This article introduces the Coincidence Algorithm (COIN) to solve several multimodal puzzles. COIN is an algorithm in the category of Estimation of Distribution Algorithms (EDAs) that makes use of probabilistic models to generate solutions. The model of COIN is a joint probability table of adjacent events (coincidence) derived from the population of candidate solutions. A unique characteristic of COIN is the ability to learn from a negative sample. Various experiments show that learning from a negative example helps to prevent premature convergence, promotes diversity and preserves good building blocks.

We present a training algorithm to create a neural network (NN) ensemble that performs classification tasks. It employs a competitive decay of hidden nodes in the component NNs as well as a selective deletion of NNs in ensemble, thus named a pruning algorithm for NN ensembles (PNNE). A node cooperation function of hidden nodes in each NN is introduced in order to support the decaying process. The training is based on the negative correlation learning that ensures diversity among the component NNs in ensemble. The less important networks are deleted by a criterion that indicates over-fitting. The PNNE has been tested extensively on a number of standard benchmark problems in machine learning, including the Australian credit card assessment, breast cancer, circle-in-the-square, diabetes, glass identification, ionosphere, iris identification, and soybean identification problems. The results show that classification performances of NN ensemble produced by the PNNE are better than or competitive to those by the conventional constructive and fixed architecture algorithms. Furthermore, in comparison to the constructive algorithm, NN ensemble produced by the PNNE consists of a smaller number of component NNs, and they are more diverse owing to the uniform training for all component NNs.