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In this paper, a novel hybrid model for forecasting low dimensional numerical data is proposed which is named as ClusFuDE . The proposed method uses an improved automatic clustering approach for clustering the historical numerical data. Further fuzzy logical relationships are used to forecast the approximate values which are then defuzzified to calculate the exact forecasted values of the data. The fuzzy logical relationships are useful in modelling the fuzzy relations and help in forecasting the fuzzy time series data in a very simplified manner. The forecasted sub-optimal candidate solutions are optimized using Differential Evolution. The Differential Evolution method uses a dynamic differential crossover rate ( C r i ) for the i th solution, for identifying and discarding suboptimal candidate solutions in early stages of the iterative run. This makes the method more suitable for iterative modification of candidate solutions by using differential mutation and crossover, and suitable for global search. The proposed method is applied for forecasting, the year wise enrollments of the University of Alabama, Lahi (crop) production, monthly amount of outpatients visit in a hospital, inventory demand and population of India from years 1930–2000 and the results are consistent. We have compared our method with the recent forecasting methods available in literature and the proposed method outperforms all the existing methods in the literature. The accuracy of the proposed method is computed by calculating the Mean square error (MSE) and Mean Absolute percentage error (MAPE). The proposed method provides the lowest MSE and MAPE when compared to all other methods available in the literature. [ABSTRACT FROM AUTHOR]

In practical applications, solving multimodal multiobjective optimization problems (MMOPs), which have multiple Pareto optimal sets (PSs) in the decision space mapping to the same Pareto front (PF) in the objective space, has great significance for decision makers. The issue of how to maintain diversity in both decision space and objective space remains a key problem for existing multimodal multiobjective evolutionary algorithms. To address this issue, a novel grey prediction evolution algorithm for multimodal multiobjective optimization, termed MMGPE, is proposed in this paper. This is the first time that the grey prediction evolution algorithm (GPE), which is a recently proposed competitive optimization algorithm with strong exploration capability, is improved for MMOPs. These improvements are conducted in the following four aspects: (1) an initialization operator based on particle swarm optimization, (2) an adaptive parameter setting strategy depending on the domain of decision variables of MMOPs, (3) an accelerating convergence mechanism inspired by the niche principle, and (4) an environmental selection operator based on a nondominated sorting mechanism and a special crowding distance approach. The performance of MMGPE is compared with two state-of-the-art multiobjective evolutionary algorithms and four multimodal multiobjective evolutionary algorithms on 11 multimodal multiobjective test functions. MMGPE is also applied to solve a practical problem. The results show the MMGPE's effectiveness and superiority in achieving the goal of finding multiple PSs while obtaining a well-distributed PF. [ABSTRACT FROM AUTHOR]