Most real-world optimization problems are multiobjective by nature, involving noncomparable objectives. Many of these problems can be formulated in terms of a set of linear objective functions that should be simultaneously optimized over a class of linear constraints. Often there is the complicating factor that some of the variables are required to be integral. The resulting class of problems is named multiobjective mixed integer programming (MOMIP) problems. Solving these kinds of optimization problems exactly requires a method that can generate the whole set of nondominated points (the Pareto-optimal front). In this paper, we first give a survey of the newly developed branch and bound methods for solving MOMIP problems. After that, we propose a new branch and bound method for solving a subclass of MOMIP problems, where only two objectives are allowed, the integer variables are binary, and one of the two objectives has only integer variables. The proposed method is able to find the full set of nondominated points. It is tested on a large number of problem instances, from six different classes of MOMIP problems. The results reveal that the developed biobjective branch and bound method performs better on five of the six test problems, compared with a generic two-phase method. At this time, the two-phase method is the most preferred exact method for solving MOMIP problems with two criteria and binary variables. This paper was accepted by Dimitris Bertsimas, optimization.

The experimental results reported in many papers suggest that making an appropriate a priori choice of an evolutionary method for a nonlinear parameter optimization problem remains an open question. It seems that the most promising approach at this stage of research is experimental, involving a design of a scalable test suite of constrained optimization problems, in which many features could be easily tuned. Then it would be possible to evaluate merits and drawbacks of the available methods as well as test new methods eciently. In this paper we propose such a test-case generator for constrained parameter optimization techniques. This generator is capable of creating various test problems with dierent characteristics, like (1) problems with dierent relative size of the feasible region in the search space; (2) problems with dierent number and types of constraints; (3) problems with convex or non-convex objective function, possibly with multiple optima; (4) problems with highly non-convex constraints consisting of (possibly) disjoint regions. Such a test-case generator is very useful for analyzing and comparing dierent constraint-handling techniques.

Recently the XHSTT format for (High) School Timetabling was introduced, which provides a uniform way of modeling problem instances and corresponding solutions. The format supports a big variety of constraints, and currently 38 real-life instances from 11 dierent countries are available. Thereby the XHSTT format serves as a common ground for researchers within this area. This paper describes the rst exact method capable of handling an arbitrary instance of the XHSTT format. The method is based on a Mixed-Integer linear Programming (MIP) model, which is solved in two steps with a commercial generalpurpose MIP solver. Computational results show that our approach is able to nd previously unknown optimal solutions for 2 instances of XHSTT, and proves optimality of 4 known solutions. For the instances not solved to optimality, new non-trivial lower bounds were found in 11 cases, and new best-known solutions were found in 9 cases. Furthermore the approach is shown to be competitive with the nalist of Round 2 of the International Timetabling Competition 2011.

Educational timetabling problems require the assignment of times and resources to events, while sets of required and desirable constraints must be considered. The XHSTT format was adopted in this work because it models the main features of educational timetabling and it is the most used format in recent studies in the eld. This work presents new cuts and reformulations for the existing integer programming model for XHSTT. The proposed