Integer Optimization addresses a wide spectrum of practically important optimization problems and represents a major challenge for algorithmics. The goal of integer optimization is to solve a system of constraints and optimization criteria over discrete variables. Integer Optimization by Local Search introduces a new approach to domain-independent integer optimization, which, unlike traditional strategies, is based on local search. It develops the central concepts and strategies of integer local search and describes possible combinations with classical methods from linear programming. The surprising effectiveness of the approach is demonstrated in a variety of case studies on large-scale, realistic problems, including production planning, timetabling, radar surveillance, and sports scheduling. The monograph is written for practitioners and researchers from artificial intelligence and operations research.

This book constitutes the refereed proceedings of the 10th International Conference on Integer Programming and Combinatorial Optimization, IPCO 2004, held in New York City, USA in June 2004. The 32 revised papers presented were carefully reviewed and selected from 109 submissions. Among the topics addressed are vehicle routing, network management, mixed-integer programming, computational complexity, game theory, supply chain management, stochastic optimization problems, production scheduling, graph computations, computational graph theory, separation algorithms, local search, linear optimization, integer programming, graph coloring, packing, combinatorial optimization, routing, flow algorithms, 0/1 polytopes, and polyhedra.

Interest in constrained optimization originated with the simple linear pro gramming model since it was practical and perhaps the only computationally tractable model at the time. Constrained linear optimization models were soon adopted in numerous application areas and are perhaps the most widely used mathematical models in operations research and management science at the time of this writing. Modelers have, however, found the assumption of linearity to be overly restrictive in expressing the real-world phenomena and problems in economics, finance, business, communication, engineering design, computational biology, and other areas that frequently demand the use of nonlinear expressions and discrete variables in optimization models. Both of these extensions of the linear programming model are NP-hard, thus representing very challenging problems. On the brighter side, recent advances in algorithmic and computing technology make it possible to re visit these problems with the hope of solving practically relevant problems in reasonable amounts of computational time. Initial attempts at solving nonlinear programs concentrated on the de velopment of local optimization methods guaranteeing globality under the assumption of convexity. On the other hand, the integer programming liter ature has concentrated on the development of methods that ensure global optima. The aim of this book is to marry the advancements in solving nonlinear and integer programming models and to develop new results in the more general framework of mixed-integer nonlinear programs (MINLPs) with the goal of devising practically efficient global optimization algorithms for MINLPs.

This book covers local search for combinatorial optimization and its extension to mixed-variable optimization. Although not yet understood from the theoretical point of view, local search is the paradigm of choice for tackling large-scale real-life optimization problems. Today's end-users demand interactivity with decision support systems. For optimization software, this means obtaining good-quality solutions quickly. Fast iterative improvement methods, like local search, are suited to satisfying such needs. Here the authors show local search in a new light, in particular presenting a new kind of mathematical programming solver, namely LocalSolver, based on neighborhood search. First, an iconoclast methodology is presented to design and engineer local search algorithms. The authors' concern regarding industrializing local search approaches is of particular interest for practitioners. This methodology is applied to solve two industrial problems with high economic stakes. Software based on local search induces extra costs in development and maintenance in comparison with the direct use of mixed-integer linear programming solvers. The authors then move on to present the LocalSolver project whose goal is to offer the power of local search through a model-and-run solver for large-scale 0-1 nonlinear programming. They conclude by presenting their ongoing and future work on LocalSolver toward a full mathematical programming solver based on local search.

In this thesis, we implement and test two algorithms for binary optimization and mixed integer optimization, respectively. We fine tune the parameters of these two algorithms and achieve satisfactory performance. We also compare our algorithms with CPLEX on large amount of fairly large-size instances. Based on the experimental results, our binary optimization algorithm delivers performance that is strictly better than CPLEX on instances with moderately dense constraint matrices, while for sparse instances, our algorithm delivers performance that is comparable to CPLEX. Our mixed integer optimization algorithm outperforms CPLEX most of the time when the constraint matrices are moderately dense, while for sparse instances, it yields results that are close to CPLEX, and the largest gap relative to the result given by CPLEX is around 5%. Our findings show that these two algorithms, especially the binary optimization algorithm, have practical promise in solving large, dense instances of both set covering and set packing problems.