In mathematics and computer science, an optimization problem (OP) is the problem of finding the best solution from all feasible solutions. OP's can be divided into two categories depending on whether the variables are continuous or discrete. An OP with discrete variables is known as a combinatorial optimization problem (COP). Over the last few years, the use of COP's has increased exponentially in many fields, marketing, industrial, security communications and aircraft problems. The aim of the research presented in this book is to investigate the use of various optimization exacts and heuristics to solve the COP's. In this book we interest in discussing three samples of COP's; machine scheduling problem (MSP), transposition cipher problem (TCP) and aircraft landing problem (ALP). For these study cases, we first discuss the mathematical modeling (single and multi-objective functions and the constraints) then different solving methods, like exact (Branch and Bound), heuristics, local search methods (Genetic Algorithm, Particle Swarm Optimization and BA) and using Neural Networks. In this book we solve some practical examples obtained from some famous sits.

Faez Hassan is Assistant Professor in Mathematics at the University of Al-Mustansiriyah, Baghdad, Iraq. He earned his B. Sc. in Mathematics, M. Sc. with "Applications of Numerical Analysis for LFSR Systems" and Ph. D. with "Combinatorial Optimization Problems" from the same university. He interest in data security, Operation Research and AI.