Benchmarks for identification of ordinary differential equations from time series data

Motivation: In recent years, the biological literature has seen a significant increase of reported methods for identifying both structure and parameters of ordinary differential equations (ODEs) from time series data. A natural way to evaluate the performance of such methods is to try them on a sufficient number of realistic test cases. However, weak practices in specifying identification problems and lack of commonly accepted benchmark problems makes it difficult to evaluate and compare different methods

An Algorithm for Large Scale 0-1 Integer Programming With Application to Airline Crew Scheduling

We present an approximation algorithm for solving large 0-1 integer programming problems where A is 0-1 and where b is integer. The method can be viewed as a dual coordinate search for solving the LPrelaxation, reformulated as an unconstrained nonlinear problem, and an approximation scheme working together with this method. The approximation scheme works by adjusting the costs as little as possible so that the new problem has an integer solution. The degree of approximation is determined by a parameter, and for different levels of approximation the resulting algorithm can be interpreted in terms of linear programming, dynamic programming, and as a greedy algorithm. The algorithm is used in the CARMEN system for airline crew scheduling used by several major airlines, and we show that the algorithm performs well for large set covering problems, in comparison to the CPLEX system, in terms of both time and quality. We also present results on some well known difficult set covering problems ..

Efficient Algorithms for Probabilistic Inference, Combinatorial Optimization and the Discovery of Causal Structure from Data

In the first article we present a network based algorithm for probabilistic inference in an undirected structure. We show that the algorithm can be used as a general purpose approximation algorithm for combinatorial optimization, and discuss issues of approximation and convergence. We show the successful use of the algorithm for the assignment problem, the queens problem, and the set covering problem. In the second article, we develop a version of this algorithm for 0-1 integer programming problems when A is 0-1 and b is integer. This version can be described in terms of an ascent algorithm for the LP-relaxation, and an approximation scheme working together with this method. The algorithm features a parameter that determines the degree of approximation. We show that the algorithm performs well for set covering problems compared to the CPLEX system. In the third article, we present an algorithm to determine the interaction structure in a multidimensional binary sample. We show that the algorithm is capable of reconstructing most of the causal structure for problems with more than a hundred variables, including many of the causal directions. The algorithm is based on an efficient method for approximate ML-estimation in a given undirected structure. When the structure is not known, the MDL-criterion is used to determine the goodness of a hypothesis, and the structure is determined incrementally by a search algorithm, working together with the parameter estimation algorithm

The design of a 0-1 integer optimizer and its application in the Carmen system

We describe the design of an optimizer for 0-1 integer programming aimed at solving large problems. The algorithm is based on very simple operations giving it a low complexity, and we show that for large set covering problems it can produce very good solutions compared to other methods. This is the only optimizer in the Carmen system for airline crew scheduling, used by several major European airlines, and we discuss how it has affected the overall design and success of this system. Keywords: 0-1 integer linear programming, efficient algorithms, set covering, airline crew scheduling. 1 Introduction In this paper I will describe the design of an optimizer for solving large 0-1 integer programs, and its application in the Carmen system for airline crew scheduling. The design of the optimizer itself has mainly been an academic research project aimed at discrete optimization in general. However, the specific application in mind has been the usually very large optimization problems that a..

Revisiting the in-the-middle algorithm and heuristic for integer programming and the max-sum problem

We consider a very simple algorithm to solve large scale 0-1 integer linear programs - and a simple heuristic to encourage convergence to an integer so- lution - which have been very successful in commercial applications. We find it useful to revisit its main ideas and establish its relation to several known algorithms, including the generalized iterative scaling algorithm. We discuss ways to relate this linear programming based approach to the max-sum prob- lem, and show that the algorithm has a close relation to convergent message passing algorithms for MAP-inference in graphical models such as max-sum diffusion. We further discuss non-conflicting and conflicting max-sum con- straint updates, show that the two algorithms match with these concepts, and that the heuristic has a relation to the max-sum algorithm. We finally give a brief overview of known applications, including a commercial system for airline crew scheduling

Revisiting the in-the-middle algorithm and heuristic for integer programming and the max-sum problem

We consider a very simple algorithm to solve large scale 0-1 integer linear programs - and a simple heuristic to encourage convergence to an integer so- lution - which have been very successful in commercial applications. We find it useful to revisit its main ideas and establish its relation to several known algorithms, including the generalized iterative scaling algorithm. We discuss ways to relate this linear programming based approach to the max-sum prob- lem, and show that the algorithm has a close relation to convergent message passing algorithms for MAP-inference in graphical models such as max-sum diffusion. We further discuss non-conflicting and conflicting max-sum con- straint updates, show that the two algorithms match with these concepts, and that the heuristic has a relation to the max-sum algorithm. We finally give a brief overview of known applications, including a commercial system for airline crew scheduling

Efficient Estimation and Model Selection in Large Graphical Models

We develop a computationally efficient method to determine the interaction structure in a multidimensional binary sample. We use an interaction model based on orthogonal functions, and give a result on independence properties in this model. Using this result we develop an efficient approximation algorithm for estimating the parameters in a given undirected model. To find the best model, we use a heuristic search algorithm in which the structure is determined incrementally. We also give an algorithm for reconstructing the causal directions, if such exist. We demonstrate that together these algorithms are capable of discovering almost all of the true structure for a problem with 121 variables, including many of the directions. Keywords: graphical models, probabilistic expert systems, machine learning, Markov models, causal structure. 1 Introduction In this paper we study the problem of determining the interaction structure in a multidimensional binary sample. As an important special ..