Abstract
This research implements a recent evolutionary-based algorithm of equilibrium optimizer to resolve the constrained combined economic emission dispatch problem. This problem has two objective functions that represent the minimizing of generation costs and minimizing the emission of environmental pollution caused by generators. The 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 of the main Pareto frontier. On the other hand, in order to deal with the infringement of constraints, a repair algorithm was used to preserve the viability of the particles. The 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.
Highlights
Academic Editor: Baogui Xin 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 of the main Pareto frontier
Complexity e second direction is to solve the single objective combined economic emission dispatch problem (CEEDP) by any single objective meta-heuristics algorithm such as artificial bee colony (ABC) [9], gravitational search algorithm (GSA) [10], and Gaussian particle swarm optimization (GPSO) [11] or by any hybrid single objective meta-heuristics algorithms such as hybrid particle swarm optimization (PSO) algorithm and firefly algorithm (FA) [12], hybrid ABC algorithm and simulated annealing algorithm (SA) [13], and PSO-GSA algorithm [14]
Summary
A broad range of applications in architecture, computer science, and many other fields include optimizing several objectives at the same time [69]. Definition 1 (formulation of multiobjective optimization problem). E vector x ∈ Rn is defined as a vector of n decision variables in the optimization problem formulation. Definition 4 (the set of Pareto optimal solutions). By using the ideal vector, the lower limits of the Pareto optimal frontier for each objective function are determined. Definition 7 (nadir objective vector) [71]. Nadir vector is the upper bound of the optimal Pareto frontier. 3. The Formulation of Combined Economic Emission Dispatch Problem e CEEDP involves the optimization of two multiple conflicting objectives, generation operation cost, and pollutant emission, which must be addressed at the same time. Objective Functions. e formulation of the objective functions of the problem, which are objective for the economy and environmental objective, is seen in this subsection
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