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The artificial bee colony (ABC) algorithm is a relatively new optimization technique which has been shown to be competitive to other population-based algorithms. However, ABC has an insufficiency regarding its solution search equation, which is good at exploration but poor at exploitation. To address this concerning issue, we first propose an improved ABC method called as CABC where a modified search equation is applied to generate a candidate solution to improve the search ability of ABC. Furthermore, we use the orthogonal experimental design (OED) to form an orthogonal learning (OL) strategy for variant ABCs to discover more useful information from the search experiences. Owing to OED's good character of sampling a small number of well representative combinations for testing, the OL strategy can construct a more promising and efficient candidate solution. In this paper, the OL strategy is applied to three versions of ABC, i.e., the standard ABC, global-best-guided ABC (GABC), and CABC, which yields OABC, OGABC, and OCABC, respectively. The experimental results on a set of 22 benchmark functions demonstrate the effectiveness and efficiency of the modified search equation and the OL strategy. The comparisons with some other ABCs and several state-of-the-art algorithms show that the proposed algorithms significantly improve the performance of ABC. Moreover, OCABC offers the highest solution quality, fastest global convergence, and strongest robustness among all the contenders on almost all the test functions.