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In this paper, a novel hybrid firefly-bat algorithm with constraints-prior object-fuzzy sorting strategy (HFBA-COFS) is put forward to solve the strictly-constrained multi-objective optimal power flow (MOOPF) problems. The hybrid firefly-bat algorithm (HFBA) integrates the dimension-based firefly algorithm and the modified bat algorithm to improve the population-diversity and global-exploration ability of original algorithm. To handle the unqualified state variables and overcome the deficiency of traditional penalty function approach (PFA), the constraints-prior Pareto-dominant rule (CPR) which takes constraints-violation and objectives-value into consideration is proposed in this paper. Furthermore, an effective constraints-prior object-fuzzy sorting (COFS) strategy based on CPR rule is presented to seek the well-distributed Pareto optimal set (POS) in solving the MOOPF problems. To validate the great advantages of HFBA-COFS algorithm, ten MOOPF cases optimizing active power loss, total emission and fuel cost are simulated on the IEEE 30-bus, IEEE 57-bus and IEEE 118-bus systems. In addition, the generational distance and SPREAD evaluation indexes powerfully demonstrate that the proposed HFBA-COFS algorithm can achieve high-quality POS, which has great significance to realize the safe and economic operation of large-scale power systems.

Multi-Objective Optimal Power Flow Based on Hybrid Firefly-Bat Algorithm and Constraints- Prior Object-Fuzzy Sorting Strategy