Functional description of MINTO, a mixed integer optimizer

MINTO is a software system that solves mixed-integer linear programs by a branch-and-bound algorithm with linear programming relaxations. It also provides automatic constraint classification, preprocessing, primal heuristics and constraint generation. Moreover, the user can enrich the basic algorithm by providing a variety of specialized application routines that can customize MINTO to achieve maximum efficiency for a problem class. This paper documents MINTO by specifying what it is capable of doing and how to use it

A branch-and-bound methodology within algebraic modelling systems

Through the use of application-specific branch-and-bound directives it is possible to find solutions to combinatorial models that would otherwise be difficult or impossible to find by just using generic branch-and-bound techniques within the framework of mathematical programming. {\sc Minto} is an example of a system which offers the possibility to incorporate user-provided directives (written in {\sc C}) to guide the branch-and-bound search. Its main focus, however, remains on mathematical programming models. The aim of this paper is to present a branch-and-bound methodology for particular combinatorial structures to be embedded inside an algebraic modelling language. One advantage is the increased scope of application. Another advantage is that directives are more easily implemented at the modelling level than at the programming level

A branch-and-price algorithm for solving the cutting strips problem

After giving a suitable model for the cutting strips problem, we present a branch-and-price algorithm for it by combining the column generation technique and the branch-and-bound method with LP relaxations. Some theoretical issues and implementation details about the algorithm are discussed, including the solution of the pricing subproblem, the quality of LP relaxations, the branching scheme as well as the column management. Finally, preliminary computational experience is reported

On solving complex multi-period location models using simulated annealing

This paper describes a study aimed at evaluating the capabilities of simulated annealing in dealing with complex, real-world multi-period location problems raised by school network planning in Portugal. The problems were formulated as mixed-integer linear optimization models. The models allow for facility closure or size reduction besides facility opening and size expansion, with sizes possibly limited to a set of pre-defined standards. They assume facility costs to be divided into a fix component and two variable components, respectively dependent on facility size and facility attendance. Results obtained through the study indicate that simulated annealing can be a useful tool for solving these kinds of models.http://www.sciencedirect.com/science/article/B6VCT-426XWHV-H/1/42defe9695efc3f796150d9a3e24bc3

A Literature Review On Combining Heuristics and Exact Algorithms in Combinatorial Optimization

There are several approaches for solving hard optimization problems. Mathematical programming techniques such as (integer) linear programming-based methods and metaheuristic approaches are two extremely effective streams for combinatorial problems. Different research streams, more or less in isolation from one another, created these two. Only several years ago, many scholars noticed the advantages and enormous potential of building hybrids of combining mathematical programming methodologies and metaheuristics. In reality, many problems can be solved much better by exploiting synergies between these approaches than by “pure” classical algorithms. The key question is how to integrate mathematical programming methods and metaheuristics to achieve such benefits. This paper reviews existing techniques for such combinations and provides examples of using them for vehicle routing problems

The Robust Network Loading Problem under Hose Demand Uncertainty: Formulation, Polyhedral Analysis, and Computations

Cataloged from PDF version of article.We consider the network loading problem (NLP) under a polyhedral uncertainty description of traffic demands. After giving a compact multicommodity flow formulation of the problem, we state a decomposition property obtained from projecting out the flow variables. This property considerably simplifies the resulting polyhedral analysis and computations by doing away with metric inequalities. Then we focus on a specific choice of the uncertainty description, called the “hose model,” which specifies aggregate traffic upper bounds for selected endpoints of the network. We study the polyhedral aspects of the NLP under hose demand uncertainty and use the results as the basis of an efficient branch-and-cut algorithm. The results of extensive computational experiments on well-known network design instances are reported

Polyhredral techniques in combinatorial optimization I: theory

Combinatorial optimization problems appear in many disciplines ranging from management and logistics to mathematics, physics, and chemistry. These problems are usually relatively easy to formulate mathematically, but most of them are computationally hard due to the restriction that a subset of the variables have to take integral values. During the last two decades there has been a remarkable progress in techniques based on the polyhedral description of combinatorial problems, leading to a large increase in the size of several problem types that can be solved. The basic idea behind polyhedral techniques is to derive a good linear formulation of the set of solutions by identifying linear inequalities that can be proved to be necessary in the description of the convex hull of feasible solutions. Ideally we can then solve the problem as a linear programming problem, which can be done eciently. The purpose of this manuscript is to give an overview of the developments in polyhedral theory, starting with the pioneering work by Dantzig, Fulkerson and Johnson on the traveling salesman problem, and by Gomory on integer programming. We also present some modern applications, and computational experience