A Novel Fuzzy Histogram Based Estimation of Distribution Algorithm for Global Numerical Optimization

Abstract

Applying Estimation of Distribution Algorithms (EDAs) to solve continuous problems is a significant and challenging task in the field of evolutionary computation. So far, various continuous EDAs have been developed based on different probability models. Initially, the EDAs based on a single Gaussian probability model are widely used but they have trouble in solving multimodal problems. Later EDAs based on a mixture model and on a clustering technique are then introduced to conquer such drawback. However, they are either time consuming or need prior knowledge of the problems. Recently, the histogram has begun to be used in continuous EDAs, but the histogram based EDAs (HEDAs) usually need too much time and space to gain a highly accurate solution. On the basis of pioneering contributions, this paper proposes a fuzzy histogram based EDA (FHEDA) for continuous optimization. In the FHEDA, the estimated range of the fuzzy histogram is adjusted adaptively by the current promising solutions, which leads the algorithm to search good solutions efficiently. A mutation mechanism is also introduced in the sampling operation to avoid being trapped in local optima. The performance of the proposed FHEDA is evaluated by testing seven benchmark functions with different characteristics. Two Gaussian based EDAs and the sur-shr-HEDA are studied for comparison. The results show that among all experimental algorithms, the FHEDA can give comparatively satisfying performance on unimodal and multimodal functions.