This paper concerns a method of selecting a subset of features for a logistic regression model. Information criteria, such as the Akaike information criterion and Bayesian information criterion, are employed as a goodness-offit measure. The feature subset selection problem is formulated as a mixed integer linear optimization problem, which can be solved with standard mathematical optimization software, by using a piecewise linear approximation. Computational experiments show that, in terms of solution quality, the proposed method has superiority over common stepwise methods.

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This paper describes the traveling tournament problem, a well-known benchmark problem in the field of tournament timetabling. We propose an approximation algorithm for the traveling tournament problem with the constraints such that both the number of consecutive away games and that of consecutive home games are at most k. When k ≤ 5, the approximation ratio of the proposed algorithm is bounded by (2k − 1)/k + O(k/n) where n denotes the number of teams; when k > 5, the ratio is bounded by (5k − 7)/(2k) + O(k/n). For k = 3, the most investigated case of the traveling tournament problem to date, the approximation ratio of the proposed algorithm is 5/3 + O(1/n); this is better than the previous approximation algorithm proposed for k = 3, whose approximation ratio is 2 + O(1/n).

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A 2.75-approximation algorithm is proposed for the unconstrained traveling tournament problem, which is a variant of the traveling tournament problem. For the unconstrained traveling tournament problem, this is the first proposal of an approximation algorithm with a constant approximation ratio. In addition, the proposed algorithm yields a solution that meets both the norepeater and mirrored constraints. Computational experiments show that the algorithm generates solutions of good quality.