Sentence compression holds promise for many applications ranging from summarization to subtitle generation. Our work views sentence compression as an optimization problem and uses integer linear programming (ILP) to infer globally optimal compressions in the presence of linguistically motivated constraints. We show how previous formulations of sentence compression can be recast as ILPs and extend these models with novel global constraints. Experimental results on written and spoken texts demonstrate improvements over state-of-the-art models. 1.

The branch and bound procedure for solving mixed integer programming (MIP) problems using linear programming relaxations has been used with great success for decades. Over the years, a variety of researchers have studied ways of making the basic algorithm more effective. Breakthroughs in the fields of computer hardware, computer software, and mathematics have led to increasing success at solving larger and larger MIP instances. The goal of this paper is to survey many of the results regarding branch and bound search strategies and evaluate them again in light of the other advances that have taken place over the years. In addition, novel search strategies are presented and shown to often perform better than those currently used in practice. October 1997 The effectiveness of the branch and bound procedure for solving mixed integer programming (MIP) problems using linear programming relaxations is well documented. After the introduction of this procedure in the 1960's [26] [10]...

this paper, now include cutting-plane capabilities as well as other ideas from the backlog of accumulated theory. As suggested by the title of this paper, the gap between theory and practice is indeed closing

The first computer implementation of the Dantzig-Fulkerson-Johnson cutting-plane method for solving the traveling salesman problem, written by Martin, used subtour inequalities as well as cutting planes of Gomory’s type. The practice of looking for and using cuts that match prescribed templates in conjunction with Gomory cuts was continued in computer codes of Miliotis, Land, and Fleischmann. Grötschel, Padberg, and Hong advocated a different policy, where the template paradigm is the only source of cuts; furthermore, they argued for drawing the templates exclusively from the set of linear inequalities that induce facets of the TSP polytope. These policies were adopted in the work of Crowder and Padberg, in the work of Grötschel and Holland, and in the work of Padberg and Rinaldi; their computer codes produced the most impressive computational TSP successes of the nineteen eighties. Eventually, the template paradigm became the standard frame of reference for cutting planes in the TSP. The purpose of this paper is to describe a technique

We describe FATCOP 2.0, a new parallel mixed integer program solver that works in an opportunistic computing environment provided by the Condor resource management system. We outline changes to the search strategy of FATCOP 1.0 that are necessary to improve resource utilization, together with new techniques to exploit heterogeneous resources. We detail several advanced features in the code that are necessary for successful solution of a variety of mixed integer test problems, along with the different usage schemes that are pertinent to our particular computing environment. Computational results demonstrating the effects of the changes are provided and used to generate effective default strategies for the FATCOP solver.

Cutting plane algorithms have turned out to be practically successful computational tools in combinatorial optimization, in particular, when they are embedded in a branch and bound framework. Implementations of such "branch and cut" algorithms are rather complicated in comparison to many purely combinatorial algorithms. The purpose of this article is to give an introduction to cutting plane algorithms from an implementor's point of view. Special emphasis is given to control and data structures used in practically successful implementations of branch and cut algorithms. We also address the issue of parallelization. Finally, we point out that in important applications branch and cut algorithms are not only able to produce optimal solutions but also approximations to the optimum with certified good quality in moderate computation times. We close with an overview of successful practical applications in the literature.

This article briefly summarizes the work that has been done and presents the current standing of neural networks for combinatorial optimization by considering each of the major classes of combinatorial optimization problems. Areas which have not yet been studied are identified for future research.

Abstract. Recent improvements in propositional satisfiability techniques (SAT) made it possible to tackle successfully some hard real-world problems (e.g. model-checking, circuit testing, propositional planning) by encoding into SAT. However, a purely boolean representation is not expressive enough for many other real-world applications, including the verification of timed and hybrid systems, of proof obligations in software, and of circuit design at RTL level. These problems can be naturally modeled as satisfiability in Linear Arithmetic Logic (LAL), i.e., the boolean combination of propositional variables and linear constraints over numerical variables. In this paper we present MATHSAT, a new, SAT-based decision procedure for LAL, based on the (known approach) of integrating a state-of-the-art SAT solver with a dedicated mathematical solver for LAL. We improve MATHSAT in two different directions. First, the top level procedure is enhanced, and now features a tighter integration between the boolean search and the mathematical solver. In particular, we allow for theory-driven backjumping and learning, and theory-driven deduction; we use static learning in order to reduce the number of boolean models that are mathematically inconsistent; we exploit problem clustering in order to partition

The solution of convex Mixed Integer Quadratic Programming (MIQP) problems with a general branch--and--bound framework is considered. It is shown how lower bounds can be computed efficiently during the branch--and--bound process. Improved lower bounds such as the ones derived in this paper can reduce the number of QP problems that have to be solved. The branch--and--bound approach is also shown to be superior to other approaches to solving MIQP problems. Numerical experience is presented which supports these conclusions. Key words : Integer Programming, Mixed Integer Quadratic Programming, Branch--and--Bound AMS subject classification: 90C10, 90C11, 90C20 1 Introduction One of the most successful methods for solving mixed--integer nonlinear problems is branch--and--bound. Land and Doig [16] first introduced a branch--and--bound algorithm for the travelling salesman problem. Dakin [3] introduced the now common branching dichotomy and was the first to realize that it is possible to so...

This paper develops new algorithms for coalition formation within multi-sensor networks tasked with performing widearea surveillance. Specifically, we cast this application as an instance of coalition formation, with overlapping coalitions. We show that within this application area sub-additive coalition valuations are typical, and we thus use this structural property of the problem to derive two novel algorithms (an approximate greedy one that operates in polynomial time and has a calculated bound to the optimum, and an optimal branch-and-bound one) to find the optimal coalition structure in this instance. We empirically evaluate the performance of these algorithms within a generic model of a multi-sensor network performing wide area surveillance. These results show that the polynomial algorithm typically generated solutions much closer to the optimal than the theoretical bound, and prove the effectiveness of our pruning procedure.