Introdução à Otimização Combinatória

Abstract

Most of the computational problems are discrete in nature and involve the search of a solution satisfying certain properties, with possible alternatives growing in a combina- torial way. A classic example is the sorting problem, where one must find a permutation of a sequence in non-decreasing order. Moreover, real problems of this type become more complex, when we consider that available resources are limited and the need to optimize their use. Consider, for example, a city road network and a set of bus stops where employ- ees of a company pick up a bus having sufficient capacity to transport them all. The bus route starts in the garage, pass through the points and take the employees to the work place. However, when we consider the transportation cost, usually proportional to the total traveled distance, it is desirable that the bus go through the shortest route. This is a typical combinatorial optimization problem. In addition to vehicle routing problems, several other applications can be found in various fields of knowledge. In this mini-course, we present some of the main algorithmic techniques for combinatorial optimization problems.