“…Yokoyama et al [2] used a new approach based on probability security criteria. Goal programming techniques to solve this multiple criteria decision making problem and evaluate the better environmental marginal cost was proposed by Kermanshahi et al [3]. A recursive quadratic programming method to solve the emission constrained dynamic economic dispatch by fuel switching was presented by Granelli et al [4].…”
“…Yokoyama et al [2] used a new approach based on probability security criteria. Goal programming techniques to solve this multiple criteria decision making problem and evaluate the better environmental marginal cost was proposed by Kermanshahi et al [3]. A recursive quadratic programming method to solve the emission constrained dynamic economic dispatch by fuel switching was presented by Granelli et al [4].…”
“…Several models have been used to represent emission levels. Zahavi and Eisenberg [3] used a second order polynomial, while Kermanshahi, et al [4] used the sum of a quadratic and an exponential term. Gent and Lamont [5] used a combination of a straight line and an exponential term.…”
The combinatorial problem of the economic load dispatch is solved to find the generation levels that minimize the cost or minimize the emission level while satisfying the power balance equation. The environmental emission levels are also taken as the constraints in cost optimization problem. The solutions to the above problems is attempted using Modified Hopfield Neural Network (MHNN), which has the flexibility of handling objective function and the constraints separately and works on the principal of minimizing the energy function and therefore ensure convergence. The study is carried out for Cost optimization, NOx emission optimization, SOx emission optimization and Cost optimization with SOx and NOx emissions as constraint. The simulation results are presented for standard 3-Generator data while considering the losses and neglecting them.
“…Goal programming method was also proposed for multi-objective EED problem [7]. In this method, a target or a goal to be achieved for each objective is assigned and the objective function will then try to minimize the distance from the targets to the objectives.…”
A reference point based multi-objective optimization using a combination between trust region (TR) algorithm and particle swarm optimization (PSO) to solve the multi-objective environmental/economic dispatch (EED) problem is presented in this paper. The EED problem is handled by Reference Point Interactive Approach. One of the main advantages of the proposed approach is integrating the merits of both TR and PSO, where TR has provided the initial set (close to the Pareto set as possible and the reference point of the decision maker) followed by PSO to improve the quality of the solutions and get all the points on the Pareto frontier. The performance of the proposed algorithm is tested on standard IEEE 30-bus 6-genrator test system and is compared with conventional methods. The results demonstrate the capabilities of the proposed approach to generate true and well-distributed Pareto-optimal non-dominated solutions in one single run. The comparison with the classical methods demonstrates the superiority of the proposed approach and confirms its potential to solve the multi-objective EED problem.
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