algorithm we have chosen a highly constrained optimization problem namely economic/emission dispatch. Economic dispatch is a constrained optimization problem in power system to distribute the load demand among the committed generators economically. Now-a-days environmental concern that arises due to the operation of fossil fuel fired electric generators and global warming, transforms the classical economic load dispatch problem into multiobjective environmental/economic dispatch (EED). In the proposed work, we have considered the standard IEEE 30-bus six-generator test system on which several other multiobjective evolutionary algorithms are tested. We have also made a comparative study of the proposed algorithm with that of reported in the literature. Results show that the proposed algorithm is a capable candidate in solving the multiobjective economic emission load dispatch problem.

Multiobjective fuzzy dominance based bacterial foraging algorithm to solve economic emission dispatch problem

Abstract This paper proposes the bacterial foraging meta-heuristic algorithm for multiobjective optimization. In this multiobjective bacterial foraging optimization technique, the most recent bacterial locations are obtained by chemotaxis process. Next, Fuzzy dominance based sorting procedure is used here to select the Pareto optimal front (POF). To test the suitability of our proposed algorithm we have considered a highly constrained optimization problem namely economic/emission dispatch. Now-a-days environmental concern that arises due to the operation of fossil fuel fired electric generators and global warming, transforms the classical economic load dispatch problem into multiobjective environmental/economic dispatch (EED) problem. In the proposed work, we have considered the standard IEEE 30-bus six-generator test system and the results obtained by proposed algorithm are compared with the other recently reported results. Simulation results demonstrate that the proposed algorithm is a capable candidate in solving the multiobjective economic emission load dispatch problem.

Application of Biogeography-based Optimization for Solving Multi-objective Economic Emission Load Dispatch Problems

This article presents a biogeography-based optimization algorithm to solve complex economic emission load dispatch problems of thermal generators of power systems. Different emission substances, such as NOX, SOX, and COX, are considered for case studies. The methodology considers the power demand equality constraint and the operating limit constraint during the time of solving economic emission load dispatch problems. Biogeography deals with the geographical distribution of biological organisms. Mathematical models of biogeography describe how species migrate from one habitat to another, how species arise, and how species become extinct. Here, it will be discussed how biogeography-based optimization can be used to solve economic emission load dispatch problems. This algorithm searches the global optimum mainly through two steps: migration and mutation. To show the advantages of the proposed algorithm, this algorithm has been applied for solving multi-objective economic emission load dispatch problems in a six-generator system considering NOX emission for different loading condition; in a three-generator system with NOX and SOX emission; in a six-generator system with SOX, NOX, and COX emissions; and in a six-generator system addressing both valve-point loading and NOX emission. Compared with the other existing techniques, the current proposal is found to be better in terms of quality of the compromising and individual solution obtained.

An ɛ-dominance-based multiobjective genetic algorithm for economic emission load dispatch optimization problem

In this paper, a novel multiobjective genetic algorithm approach for economic emission load dispatch (EELD) optimization problem is presented. The EELD problem is formulated as a non-linear constrained multiobjective optimization problem with both equality and inequality constraints. A new optimization algorithm which is based on concept of co-evolution and repair algorithm for handling non-linear constraints is presented. The algorithm maintains a finite-sized archive of non-dominated solutions which gets iteratively updated in the presence of new solutions based on the concept of ɛ-dominance. The use of ɛ-dominance also makes the algorithms practical by allowing a decision maker to control the resolution of the Pareto-set approximation by choosing an appropriate ɛ value. The proposed approach is carried out on the standard IEEE 30-bus 6-genrator test system. The results demonstrate the capabilities of the proposed approach to generate true and well-distributed Pareto-optimal non-dominated solutions of the multiobjective EELD problem in one single run. Simulation results with the proposed approach have been compared to those reported in the literature. The comparison demonstrates the superiority of the proposed approach and confirms its potential to solve the multiobjective EELD problem.