An improved firefly algorithm for identifying parameters of nonlinear empirical models

The nonlinear model is to describe the vortex-induced resonance of long-span bridges under the action of natural wind. The identification accuracy of its parameters directly affects people's understanding of vortex-induced vibration. People have been trying different algorithms to solve this parameter identification problem, but the efficiency and accuracy of algorithms are not satisfied. In this work, a firefly algorithm based on local chaos search and brightness variant (FACLBV) is proposed. The characteristics of chaos make FACLBV search the widely local scope and improve the accuracy of the solution. FACLBV modifies the fixed initial brightness, discards the absorption coefficient of light intensity, links the initial brightness of every firefly with the position of its solution space, and sets the attraction of every firefly as a simple linear function, which reduces the complexity of the algorithm and improves the efficiency. In order to better verify the superiority of FACLBV, the simulation experiment includes three parts: the comparison between FACLBV and other firefly algorithms, the verification of the parameters identified by FACLBV, and the nonparametric test between FACLBV and other intelligent algorithms. Simulation results show that FACLBV is better than other algorithms in performance.

IFA-EO: An Improved Firefly Algorithm Hybridized With Extremal Optimization for Continuous Unconstrained Optimization Problems

As one of the evolutionary algorithms, firefly algorithm (FA) has been widely used to solve various complex optimization problems. However, FA has significant drawbacks in slow convergence rate and is easily trapped into local optimum. To tackle these defects, this paper proposes an improved FA combined with extremal optimization (EO), named IFA-EO, where three strategies are incorporated. First, to balance the tradeoff between exploration ability and exploitation ability, we adopt a new attraction model for FA operation, which combines the full attraction model and the single attraction model through the probability choice strategy. In the single attraction model, small probability accepts the worse solution to improve the diversity of the offspring. Second, the adaptive step size is proposed based on the number of iterations to dynamically adjust the attention to the exploration model or exploitation model. Third, we combine an EO algorithm with powerful ability in local-search into FA. Experiments are tested on two group popular benchmarks including complex unimodal and multimodal functions. Our experimental results demonstrate that the proposed IFA-EO algorithm can deal with various complex optimization problems and has similar or better performance than the other eight FA variants, three EO-based algorithms, and one advanced differential evolution variant in terms of accuracy and statistical results.

A multi-objective optimization operation strategy for ice-storage air-conditioning system based on improved firefly algorithm

Reasonable distribution of cooling load between chiller and ice tank is the key to realize the economical and energy-saving operation of ice-storage air-conditioning (ISAC) system. A multi-objective optimization model based on improved firefly algorithm (IFA) was established in this study to fully exploit the energy-saving potential and economic benefit of the ISAC system. The proposed model took the partial load rate of each chiller and the cooling ratio of the ice tank as optimization variables, and the lowest energy consumption loss rate and the lowest operating cost of the ISAC system were calculated. Chaotic logic self-mapping was used to initialize population to avoid falling into local optimum, and Cauchy mutation was used to increase the population’s diversity to improve the algorithm’s global search ability. The experimental results show that compared with the operation strategy based on constant proportion, particle swarm optimization (PSO) algorithm, and firefly algorithm (FA), the optimal operation strategy based on IFA can achieve more significant energy-saving and economic benefits. Meanwhile, the convergence accuracy and stability of the algorithm are significantly improved. Practical application: The optimized operation strategy of the ice-storage air-conditioning system can reduce energy loss and operating costs. The traditional operation strategies have the problems of low optimization precision and poor optimization effect. Therefore, this study presents an optimal operation strategy based on IFA. The convergence accuracy and stability of the algorithm are increased after the algorithm is improved. The operation strategy can get the maximum energy-saving effect and economic benefit of the ISAC system.

An improved firefly algorithm with dynamic self-adaptive adjustment

The firefly algorithm (FA) is proposed as a heuristic algorithm, inspired by natural phenomena. The FA has attracted a lot of attention due to its effectiveness in dealing with various global optimization problems. However, it could easily fall into a local optimal value or suffer from low accuracy when solving high-dimensional optimization problems. To improve the performance of the FA, this paper adds the self-adaptive logarithmic inertia weight to the updating formula of the FA, and proposes the introduction of a minimum attractiveness of a firefly, which greatly improves the convergence speed and balances the global exploration and local exploitation capabilities of FA. Additionally, a step-size decreasing factor is introduced to dynamically adjust the random step-size term. When the dimension of a search is high, the random step-size becomes very small. This strategy enables the FA to explore solution more accurately. This improved FA (LWFA) was evaluated with ten benchmark test functions under different dimensions (D = 10, 30, and 100) and with standard IEEE CEC 2010 benchmark functions. Simulation results show that the performance of improved FA is superior comparing to the standard FA and other algorithms, i.e., particle swarm optimization, the cuckoo search algorithm, the flower pollination algorithm, the sine cosine algorithm, and other modified FA. The LWFA also has high performance and optimal efficiency for a number of optimization problems.

Cooperative trading of a price-maker wind power producer: A data-driven approach considering uncertainty

This paper presents a novel framework for cooperative trading in a price-maker wind power producer, that participates in the short-term electricity balance markets. In this framework, market price uncertainty is first modeled using a price uncertainty predictor, consisting of ridge regression (RR), nonpooling convolutional neural network (NPCNN), and linear quantile regression (LQR). RR is employed to select the correlated features to the corresponding forecast day, NPCNN is employed to extract the nonlinear features, and LQR is employed to estimate the price uncertainty. Then, an improved firefly algorithm (IFA) is proposed to solve the optimization problem. IFA uses the adaptive moment estimation method to improve the convergence speed and search for the global solution. Finally, the Shapley value is employed for the profit distribution of cooperative power producers. Illustrative examples show the effectiveness of the proposed framework and optimization model

Cooperative trading of a price-maker wind power producer: A data-driven approach considering uncertainty

This paper presents a novel framework for cooperative trading in a price-maker wind power producer, that participates in the short-term electricity balance markets. In this framework, market price uncertainty is first modeled using a price uncertainty predictor, consisting of ridge regression (RR), nonpooling convolutional neural network (NPCNN), and linear quantile regression (LQR). RR is employed to select the correlated features to the corresponding forecast day, NPCNN is employed to extract the nonlinear features, and LQR is employed to estimate the price uncertainty. Then, an improved firefly algorithm (IFA) is proposed to solve the optimization problem. IFA uses the adaptive moment estimation method to improve the convergence speed and search for the global solution. Finally, the Shapley value is employed for the profit distribution of cooperative power producers. Illustrative examples show the effectiveness of the proposed framework and optimization model