Ryuhei Miyashiro

Characterizing Feasible Pattern Sets with a Minimum Number of Breaks

In sports timetabling, creating an appropriate timetable for a round-robin tournament with home–away assignment is a significant problem. To solve this problem, we need to construct home–away assignment that can be completed into a timetable; such assignment is called a feasible pattern set. Although finding feasible pattern sets is at the heart of many timetabling algorithms, good characterization of feasible pattern sets is not known yet. In this paper, we consider the feasibility of pattern sets, and propose a new necessary condition for feasible pattern sets. In the case of a pattern set with a minimum number of breaks, we prove a theorem leading a polynomial-time algorithm to check whether a given pattern set satisfies the necessary condition. Computational experiment shows that, when the number of teams is less than or equal to 26, the proposed condition characterizes feasible pattern sets with a minimum number of breaks.

Semidefinite programming based approaches to the break minimization problem

This paper considers the break minimization problem in sports timetabling. The problem is to find, under a given timetable of a round-robin tournament, a home-away assignment that minimizes the number of breaks, i.e., the number of occurrences of consecutive matches held either both at away or both at home for a team. We formulate the break minimization problem as MAX RES CUT and MAX 2SAT, and apply Goemans and Williamsons approximation algorithm using semidefinite programming. Computational experiments show that our approach quickly generates solutions of good approximation ratios.

A polynomial-time algorithm to find an equitable home-away assignment

We propose a polynomial-time algorithm to find an equitable home-away assignment for a given timetable of a round-robin tournament. Our results give an answer to a problem raised by Elf et al. (Oper. Res. Lett. 31 (2003) 343), which concerns the computational complexity of the break minimization problem in sports timetabling.

Mixed integer second-order cone programming formulations for variable selection in linear regression

This study concerns a method of selecting the best subset of explanatory variables in a multiple linear regression model. Goodness-of-fit measures, for example, adjusted R2, AIC, and BIC, are generally used to evaluate a subset regression model. Although variable selection with regard to these measures is usually performed with a stepwise regression method, it does not always provide the best subset of explanatory variables. In this paper, we propose mixed integer second-order cone programming formulations for selecting the best subset of variables with respect to adjusted R2, AIC, and BIC. Computational experiments show that, in terms of these measures, the proposed formulations yield better solutions than those provided by common stepwise regression methods.

Feature subset selection for logistic regression via mixed integer optimization

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-of-fit measure. The purpose of our work is to establish a computational framework for selecting a subset of features with an optimality guarantee. For this purpose, we devise mixed integer optimization formulations for feature subset selection in logistic regression. Specifically, we pose the problem as a mixed integer linear optimization problem, which can be solved with standard mixed integer optimization software, by making a piecewise linear approximation of the logistic loss function. The computational results demonstrate that when the number of candidate features was less than 40, our method successfully provided a feature subset that was sufficiently close to an optimal one in a reasonable amount of time. Furthermore, even if there were more candidate features, our method often found a better subset of features than the stepwise methods did in terms of information criteria.

An approximation algorithm for the traveling tournament problem

This paper describes the traveling tournament problem, a well-known benchmark problem in the field of tournament timetabling. We propose a new lower bound for the traveling tournament problem, and construct a randomized approximation algorithm yielding a feasible solution whose approximation ratio is less than 2+(9/4)/(n−1), where n is the number of teams. Additionally, we propose a deterministic approximation algorithm with the same approximation ratio using a derandomization technique. For the traveling tournament problem, the proposed algorithms are the first approximation algorithms with a constant approximation ratio, which is less than 2+3/4.

Subset selection by Mallows’ Cp: A mixed integer programming approach

Abstract This paper concerns a method of selecting the best subset of explanatory variables for a linear regression model. Employing Mallows’ C p as a goodness-of-fit measure, we formulate the subset selection problem as a mixed integer quadratic programming problem. Computational results demonstrate that our method provides the best subset of variables in a few seconds when the number of candidate explanatory variables is less than 30. Furthermore, when handling datasets consisting of a large number of samples, it finds better-quality solutions faster than stepwise regression methods do.

Subset selection by Mallows' C p

Abstract This paper concerns a method of selecting the best subset of explanatory variables for a linear regression model. Employing Mallows’ C p as a goodness-of-fit measure, we formulate the subset selection problem as a mixed integer quadratic programming problem. Computational results demonstrate that our method provides the best subset of variables in a few seconds when the number of candidate explanatory variables is less than 30. Furthermore, when handling datasets consisting of a large number of samples, it finds better-quality solutions faster than stepwise regression methods do.

Semidefinite programming based approaches to home-away assignment problems in sports scheduling

For a given schedule of a round-robin tournament and a matrix of distances between homes of teams, an optimal home-away assignment problem is to find a home-away assignment that minimizes the total traveling distance. We propose a technique to transform the problem to MIN RES CUT . We apply Goemans and Williamsons 0.878-approximation algorithm for MAX RES CUT, which is based on a positive semidefinite programming relaxation,to the obtained MIN RES CUT instances. Computational experiments show that our approach quickly generates solutions of good approximation ratios.

A 2.75-approximation algorithm for the unconstrained traveling tournament problem

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 no-repeater and mirrored constraints. Computational experiments show that the algorithm generates solutions of good quality.