Research Article
Constrained Multiobjective Equilibrium Optimizer Algorithm for
Solving Combined Economic Emission Dispatch Problem
M. A. El-Shorbagy
1,2
and A. A. Mousa
3
1
Department of athematics, College of Science and Humanities in Al-Kharj, Prince Sattam Bin Abdulaziz University,
Al-Kharj 11942, Saudi Arabia
2
Department of Basic Engineering Science, Faculty of Engineering, enoufia University, Shebin El-Kom 32511, Egypt
3
Department of athematics and Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia
Correspondence should be addressed to M. A. El-Shorbagy; mohammed_shorbagy@yahoo.com
Received 14 November 2020; Revised 22 December 2020; Accepted 29 December 2020; Published 15 January 2021
Academic Editor: Baogui Xin
Copyright © 2021 M. A. El-Shorbagy and A. A. Mousa. is is an open access article distributed under the Creative Commons
Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is
properly cited.
is research implements a recent evolutionary-based algorithm of equilibrium optimizer to resolve the constrained combined
economic emission dispatch problem. is problem has two objective functions that represent the minimizing of generation costs
and minimizing the emission of environmental pollution caused by generators. e proposed algorithm integrates the dominant
criteria for multiobjective functions that allow the decision-maker to detect all the Pareto boundaries of constrained combined
economic emission dispatch problem. In order to save the effort for the decision-maker to select the best compromise alternative, a
cluster study was carried out to minimize the size of the Pareto boundary to an acceptable size, representing all the characteristics
ofthemainParetofrontier.Ontheotherhand,inordertodealwiththeinfringementofconstraints,arepairalgorithmwasusedto
preserve the viability of the particles. e proposed algorithm is applied to solve the standard 30-bus IEEE system with 6
generators to validate its robustness and efficiency to produce a well-distributed Pareto frontier for constrained combined
economic emission dispatch problem. Compared with other studies, good results in solving constrained combined economic
emission dispatch problem are obtained and a reasonable reduced Pareto set is found.
1. Introduction
e robust and efficient economic planning, operation, and
distribution of power systems have always presided a vital
role in the power system industry. Saving a small percent in
the operation of the power systems produces a reasonable
reduction in the operating cost and in the amount of fuel
consumed [1]. Finding the optimum operating cost is the key
purpose of the classic constrained combined economic
emission dispatch problem (CEEDP) [2]. Recently, for large
scale electric power system, modern system optimization
theory methods are applied with the cost savings [3]. ere
are three directions to solve CEEDP [4].
Traditionally, the first direction is to simplify the mul-
tiobjective optimization problem (MOP) to a single objective
problem. Traditional methods used to convert MOP into a
single objective problem are either the aggregating of ob-
jective functions as in the weighted sum method or the
optimization of the most important objective and the
treatment of others as constraints as in the ε-constraint
method or the penalty factor approach [5]. en, various
numerical optimization methods have been employed to
handle this single objective problem such as the augmented
Lagrangian method and gradient method, for example, in
weighted sum [6], the ε-constraint method [7]. e most
important weaknesses of these methods are that it cannot
deal with nonconvex function and tends to find weak set of
nondominated solutions. On the other hand, goal pro-
gramming is also implemented to deal with CEEDP [8]. In
this approach, a specified target is assigned for each objective
to be achieved and then aims to minimize the deviation from
the desired targets to the objective functions.
Hindawi
Complexity
Volume 2021, Article ID 6672131, 14 pages
https://doi.org/10.1155/2021/6672131