Memetic Algorithms and Fitness Landscapes in Combinatorial Optimization

Introduction

Combinatorial optimization problems (COPs) arise in many practical applications in the fields of management science, biology, chemistry, physics, engineering, and computer science. Although the search space is comprised of a finite number of candidate solutions, many of these problems are very complex and thus hard to solve. Often, the search space grows exponentially with the problem size rendering enumeration schemes impractical.Moreover, for many problems it has been shown that they are NP-hard, hence no polynomial time algorithm is known to find optimum solutions. Therefore, effective meta-heuristics are required to find (near) optimum solutions in short time. Memetic algorithms are known to perform well for a wide range of combinatorial optimization problems. Still, an open question is when and why they perform so well. After providing an overview and a common outline of memetic algorithms for combinatorial optimization problems in section 2, we introduce the concept of fitness landscapes in section 3 to address these two questions. In Section 4 and 5 we present case studies of the TSP and the BQP, respectively, in which we show and discuss results from the fitness landscape analysis. Furthermore, we discuss the state-of-the-art meta-heuristics for these problems. Section 6 concludes the chapter.