Structure and Metaheuristics

European Journal of Operational Research, 2003

The 18th EURO Summer/Winter Institute (ESWI XVIII) took place during the spring 2000 in Switzerland. The topic of ESWI XVIII, ''Meta-heuristics in Combinatorial Optimization'', was selected due to its great current scientific interest: indeed, in recent years, several meta-heuristics have proved to be highly efficient for the solution of difficult combinatorial optimization problems. The Institute was focused more particularly on the development and the use of local search and population search algorithms. Applications of these meta-heuristics on academic or real life problems were also discussed.

The field of metaheuristics for the application to combinatorial optimization problems is a rapidly growing field of research. This is due to the importance of combinatorial optimization problems for the scientific as well as the industrial world. We give a survey of the nowadays most important metaheuristics from a conceptual point of view. We outline the different components and concepts that are used in the different metaheuristics in order to analyze their similarities and differences. Two very important concepts in metaheuristics are intensification and diversification. These are the two forces that largely determine the behavior of a metaheuristic. They are in some way contrary but also complementary to each other. We introduce a framework, that we call the I&D frame, in order to put different intensification and diversification components into relation with each other. Outlining the advantages and disadvantages of different metaheuristic approaches we conclude by pointing out the importance of hybridization of metaheuristics as well as the integration of metaheuristics and other methods for optimization.

Journal of Heuristics, 2017

Combinatorial optimization is a discipline in computer science and applied mathematics. The goal is to find an optimal solution from a finite, but typically exponentially large set, according to an objective function. If there is more than one objective, we speak of multiobjective combinatorial optimization and the goal is to find a set of Pareto-optimal solutions. Combinatorial optimization problems arise widely in industry and academia and, unfortunately, many of them are NP-hard and no polynomial time algorithm can guarantee their solution to a certified optimality unless P = N P. Techniques for solving these problems can roughly be classified into two main categories: exact and heuristic algorithms. Exact algorithms are guaranteed to find an optimal solution and to prove its optimality. However, the run-time often increases dramatically with a problem instance's size, and therefore they are less applicable for real-world applications. For larger instances it is reasonable to use heuristic or metaheuristic algorithms, which are designed to obtain good but not necessarily optimal solutions in acceptable time. These methods are the primary scope of this special issue. The papers in this issue have been selected among 56 submissions after a thorough peer review process. The final selection contains 12 high quality papers addressing practical applications and theoretical analyses of metaheuristic algorithms in the context of combinatorial optimization problems. Six of them are extended versions of conference papers from the

In recent years, there have been significant advances in the theory and application of metaheuristics to approximate solutions of complex optimization problems. The $\mathrm{m}\mathrm{e}\mathrm{t}\mathrm{a}-\mathrm{h}\mathrm{e}\mathrm{u}\mathrm{r}\mathrm{i}\mathrm{s}\mathrm{t}\dot{\mathrm{i}}\mathrm{c}\mathrm{s}$ term was used: as a language and a program for stating and solving combinatorial problems in [1]; to describe tabu search in [2] and [3]; to classify recent approaches such as adaptive memory programming, ants systems, evolutionary methods, genetics algorithm, greedy randomized adaptive search procedures, guided local search, neural networks, problem-space search, simulated annealing, scatter search, tabu search, threshold algorithms, and their hybrids in [4, 5, 6 and 7] and as a title for the biennial series of the metaheuristics international conferences (MIC-95, MIC-97, MIC-99, MIC-01). A metaheuristic was defined in $[7, 8]$ an iterative master process that guides and modifies the operations of subordinate heuristics to efficiently produce high quality solutions. It may combine intelligently different concepts for exploring the search space and uses learning strategies to structure information. It may manipulate a complete (or incomplete) single solution or a collections of solutions at each iteration. The subordinate heuristics may be high ($\mathrm{o}\mathrm{I}^{\cdot}$ low) level procedures, or a simple local search, or just a construction method. Metaheuristics provide decision makers with robust tools that obtain high quality solutions, in a reasonable computational effort, to important applications in business, engineering, economics and the sciences. Finding exact solutions to these applications still poses a real challenge despite the impact of recent advances in computer technology and the great interaction between computer science, management $\mathrm{s}\mathrm{c}\mathrm{i}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{e}/\mathrm{o}\mathrm{p}\mathrm{e}\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{s}$ research and mathematics. For more details on theory and applications, we refer to the comprehensive bibliography on metaheuristics in [5], the books in [6-16]. A metaheuristic may have four components: initial space of solutions; search engines; learning and guideline strategies; management of information structures. In this paper, the most efficient metaheuristics and their associated components are briefly described. The unified-metaheuristic framework presented [4] is extended into a more general one to show how the existing metaheuristics can fit into it. The general framework invites extra research into desiging new innovative and unexplored metaheuristics. Finally, we conclude by highlighting current trends and future research directions in this active area of the science of heuristics.

2012

Metaheuristics are successfully applied in many different application domains as they provide a reasonable tradeoff between computation time and achievable solution quality. However, choosing an appropriate algorithm for a certain problem is not trivial, as problem characteristics can change remarkably for different instances and the performance of a metaheuristic may vary considerably for different parameter settings. Therefore it always takes qualified algorithm experts to select and tune a metaheuristic algorithm for a specific application. This process of algorithm selection and parameter tuning is frequently done manually and intuitively and requires a large number of empirical tests. In this contribution the authors propose several measurement values to characterize the search behavior of different metaheuristics for solving combinatorial optimization problems. Based on these measurements algorithms can be classified and models can be learnt to predict the algorithms behavior ...