Mathematical Programming Solver Based on Local Search

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.

Acknowledgments vii

Preface ix

Introduction  xi

Chapter 1 Local Search: Methodology and Industrial Applications 1

1.1 Our methodology: back to basics 1

1.2 Car sequencing for painting and assembly lines 10

1.3 Vehicle routing with inventory management 17

Chapter 2 Local Search for 0-1 Nonlinear Programming 29

2.1 The LocalSolver project 29

2.2 State-of-the-art 32

2.3 Enriching modeling standards 33

2.4 The core algorithmic ideas 39

2.5 Benchmarks 44

Chapter 3 Toward an Optimization Solver Based on Neighborhood Search 53

3.1 Using neighborhood search as global search strategy 53

3.2 Extension to continuous and mixed optimization 56

3.3 Separating the computation of solutions and bounds 59

3.4 A new-generation, hybrid mathematical programming solver 62

Bibliography 65

Lists of Figures and Tables 79

Index 81

Frédéric Gardi is a Senior Expert and Vice President of Products at Innovation 24, a subsidiary of Bouygues in Paris, France, and Product Manager of LocalSolver. He specializes in the design and engineering of local search algorithms.

Thierry Benoist is a Senior Expert in charge of operations research projects at Innovation 24.

Julien Darlay is an Expert at Innovation 24. His fields of expertise include algorithmics, combinatory and numerical optimization, forecast, statistical and logical data analysis and simulation.

Bertrand Estellon is Professor in the IT Department and the Faculty of Science at Aix-Marseille University in France and a member of the combinatory and operational research team of the Laboratoire d'Informatique Fondamentale de Marseille.

Romain Megel is an Expert at Innovation 24. His fields of expertise include algorithmics, optimization, inference-based systems (constraint programming, expert systems), and business rule management.