Chapter 1 Memetic Algorithms and Complete Techniques Carlos Cotta, Antonio J. Fern´ andez Leiva, and Jos´ e E. Gallardo 1.1 Introduction As mentioned in previous chapters in this volume, metaheuristics (and specif- ically MAs) have a part of their raison d’etre in practically solving problems whose resolution would be otherwise infeasible by means of other non-heuristic approaches. Such alternative non-heuristic approaches are complete methods that –unlike heuristics– do guarantee that the deviation from optimality of the solution they will provide is somehow bounded (and as a particular case, that the optimal solution will be found). These methods are eventually limited by the curse of di- mensionality, yet they may still constitute a very interesting resource either from the application point of view, or from the lessons that can be learnt from them. Indeed, in some sense these approaches could be considered complementary to metaheuris- tics rather that mere “rivals”. Even more so in the case of MAs, whose philosophy has been since its inception much more flexible and integrative rather than dogmatic or exclusive. This said, despite the eclosion of metaheuristics as powerful optimization tech- niques during the 80s and 90s, inter-breeding between the fields of provably problem- solving and heuristic problem-solving was relatively limited until the last decade (some seminal works dating back from the mid 90s – e.g., [10]). The last years have however witnessed a remarkable increase in the number of works trying to combine ideas from these two areas. Certainly, MAs have also played an important role in this cross-fertilization of search paradigms. Along this chapter we will review some of the lines of research that have emerged in this regard. To this end, we will begin by briefly revisiting complete techniques to highlight their strengths and weaknesses, and what they have to offer to metaheuristics. Subsequently, we will outline some Carlos Cotta · Antonio J. Fern´ andez Leiva · Jos´ e E. Gallardo Dept. Lenguajes y Ciencias de la Computaci ´ on, Universidad de M´ alaga, ETSI Inform´ atica, Campus de Teatinos, 29071 M´ alaga, Spain e-mail: {ccottap, afdez, pepeg}@lcc.uma.es 1