Support Vector Machine has shown to have good performance in many practical classification settings. In this paper we propose, for multi-group classification, a biobjective optimization model in which we consider not only the generalization ability (modelled through the margin maximization), but also costs associated with the features. This cost is not limited to an economical payment, but can ...

We investigate the problem of approximating the Pareto set of biobjective optimization problems with a given number of solutions. This task is relevant for two reasons: (i) Pareto sets are often computationally hard so approximation is a necessary tradeoff to allow polynomial time algorithms; (ii) limiting explicitly the size of the approximation allows the decision maker to control the expecte...

A number of variants of the classical Markowitz mean-variance optimization model for portfolio selection have been investigated to render it more realistic. Recently, it has been studied the imposition of a cardinality constraint, setting an upper bound on the number of active positions taken in the portfolio, in an attempt to improve its performance and reduce transactions costs. However, one ...

In ordinal regression, a score function and threshold values are sought to classify a set of objects into a set of ranked classes. Classifying an individual in a class with higher (respectively lower) rank than its actual rank is called an upgrading (respectively downgrading) error. Since upgrading and downgrading errors may not have the same importance, they should be considered as two differe...

In this study, biobjective mixed-integer linear programming problems are considered and a search-andremove (SR) algorithm is presented. At each stage of the algorithm, Pareto outcomes are searched with the dichotomic search algorithm and these outcomes are excluded from the objective space with the help of Tabu constraints. The algorithm is also enhanced with lower and upper bounds, which are u...

Motivated by Online Ad allocation when there are multiple conflicting objectives, we introduce and study the problem of Biobjective Online Bipartite Matching, a strict generalization of the standard setting of Karp, Vazirani and Vazirani [9], where we are allowed to have edges of two colors, and the goal is to find a matching that is both large and balanced at the same time. We study both deter...

In this paper, we consider the problem of network design for hazardous material transportation where the government designates a network, and the carriers choose the routes on the network. We model the problem as a bilevel network flow formulation and analyze the bilevel design problem by comparing it to three other decision scenarios. The bilevel model is difficult to solve and may be ill-pose...