Quantum-behaved bat algorithm for many-objective combined economic emission dispatch problem using cubic criterion function

In this research, a quantum computing idea based bat algorithm (QBA) is proposed to solve many-objective combined economic emission dispatch (CEED) problem. Here, CEED is represented using cubic criterion function to reduce the nonlinearities of the system. Along with economic load dispatch, emissions of SO₂, NO_x, and CO₂ are considered as separate three objectives, thus making it a four-objective (many-objective) optimization problem. A unit-wise price penalty factor is considered here to convert all the objectives into a single objective in order to compare the final results with other previously used methods like Lagrangian relaxation (LR), particle swarm optimization, and simulated annealing. QBA is applied in six-unit power generation system for four different loads. The obtained results show QBA successfully solve many-objective CEED problem with greater superiority than other methods found in the literature in terms of quality results, robustness, and computational performance. In the end of this paper, a detailed future research direction is provided based on the simulation results and its analysis. The outcome of this research demonstrates that the inclusion of quantum computing idea in metaheuristic technique provides a useful and reliable tool for solving such many-objective optimization problem.