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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]

This paper aims to improve premature convergence and low precision of the differential evolution algorithm. An adaptive constrained differential evolution algorithm based on a probability interval update mechanism (PIMDE) is proposed. First, the interval probability update mechanism is developed to adaptively generate the mutation probability value, and the hybrid mutation strategy is formulated by effectively selecting complementary mutation strategies based on the mutation probability. Subsequently, the adaptive mechanism is employed to dynamically adjust the mutation strategy and parameters; as a result, the global detection and local search ability of the algorithm can be balanced, and the search efficiency of the algorithm can be enhanced. To verify determine the performance of the proposed algorithm, ten standard constrained optimization problems and five engineering optimization problems are analyzed. As revealed from experimental results, PIMDE can effectively solve COPs with high precision and robustness. [ABSTRACT FROM AUTHOR]

The vehicle problem (VRP) is a typical optimization problem in logistics and transportation. The objective function is to find the shortest route distances visited by all vehicles originating from a central deport to travel customers, and the sum of deliveries of each vehicle should meet the capacity constraint. This problem belongs to NP hard problems, so it is not easy to resolve it with common methods. Ant colony optimization (ACO) has shown prominent performance for many practical applications. However, it is inclined to premature convergence. The paper offers a hybrid ACO&DE algorithm, which hybridizes ant colony optimization (ACO) with differential evolution (DE) for the VRP. The main feature of the ACO&DE can make full use of advantages of the ACO and DE algorithm to make up for its own weakness, i.e., the ACO has fast construction mechanism, and the DE can extend the search scope of the ACO. Moreover, to make the DE suitable for solving the VRP, both strategies of mutation operator and crossover operator have been redesigned to implement the discrete DE directly. In addition, to increase the solution diversity by expanding the search space, we present a new selection strategy with probabilistic mechanism to determine new target vectors in the next iteration. Meanwhile, 2-opt heuristic and 2-exchange neighborhood is embedded in the ACO&DE to improve the local search performance. The results have shown that the proposed ACO&DE algorithm is competitive with existing optimal methods in solving the VRP, and thus can be further extended in variants of the VRP and other logistics transportation fields. [ABSTRACT FROM AUTHOR]

To solve the problems of the waste of resources caused by the small explosion amplitude (even close to 0) of the best firework in the conventional fireworks algorithm (FWA), and the relatively weak local search ability caused by the minimal explosion amplitude check method in the enhanced fireworks algorithm (EFWA), this paper proposes two improved strategies for FWA. First, based on the heuristic information of the distance between the best firework and other fireworks, an adaptive explosion amplitude strategy is proposed to search the local area accurately at the final phase of the FWA. Second, the highly random Lévy flight strategy is adopted instead of the Gaussian sparks strategy to generate mutation sparks in the EFWA to enhance the diversity of local search. Simulation results on 12 standard benchmark functions and their shifted functions indicate that the proposed algorithm improves the optimization precision and obtains better performance in high-dimensional complex optimization problems compared with the EFWA, the hybrid fireworks algorithm with differential evolution operator (FWADE), and the particle swarm optimization algorithm (PSO). [ABSTRACT FROM AUTHOR]

Network Function Virtualization (NFV) can provide the resource according to the request and can improve the flexibility of the network. It has become the key technology of 5G communication. Resource scheduling for virtual network function service chain (VNF-SC) is the key issue of the NFV. In this paper, the problem of routing and VNFs deployment for VNF service chain (VNF-SC) in inter-data center elastic optical networks (inter-DC EONs) is investigated.We investigate the inter-DC EONs that each data center only can provide some specific VNFs, and the system resources of all the data centers are limited. In addition, part of requiblack VNFs in each VNF-SC is dependent, i.e., the relative order of requiblack VNFs is fixed. To solve the challenging problem, we first establish a mix-integer programming model. Then, to make the population distributed on the search domain uniformly, uniform design method was developed. In addition, an improved artificial raindrop algorithm (IARA) for the established model, which inspired by particle swarm optimization and differential evolution, is proposed to solve the maximum model efficiently. Finally, to demonstrate high performance of the designed algorithm, a series of experiments are conducted in several different experimental scenes. Experimental results indicate that the proposed algorithm can obtain the better results than compared algorithm. [ABSTRACT FROM AUTHOR]

Virtual network function (VNF) is the key issue and can provide various network services and is widely deployed in 5G communication. Routing and VNF deployment for the VNF service chain (VNF-SC) is a very important and wellknown NP-hard problem. For this problem, if determining the number and locations of data centers is additionally considered, it will be more complexity. In this paper, we investigate a network planning problem by determining all these factors, i.e, by determining not only the optimal routing and the optimal VNF deployment for VNF-SCs, but also the optimal number and locations of data centers. To achieve this purpose, a three objectives optimization model, which minimizes capital expenditure, the maximum index of used frequency slots and the number of deployed VNFs on all data centers, is estimated. To solve this model efficiency, we integrate three objectives into one objective by using a weighted sum strategy. Then, a high-performance memetic algorithm with three populations (tp-MA), which includes well-designed crossover, mutation, and local search operators, is proposed. To demonstrate reasonable of the model and high performance of the designed algorithm, a series of experiments are conducted in several different experimental scenes. Experimental results indicate that the effectiveness of the proposed model and the efficiency of the proposed algorithm. [ABSTRACT FROM AUTHOR]