Foundations of Metaheuristics

Abstract

Many real-world problems with practical importance are large and complex, differing from standard problems. Often they belong to the class NP making them computationally intractable using exact optimization algorithms. Metaheurstics are general-purpose improvement heuristics that are used to solve NP-hard problems. Some problem-specific adaptions of the metaheuristic are necessary to achieve an efficient search process. This problem customization focuses on four basic design elements that every metaheuristic incorporates and that are presented in detail in this chapter: the combination of representation and search operators, the fitness function, the initialization, and the search strategy. With respect to the search strategy, in general the different variants of metaheuristics can be classified into two groups: techniques based on local search and techniques using recombination-based search operators. For each search concept, one metaheuristic was specified as a representative example: threshold accepting as a local search routine and genetic algorithms as a recombination-based search. They are the underlying techniques of the simultaneous airline scheduling process presented in this work.