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

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.

This paper attempts to propose particle swarm optimization algorithm with smart inertia factor (PSO-SIF) to solve the problem of economic emission load dispatch (EELD) in thermal power plants. The aim of EELD solution is synchronous reduction of both fuel costs and emission level. EELD problem is a non-linear and non-convex problem which uses evolutionary algorithms as efficient to solve such problems due to its complicated characteristics. PSO-SIF algorithm is an efficient and robust algorithm to exploit universal optimal point of optimization problems. Tests implemented on 10-unite systems, considering valve-point loading effects, network losses with Multi-objective functions such as system fuel cost and emission level, to show PSO-SIF algorithm capabilities in solving EELD problems. Results obtained from present investigation indicated universal optimal point exploitation of the problems and superiority of the proposed algorithm compared to other new and efficient algorithms.

Scarcity of energy resources, rising electricity generating costs, environmental impacts, and ever-increasing demand for electrical power need optimal economic dispatch in the modern scenario. The expense of generator fuel determines the percentage of a power plant's operating costs, which are minimized via optimal load dispatch (OLD). The OLD problem is determining the best and cheapest power generating strategy among a set of on-line producing units to supply the whole power requirements at a particular period. This paper presents bio-inspired meta-heuristic Ant Lion Optimizer (ALO) techniques to solve the economic load dispatch problem. The main objective of this paper is to reduce the generation fuel cost while meeting equality and inequality requirements. The obtained results demonstrate that the proposed approach can significantly reduce generating expenses even while satisfying the constraints (Power Stability as well as Generation Limit).

A multi-objective particle swarm optimization (MOPSO) approach for multi-objective economic load dispatch problem in power system is presented in this paper. The economic load dispatch problem is a non-linear constrained multi-objective optimization problem. The proposed MOPSO approach handles the problem as a multi-objective problem with competing and non-commensurable fuel cost, emission and system loss objectives and has a diversity-preserving mechanism using an external memory (call “repository”) and a geographically-based approach to find widely different Pareto-optimal solutions. In addition, fuzzy set theory is employed to extract the best compromise solution. Several optimization runs of the proposed MOPSO approach were carried out on the standard IEEE 30-bus test system. The results revealed the capabilities of the proposed MOPSO approach to generate well-distributed Pareto-optimal non-dominated solutions of multi-objective economic load dispatch. Comparison with Multi-objective Evolutionary Algorithm (MOEA) showed the superiority of the proposed MOPSO approach and confirmed its potential for solving multi-objective economic load dispatch.

The growing incidence of thermal power generation plants and strict environmental laws have constituted the Economic Emission Load Dispatch (EELD) issue into a challenging problem in contemporary power systems operation. This issue comprises the strategy of reducing the cost of fuel and pollutant emission at the same time and meeting the power balance within the system and the operating limits of the generator as well as the transmission losses. Due to the nonlinearity and conflict of these aims, the traditional single-objective optimization methods do not give flexible and environmentally sustainable solutions. An Interactive Fuzzy Goal Programming (IFGP) methodology is suggested in this work to be used to solve the multi-objective EELD problem. The technique converts the economic and emission targets to fuzzy target in terms of linear membership functions based on the ideal and anti-ideal solutions. This is an interactive decision-making mechanism, which enables the levels of aspiration to be updated stochastically until a satisfying compromise solution has been reached. The approach suggested is verified on three generators thermal power system where the transmission losses are modeled using B-coefficients. Extensive graphical explanations such as cost and emission change with demand of load, trade-off properties, and relative comparison with classical Economic Load Dispatch (ELD), are given. The findings indicate a high level of emission reduction by the IFGP approach at a small cost addition to fuel as opposed to traditional ELD. The suggested framework has increased flexibility, clear sightedness, and decision support and is thus a great fit to sustainable and viable power system planning and operation.

Economic Load Dispatch (ELD) optimization is an important and difficult task in power system planning. Previously, most of the research mainly focused on proposing various evolutionary algorithms (EAs) to pursue better results of ELD problems. However, few comprehensive analysis of the effects of various constraint handling techniques (CHTs) on the performance of EA-based techniques are available so far. In this paper, we try to fill this gap by experimentally testing the algorithmic variants of combining four effective and widely used EAs with three CHTs. From the experimental results on the ELD problems with valve-point and those problems with both valve-point and multiple-fuel effect, several important conclusions can be achieved, including 1) for the low scale ELD problem with valve-point only, the selection of EAs is more important than CHTs; 2) for the large scale problems, CHTs play crucial roles; 3) the appropriate combination of EA and CHT is helpful to achieve better performance. This study is also expected to provide solid basis for further strengthening the robustness of EAs for ELD optimization. It is also interesting to observe that the experimental results obtained in this paper are much better than those of the previous effective ELD optimization algorithms.

In this paper we propose an Interval based Differential Evolution (IDE) algorithm, an improved version of Differential Evolution (DE) algorithm using interval arithmetic. After estimating the global minimum roughly, the IDE algorithm constructs a mechanism which updates the upper bound of global minimum at each generation and defines an efficient termination criterion. Also at each generation it modifies the new population using the subset of current population and thus reduces the computational effort. We apply the proposed algorithm to the Combined Economic Emission Load Dispatch (CEELD) problem which obtains the optimal amount of generated power for the thermal generating units in the system by simultaneously minimising the fuel and emission costs. We find the proposed algorithm to be more efficient than the conventional DE when applied to IEEE 6 generators system. We also find that these results using the IDE algorithm are better than some recently reported evolutionary algorithms.

The Economic Dispatch (ED) is one of the most important optimization problems in power systems the ultimate goal of the ED is to minimize the cost of operations in a power generation. In this paper, the Woodpecker Mating Algorithm (WMA) is used to solve the ED problem considering the nonlinear properties of generators such as valve point effects (VPE), prohibited operating zones (POZ), ramp rate limits, multiple fuel options, and transmission loss. The WMA algorithm is a novel metaheuristic algorithm inspired by the mating behavior of woodpeckers and sound intensity (a physical quantity). The WMA is implemented on six test systems of different operational dimensions and characteristics to show its capacity for solving the ED problem. The results are compared with the latest and most efficient methods introduced in the literature. Proving the efficiency of the WMA to solve the ED problem, simulation results are promising and offer the optimal fuel cost of production.

Thermal generating units have incorporated renewable energy sources, such solar and wind, to lower pollutant gas emissions and overall fuel costs. As a result, the incorporation of renewable sources such as wind energy makes the multi-objective EELD issue more complicated and non-linear. An Artificial Ecosystem-Based Optimization (AEO) method has been presented to address this issue by optimizing the wind-solar-thermal model's cost and emissions while accounting for uncertainty in the outputs of solar and wind power. Key components of the AEO algorithm, which draw inspiration from ecosystem dynamics, enable search agents to more quickly converge to global optima and successfully escape local optima. Two systems—one with 40 heat producing units and the other with 13—have been used to test the suggested method.

Evolutionary multi-objective optimization algorithms are generally employed to generate Pareto optimal solutions by exploring the search space. To enhance the performance, exploration by global search can be complemented with exploitation by combining it with local search. In this paper, we address the issues in integrating local search with global search such as: how to select individuals for local search; how deep the local search is performed; how to combine multiple objectives into single objective for local search. We introduce a Preferential Local Search mechanism to fine tune the global optimal solutions further and an adaptive weight mechanism for combining multi-objectives together. These ideas have been integrated into NSGA-II to arrive at a new memetic algorithm for solving multi-objective optimization problems. The proposed algorithm has been applied on a set of constrained and unconstrained multi-objective benchmark test suite. The performance was analyzed by computing different metrics such as Generational distance, Spread, Max spread, and HyperVolume Ratio for the test suite functions. Statistical test applied on the results obtained suggests that the proposed algorithm outperforms the state-of-art multi-objective algorithms like NSGA-II and SPEA2. To study the performance of our algorithm on a real-world application, Economic Emission Load Dispatch was also taken up for validation. The performance was studied with the help of measures such as Hypervolume and Set Coverage Metrics. Experimental results substantiate that our algorithm has the capability to solve real-world problems like Economic Emission Load Dispatch and is able to produce better solutions, when compared with NSGA-II, SPEA2, and traditional memetic algorithms with fixed local search steps.

In this research paper a recently developed meta-heuristic technique whale algorithm with fuzzy decision making is proposed to solve the Economic emission load dispatch which focuses on optimizing the generation cost and emission function. Economic and emission both objectives are conflicting in nature so this is a multi-objective optimization problem known as multi-objective economic load dispatch (MELD). In this work fuzzy decision making is used to decide optimum point between these objectives. Transmission losses and valve pointing loading are taken into account with MELD to provide practical application to the proposed method. Penalty membership function is used to handle the equality constraints. Proposed approach of MELD is applied to six and ten unit generating systems.

Solving non-convex economic load dispatch problem via artificial cooperative search algorithm

This paper presents a Bat Algorithm (BA) for solving economic emission dispatch (EELD) problem with quadratic fuel function. The BA is a new meta-heuristic algorithm which is a powerful optimal solution search algorithm owing easily selected control parameters and high successful rate as well as high ability for dealing with complex constraints. In addition to minimizing electricity generation fuel cost, emission released into the air from thermal plants is also another main objective needs to be minimized. In order to test the performance of the proposed BA one system with two load cases is employed. The obtained result by the BA compared to that from other methods has revealed that the proposed BA is a very promising meta-heuristic algorithm for solving economic emission load dispatch problem.

This paper proposes an augmented Lagrange Hopfield Network (ALHN) based method for solving economic emission dispatch (EELD) problem with quadratic fuel function. The ALHN is the combination of augmented Lagrange function and Hopfield neural network in aim to improve performance in terms of convergence speed and getting global optimization. In addition to minimizing electricity generation fuel cost, emission released into the air from thermal plants is also another main objective needs to be minimized. In order to test the performance of the proposed ALHN two systems including a three unit system with one load case and a six unit system with three load cases are employed. The obtained result by the ALHN compared to that from other methods has revealed that the proposed ALHN is a very promising artificial intelligent algorithm for solving economic emission load dispatch problem.

In this paper a linear Hopfield model is used to solve the problem of combined economic emission dispatch (CEED). The objective function of CEED problem comprises of power mismatch, total fuel cost and total emission subjected to equality/inequality constraints. In proposed methodology, inclusion of power mismatch in objective function exhibits the ability of attaining power mismatch to any desirable extent and may be employed for large-scale highly constrained nonlinear and complex systems. A systematic procedure for the selection of weighting factor adopted. The proposed method employs a linear input-output model for neurons. The efficacy and viability of the proposed method is tested on three test systems and results are compared with those obtained using other methods. It is observed that the proposed algorithm is accurate, simple, efficient, and fast.