In dealing with constrained multi-objective optimization problems (CMOPs), a key issue of multi-objective evolutionary algorithms (MOEAs) is to balance the convergence and diversity of working populations.
This letter suggests an approach for decomposing a multiobjective optimization problem (MOP) into a set of simple multiobjective optimization subproblems. Using this approach, it proposes MOEA D-M2M, a new version of multiobjective optimization evolutionary algorithm-based decomposition. This proposed algorithm solves these subproblems in a collaborative way. Each subproblem has its own population and receives computational effort at each generation. In such a way, population diversity can be maintained, which is critical for solving some MOPs. Experimental studies have been conducted to compare MOEA D-M2M with classic MOEA D and NSGA-II. This letter argues that population diversity is more important than convergence in multiobjective evolutionary algorithms for dealing with some MOPs. It also explains why MOEA D-M2M performs better. Abstract This paper proposes a parallel hurricane optimization algorithm (PHOA) for solving economic emission load dispatch (EELD) problem in modern power systems. In PHOA, several sub-populations moving independently in the search space with the aim of simultaneously optimizing the problem objectives considering the local behavior between sub-populations. By this way, it is intended to search for the Pareto optimal solutions which are contrasting to the single optimal solution. The inherent characteristics of parallelization strategy can enhance the Pareto solutions and increase the convergence to reach the Pareto optimal solutions. Simulations are conducted on three test systems and comparisons with other optimization techniques that reported in the literature are demonstrated. The obtained results demonstrate the superiority of the proposed PHOA compared to other optimization techniques. Additional economic benefits with secure settings are fulfilled, while preserving all system constraints within their permissible limits. Added to that, two security indices are proposed from generation units and transmission lines. The highest security index from generation units reflects that the operating condition achieves more power reserve. In transmission lines, the highest security index means that the transmission lines operated beyond their congestion limits. For justification of the proposed security indices, the proposed solution methodology is employed to assure their benefits in terms of economical and environmental issues. The proposed algorithm improves the economic issue as well as enhances the power system operation in the technical point of view with acceptable levels of emissions. Moreover, design of experiments using the Taguchi approach is employed to calibrate the parameters of the algorithms. So, it can be considered as a promising alternative algorithm for solving problems in practical large-scale power systems.