Classification is an essential task in the field of machine learning, where finding a maximum margin classifier is one of its central problems. In this work, an evolutionary algorithm is constructed, relying on the convexity properties of the version space, to evolve a population of perceptron classifiers in order to find a solution that approximates the maximum margin. Unlike other methods whose solutions explore the problem’s dual formulation, usually requiring the solution of a linear constraint quadratic programming problem, the proposed method requires only the evaluation of the margin values. Hyperspherical coordinates are used to guarantee feasibility when generating new individuals and for the population to be uniformly distributed through the search space. To control the number of generations, we developed a stop criteria based on a lower bound function which asymptotically approximates the margin curves providing a stop margin that satisfies a \(\beta \)-approximation of the optimal margin. Experiments were performed on artificial and real datasets, and the obtained results indicate the potential to adopt the proposed algorithm for solving practical problems.

分类是机器学习领域中的一项基本任务，在该机器学习中，找到最大余量分类器是其核心问题之一。在这项工作中，构建了一种进化算法，该算法依靠版本空间的凸性来演化感知器分类器的总体，以找到近似最大余量的解决方案。与其他解决方案探索问题的对偶表示法（通常需要求解线性约束二次规划问题）的其他方法不同，所提出的方法仅需要评估裕度值。超球面坐标用于确保生成新个体时的可行性，并使种群在搜索空间中均匀分布。为了控制世代数，\（\ beta \） -最佳边距的近似值。在人工和真实数据集上进行了实验，获得的结果表明采用所提出的算法解决实际问题的潜力。