An adaptive ant colony optimization algorithm for constructing cognitive diagnosis tests

Abstract

A critical issue in the applications of cognitive diagnosis models (CDMs) is how to construct a feasible test that achieves the optimal statistical performance for a given purpose. As it is hard to mathematically formulate the statistical performance of a CDM test based on the items used, exact algorithms are inapplicable to the problem. Existing test construction heuristics, however, suffer from either limited applicability or slow convergence. In order to efficiently approximate the optimal CDM test for different construction purposes, this paper proposes a novel test construction method based on ant colony optimization (ACO-TC). This method guides the test construction procedure with pheromone that represents previous construction experience and heuristic information that combines different item discrimination indices. Each test constructed is evaluated through simulation to ensure convergence towards the actual optimum. To further improve the search efficiency, an adaptation strategy is developed, which adjusts the design of heuristic information automatically according to the problem instance and the search stage. The effectiveness and efficiency of the proposed method is validated through a series of experiments with different conditions. Results show that compared with traditional test construction methods of CDMs, the proposed ACO-TC method can find a test with better statistical performance at a faster speed.