The nine universities in the Atlantic Coast Conference #ACC# have a basketball competition in which eachschool plays home and away games against each other over a nine-week period. The creation of a suitable schedule is a very di#cult problem with a myriad of con#icting requirements and preferences. We develop an approachto scheduling problems that uses a combination of integer programming and enumerative techniques. Our approach yields reasonable schedules very quickly and gaveaschedule that was accepted by the ACC for play in 1997#1998.

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this paper occur at the tactical level. Strategic planning focuses on resource acquisition for the period from five to fifteen years ahead. Network planning problems may be viewed as the main strategic issues, but, in order to evaluate possible strategic alternatives, the subsequent stages including at least line planning and train schedule generation have to be considered. The disadvantages of the hierarchical planning are obvious, since the optimal output of a subtask which serves as the input of a subsequent task, will not result, in general, in an overall optimal solution.

The minimum-cost multicommodity flow problem involves simultaneously shipping multiple commodities through a single network so that the total flow obeys arc capacity constraints and has minimum cost.

We present some preliminary work on modeling AI planning as a Mixed Integer Programming (MIP) problem. We discuss the main advantages and disadvantages of the approach and compare it to traditional planning frameworks. We investigate a number of MIP models of specific problems, each of them exploiting different strengths of the MIP formulation, and present our computational experience with these models. 1

I introduce a new search heuristic for propositional STRIPS planning that is based on transforming planning instances to linear programming instances. The linear programming heuristic is admissible for finding minimum length plans and can be used by partial-order planning algorithms. This heuristic appears to be the first non-trivial admissible heuristic for partial-order planning. An empirical study compares Lplan, a partial-order planner incorporating the heuristic, to Graphplan, Satplan, and UCPOP on the tower of Hanoi domain, random blocks-world instances, and random planning instances. Graphplan is far faster in the study than the other algorithms. Lplan is often slower because the heuristic is time-consuming, but Lplan shows promise because it often performs a small search. Introduction Planning is the problem of finding a combination of actions that achieves a goal (Allen, Hendler, & Tate 1990; Hendler, Tate, & Drummond 1990). So far, there is limited success in general-purpose...

. We consider a new nonlinear relaxation for the Constrained Maximum Entropy Sampling Problem -- the problem of choosing the s \Theta s principal submatrix with maximal determinant from a given n \Theta n positive definite matrix, subject to linear constraints. We implement a branch-and-bound algorithm for the problem, using the new relaxation. The performance on test problems is far superior to a previous implementation using an eigenvalue-based relaxation. 1 Introduction Let n be a positive integer. For N := f1; : : : ; ng, let YN := fY j j j 2 Ng be a set of n random variables, with joint-density function g N (\Delta). Let s be an integer satisfying 0 ! s n. For S ae N , j S j = s, let YS := fY j j j 2 Sg, and denote the marginal joint-density function of YS by gS (\Delta). The entropy of S is defined by h(S) := \GammaE[ln gS (YS )]: Let m be a nonnegative integer, and let M := f1; 2; : : : mg. The Constrained Maximum-Entropy Sampling Problem is then the problem of choosing a s...

We consider a new nonlinear relaxation for the Constrained Maximum-Entropy Sampling Problem -- the problem of choosing the s × s principal submatrix with maximal determinant from a given n × n positive definite matrix, subject to linear constraints. We implement a branch-and-bound algorithm for the problem, using the new relaxation. The performance on test problems is far superior to a previous implementation using an eigenvalue-based relaxation. A parallel implementation of the algorithm exhibits approximately linear speed-up for up to 8 processors, and has successfully solved problem instances that were heretofore intractable.

We discuss the optimal choice of traffic lines with periodic timetables on a railway system. A chosen line system has to offer sufficient capacity in order to serve the known amount of traffic on the system. The line optimization problem aims at the construction of a feasible line system optimizing certain objectives. We introduce a mixed integer linear programming formulation. For real world data we succeed in solving the model by means of suitable relaxations and sufficiently strong cutting planes with the commercial LP solver CPLEX 3.0. Keywords: integer programming, railway networks, periodic timetable, line optimization, cutting planes. 1 Introduction Nowadays planning problems of railway systems become more manageable due to efficient algorithms and better implementations on faster computers. Especially solving huge linear programs, which is a substantial part of solving mixed integer problems, became much more efficient in the last ten years. Nevertheless a lot of mathematical ...

A common characteristic of many embedded applications is that they are aimed at the high-volume consumer market, which is extremely cost-sensitive. However many of them impose stringent performance demands on the underlying system. Therefore, the code generation must take into account the restrictions and features given by the target architecture while satisfying these performance demands. High-level language compilers often are unable to generate code meeting these requirements. One reason is the phase coupling problem between instruction scheduling and register allocation. Many compilers perform these tasks separately with each phase ignorant of the requirements of the other. Commonly, each task is accomplished by using heuristic methods. As the goals of the two phases often conflict, whichever phase is performed first imposes constraints on the other, sometimes producing inefficient code. Integer linear programming (ILP) provides an integrated approach to the combined instruction sc...