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Multi-objective problems have gained much attention during the last decade. To balance the diversity and the convergence of the multi-objective differential evolution algorithm (MODE), an improved MODE is proposed based on the affinity propagation clustering (APC) and the non-dominated count approach in this paper. The proposed algorithm is referred to as AP-MODE, which improves the search efficiency by utilizing the affinity propagation approach to find out the population distribution structure for guiding search. In addition, mating restriction probability is used to select parent individuals for recombination from the neighborhoods or the whole population. Meanwhile, the mating restriction probability is updated according to the non-dominated count approach at each generation. This proposed algorithm is verified by comparing it with some state-of-the-art multi-objective evolutionary algorithms, and the simulation results on DTLZ test problems indicate that AP-MODE can efficiently achieve two goals of multi-objective optimization, i.e., the convergence to actual Pareto front and uniform spread of individuals along Pareto front. [ABSTRACT FROM AUTHOR]

In this paper, a modified and hybrid flower pollination algorithms (MHFPA) is proposed for dealing with the multi-objective optimal power flow (MOOPF) problem with conflictive objectives. The algorithm combines the mutation and crossover process in the differential evolution (DE) algorithm, introduces the sinusoidal nonlinear dynamic switching probability (SNDSP) and the elite strategy of elder generation (ESEG), which can improve the shortcomings of the original pollen algorithm that it is easy to fall into the local optimum and the diversity is insufficient. A screening approach with Pareto-dominant rule (SAPR) is proposed to ensure that the state variable can satisfy the inequality constraints of the power system. A uniformly distributed Pareto optimal set (POS) is obtained by the non-dominant sorting with elite strategy (NSES) based on Rank and Density estimation, and the best trade-off solution (BTS) is determined from the POS obtained by the fuzzy affiliation theory. For practicality, the total fuel cost, active power loss, emissions and voltage deviation are selected as objective functions. Due to the limitations of the actual power system, the valve point effect is also considered. The IEEE30-, 57- and IEEE118-bus test systems are used to verify the performance of the proposed MHFPA. In addition, two performance indicators, Hypervolume (HV) and Spacing (SP), quantitatively evaluate the diversity and uniformity of the POS obtained by MHFPA. The simulation results show that, compared with the classic MOPSO and NSGA-II algorithms, the method proposed in this paper shows a greater competitive advantage in dealing with different scales and non-convex optimization problems. [ABSTRACT FROM AUTHOR]

This paper proposes an improved novel bionic intelligent Moth-Flame Optimization (MFO) algorithm optimized linear active disturbance rejection control (LADRC) strategy for automatic generation control (AGC) problems. LADRC is a control strategy that combines linear extended state observer (LESO) and traditional proportional-derivative (PD) control, with the advantages of its resistance to disturbance and simplicity. The three-order LADRC controller is designed in load frequency control (LFC) system. The Improved MFO (IMFO) algorithm is proposed by Cauchy mutation strategy and self-adaptive weight to overcome the weaknesses in easily falling into local optima and poor optimization search accuracy, and the IMFO algorithm is employed for tuning the parameters of LADRC. Besides, an objective function takes account of the performance index integral-time-multiplied-AE (ITAE) with dynamic indicators, which is used to improve the effectiveness of LADRC. The proposed control strategy is tested for robustness in a two-area non-reheat thermal system and compared with recent control methods published in the literature. As a result, its superiority is demonstrated for the lowest cost function values of ITAE = 0.0036, ITSE = 1.24E-05, ISE = 6.81E-05 and IAE= 0.0086. To further explore the potential of the LADRC controller based on the IMFO algorithm, it is also extended to a two-area nonlinear system and an unequal three-area reheat system. The performance indicator functions and dynamic performance indicators are analyzed qualitatively in the meantime. [ABSTRACT FROM AUTHOR]