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The economic load dispatch (ELD) problem plays a crucial role in power system operation. In practice, the ELD problem becomes a non-convex, multi-constraint, non-linear optimization problem when considering the valve point effects, the prohibited operation zones, the ramp rate limit, and the multi-fuel options. To effectively solve this problem, this paper puts forward an improved differential evolution (DE) named OMLIDE based on opposition-mutual learning, hybrid mutation strategy, and parameters adaptive mechanism. OMLIDE differs from the traditional DE in that: (1) an opposition-mutual learning strategy is employed for population initialization to increase the probability of finding an optimal solution; (2) two novel mutation operators named DE/elite-to-ordinary/1 and DE/elite-to-ordinary/2 are hybridized and a selection probability is introduced to regulate them adaptively at different evolutionary stages; and (3) a parameters adaptive mechanism is presented to adjust the scaling factor and crossover rate. The proposed OMLIDE is first validated by the numerical benchmark functions of CEC 2014. Then it is applied to five non-convex ELD problems with valve-point effects and multi-fuel options. Simulation results demonstrate that OMLIDE provides better or highly competitive results in different terms compared with other peer algorithms. This work was supported by the Basic Research Program of Guizhou Province (Natural Science) (QiankeheBasic-ZK[2022]General121) and the National Natural Science Foundation of China (52167007).

Effective constraint handling techniques are of great significance for evolutionary algorithms dealing with constrained optimization problems. To date, many constraint handling techniques, such as penalty function, superiority of feasible solutions, and -constraint, have been designed. However, different constraint handling techniques are usually suited to different problems, even the most appropriate technique changes along with the stages of the optimization process. Motivated by this phenomenon, we propose a voting-mechanism based ensemble framework, named VMCH, to integrate multiple constraint handling techniques for solving various constrained optimization problems. In this framework, each constraint handling technique acts as a voter, all voters vote for each pair of solutions, and the solution in each pair with the highest weighted votes is considered better. In addition, an adaptive strategy is developed to adjust the voter weights according to their historical voting performance. To investigate the performance of VMCH in improving existing algorithms, the proposed VMCH is embedded into the three best algorithms in the competition on constrained single objective real-parameter optimization at CEC 2018, namely MAgES, iLSHADE, and IUDE, to form three new algorithm versions, i.e., MAgES-VMCH, iLSHADE-VMCH, and IUDE-VMCH. They are compared with seven state-of-the-art peer algorithms. Extensive experiments are conducted on 57 real-world constrained optimization problems. The ranking results show that the new algorithm version MAgES-VMCH takes first place among the ten comparison algorithms. Moreover, all the new VMCH-enhanced versions of the three best algorithms are superior to their original versions. Therefore, the proposed VMCH framework can achieve competitive performance in solving constrained optimization problems.

In this study, we propose an efficient optimization algorithm that is a hybrid of the iterated greedy and simulated annealing algorithms (hereinafter, referred to as IGSA) to solve the flexible job shop scheduling problem with crane transportation processes (CFJSP). Two objectives are simultaneously considered, namely, the minimization of the maximum completion time and the energy consumptions during machine processing and crane transportation. Different from the methods in the literature, crane lift operations have been investigated for the first time to consider the processing time and energy consumptions involved during the crane lift process. The IGSA algorithm is then developed to solve the CFJSPs considered. In the proposed IGSA algorithm, first, each solution is represented by a 2-D vector, where one vector represents the scheduling sequence and the other vector shows the assignment of machines. Subsequently, an improved construction heuristic considering the problem features is proposed, which can decrease the number of replicated insertion positions for the destruction operations. Furthermore, to balance the exploration abilities and time complexity of the proposed algorithm, a problem-specific exploration heuristic is developed. Finally, a set of randomly generated instances based on realistic industrial processes is tested. Through comprehensive computational comparisons and statistical analyses, the highly effective performance of the proposed algorithm is favorably compared against several efficient algorithms.

Probabilistic load forecasting (PLF) has become necessary for power system operators to do efficient planning across power transmission and distribution systems. However, there are not many PLF models, and those that exist take a lot of computation time and are not efficient, especially in multiple loads. This paper proposes a novel algorithm for spatially correlated multiple loads wherein a global parameter is learned from state-space parameters of individual loads by an amalgamation of deep neural networks and state-space models. The proposed model employs complex pattern learning capabilities of recurrent neural networks and temporal pattern extraction of innovation state-space models. It is tested on GEFCom-14 and ISO-NE datasets, one with a single load and multiple loads. Different case studies are conducted to examine the involvement of temperature for load forecasting. It has been observed that in the case of multivariate loads, temperature variable doesn’t make much difference in PLF, but in the case of univariate loads, forecasting results are four-times better. The proposed method is highly interpretable and can be employed in areas where limited training data is available to the areas where colossal data is available. The proposed model has outperformed several benchmarks present in the literature on the same datasets.

Sorting solutions play a key role in using evolutionary algorithms (EAs) to solve many-objective optimization problems (MaOPs). Generally, different solution-sorting methods possess different advantages in dealing with distinct MaOPs. Focusing on this characteristic, this article proposes a general voting-mechanism-based ensemble framework (VMEF), where different solution-sorting methods can be integrated and work cooperatively to select promising solutions in a more robust manner. In addition, a strategy is designed to calculate the contribution of each solution-sorting method and then the total votes are adaptively allocated to different solution-sorting methods according to their contribution. Solution-sorting methods that make more contribution to the optimization process are rewarded with more votes and the solution-sorting methods with poor contribution will be punished in a period of time, which offers a good feedback to the optimization process. Finally, to test the performance of VMEF, extensive experiments are conducted in which VMEF is compared with five state-of-the-art peer many-objective EAs, including NSGA-III, SPEA/R, hpaEA, BiGE, and grid-based evolutionary algorithm. Experimental results demonstrate that the overall performance of VMEF is significantly better than that of these comparative algorithms.

In this paper, a new feature selection algorithm, called SFE (Simple, Fast, and Efficient), is proposed for high-dimensional datasets. The SFE algorithm performs its search process using a search agent and two operators: non-selection and selection. It comprises two phases: exploration and exploitation. In the exploration phase, the non-selection operator performs a global search in the entire problem search space for the irrelevant, redundant, trivial, and noisy features, and changes the status of the features from selected mode to non-selected mode. In the exploitation phase, the selection operator searches the problem search space for the features with a high impact on the classification results, and changes the status of the features from non-selected mode to selected mode. The proposed SFE is successful in feature selection from high-dimensional datasets. However, after reducing the dimensionality of a dataset, its performance cannot be increased significantly. In these situations, an evolutionary computational method could be used to find a more efficient subset of features in the new and reduced search space. To overcome this issue, this paper proposes a hybrid algorithm, SFE-PSO (particle swarm optimization) to find an optimal feature subset. The efficiency and effectiveness of the SFE and the SFE-PSO for feature selection are compared on 40 high-dimensional datasets. Their performances were compared with six recently proposed feature selection algorithms. The results obtained indicate that the two proposed algorithms significantly outperform the other algorithms, and can be used as efficient and effective algorithms in selecting features from high-dimensional datasets.