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Combinatorial test design is a plan of test that aims to reduce the amount of test cases systematically by choosing a subset of the test cases based on the combination of input variables. The subset covers all possible combinations of a given strength and hence tries to match the effectiveness of the exhaustive set. This mechanism of reduction has been used successfully in software testing research with t-way testing (where t indicates the interaction strength of combinations). Potentially, other systems may exhibit many similarities with this approach. Hence, it could form an emerging application in different areas of research due to its usefulness. To this end, more recently it has been applied in a few research areas successfully. In this paper, we explore the applicability of combinatorial test design technique for Fractional Order (FO), Proportional-Integral-Derivative (PID) parameter design controller, named as FOPID, for an automatic voltage regulator (AVR) system. Throughout the paper, we justify this new application theoretically and practically through simulations. In addition, we report on first experiments indicating its practical use in this field. We design different algorithms and adapted other strategies to cover all the combinations with an optimum and effective test set. Our findings indicate that combinatorial test design can find the combinations that lead to optimum design. Besides this, we also found that by increasing the strength of combination, we can approach to the optimum design in a way that with only 4-way combinatorial set, we can get the effectiveness of an exhaustive test set. This significantly reduced the number of tests needed and thus leads to an approach that optimizes design of parameters quickly. [ABSTRACT FROM AUTHOR]

This work proposes a model considering fairness in the problem of crew scheduling for bus drivers (CSP-BD) using a hybrid ant-colony optimization (HACO) algorithm to solve it. The main contributions of this work are the following: (a) a valid approach for cases with a special cost structure and constraints considering the fairness of working time and idle time; (b) an improved algorithm incorporating Gamma heuristic function and selecting rules. The relationships of each cost are examined with ten bus lines collected from the Beijing Public Transport Holdings (Group) Co., Ltd., one of the largest bus transit companies in the world. It shows that unfair cost is indirectly related to common cost, fixed cost and extra cost and also the unfair cost approaches to common and fixed cost when its coefficient is twice of common cost coefficient. Furthermore, the longest time for the tested bus line with 1108 pieces, 74 blocks is less than 30 minutes. The results indicate that the HACO-based algorithm can be a feasible and efficient optimization technique for CSP-BD, especially with large scale problems. [ABSTRACT FROM AUTHOR]