Application of modified pigeon-inspired optimization algorithm and constraint-objective sorting rule on multi-objective optimal power flow problem

To solve the non-differentiable optimal power flow (OPF) problems with multiple contradictory objectives, a modified pigeon-inspired optimization algorithm (MPIO) is put forward in this paper. Combining with the common-used penalty function method (PFM), the MPIO-PFM algorithm is proposed and applied to optimize the active power loss, emission and fuel cost (with valve-point loadings) of power system. Eight simulation trials carried out on MATLAB software validate MPIO-PFM algorithm can obtain superior Pareto Frontier (PF) comparing with the typical NSGA-II algorithm. Nevertheless, some Pareto solutions obtained by MPIO-PFM algorithm cannot satisfy all system constraints due to the difficulty in choosing the proper penalty coefficients. Thus, an innovative approach named as constraint-objective sorting rule (COSR) is presented in this paper. The bi-objective and tri-objective trials implemented on IEEE 30-node, 57-node and 118-node systems demonstrate that the Pareto optimal set (POS) obtained by MPIO-COSR algorithm realizes zero-violation of various system constraints. Furthermore, the generational-distance and hyper-volume indexes quantitatively illustrate that in contrast to NSGA-II and MPIO-PFM methods, the MPIO-COSR algorithm can determine the evenly-distributed PFs with satisfactory-diversity. The intelligent MPIO-COSR algorithm provides an effective way to handle the non-convex MOOPF problems. •Modified pigeon-inspired algorithm (MPIO) and constraint-objective sorting rule (COSR) are proposed for MOOPF problems.•MPIO-COSR algorithm is effective to reduce the active power loss, fuel cost and emission of power systems.•MPIO-COSR algorithm is examined on the IEEE 30-node, 57-node and 118-node systems by eight simulation cases.•The superiority of MPIO-COSR algorithm is validated by comparing with NSGA-II and MPIO-PFM algorithms.•Proposed MPIO-COSR algorithm obtains evenly-distributed POS & fast-convergence & zero constraint-violation.