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 behaviour 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.

Iterated Local Search has many of the desirable features of a metaheuristic: it is simple, easy to implement, robust, and highly effective. The essential idea of Iterated Local Search lies in focusing the search not on the full space of solutions but on a smaller subspace defined by the solutions that are locally optimal for a given optimization engine. The success of Iterated Local Search lies in the biased sampling of this set of local optima. How effective this approach turns out to be depends mainly on the choice of the local search, the perturbations, and the acceptance criterion. So far, in spite of its conceptual simplicity, it has lead to a number of state-of-the-art results without the use of too much problem-specific knowledge. But with further work so that the different modules are well adapted to the problem at hand, Iterated Local Search can often become a competitive or even state of the art algorithm. The purpose of this review is both to give a detailed description of this metaheuristic and to show where it stands in terms of performance. O.M. acknowledges support from the Institut Universitaire de France. This work was partially supported by the “Metaheuristics Network”, a Research Training Network funded by the Improving Human Potential programme of the CEC, grant HPRN-CT-1999-00106. The information provided is the sole responsibility of the authors and does not reflect the Community’s opinion. The Community is not responsible for any use that might be made of data appearing in this publication. 1 1

Ant System, the first Ant Colony Optimization algorithm, showed to be a viable method for attacking hard combinatorial optimization problems. Yet, its performance, when compared to more fine-tuned algorithms, was rather poor for large instances of traditional benchmark problems like the Traveling Salesman Problem. To show that Ant Colony Optimization algorithms could be good alternatives to existing algorithms for hard combinatorial optimization problems, recent research in this ares has mainly focused on the development of algorithmic variants which achieve better performance than AS. In this article, we present ¨�©� � –¨��� � Ant System, an Ant Colony Optimization algorithm derived from Ant System. ¨�©� � –¨��� � Ant System differs from Ant System in several important aspects, whose usefulness we demonstrate by means of an experimental study. Additionally, we relate one of the characteristics specific to ¨� ¨ AS — that of using a greedier search than Ant System — to results from the search space analysis of the combinatorial optimization problems attacked in this paper. Our computational results on the Traveling Salesman Problem and the Quadratic Assignment Problem show that ¨�©� � – ¨��� � Ant System is currently among the best performing algorithms for these problems.

This paper describes STAGE, a learning approach to automatically improving search performance on optimization problems. STAGE learns an evaluation function which predicts the outcome of a local search algorithm, such as hillclimbing or WALKSAT, as a function of state features along its search trajectories. The learned evaluation function is used to bias future search trajectories toward better optima. We present positive results on six large-scale optimization domains.

this paper, we explore this problem, which we call the network testbed mapping problem. We describe the interesting challenges that characterize this problem, and explore its application to other spaces, such as distributed simulation. We present the design, implementation, and evaluation of a solver for this problem, which is currently in use on the Netbed network testbed. It builds on simulated annealing to find very good solutions in a few seconds for our historical workload, and scales gracefully on large well-connected synthetic topologies

This paper describes algorithms that learn to improve search performance on largescale optimization tasks. The main algorithm, Stage, works by learning an evaluation function that predicts the outcome of a local search algorithm, such as hillclimbing or Walksat, from features of states visited during search. The learned evaluation function is then used to bias future search trajectories toward better optima on the same problem. Another algorithm, X-Stage, transfers previously learned evaluation functions to new, similar optimization problems. Empirical results are provided on seven large-scale optimization domains: bin-packing, channel routing, Bayesian network structure-finding, radiotherapy treatment planning, cartogram design, Boolean satisfiability, and Boggle board setup.

Query optimizers often limit the search space for join orderings, for example by excluding Cartesian products in subplans or by restricting plan trees to left-deep vines. Such exclusions are widely assumed to reduce optimization effort while minimally affecting plan quality. However, we show that searching the complete space of plans is more affordable than has been previously recognized, and that the common exclusions may be of little benefit. We start by presenting a Cartesian product optimizer that requires at most a few seconds of workstation time to search the space of bushy plans for products of up to 15 relations. Building on this result, we present a join-order optimizer that achieves a similar level of performance, and retains the ability to include Cartesian products in subplans wherever appropriate. The main contribution of the paper is in fully separating join-order enumeration from predicate analysis, and in showing that the former problem in particular can be solved swift...

Ant algorithms [18, 14, 19] are a recently developed, population-based approach which has been successfully applied to several NP-hard combinatorial

In complex sequential decision problems suchasscheduling factory production, planning medical treatments, and playing backgammon, optimal decision policies are in general unknown, and it is often difficult, even for human domain experts, to manually encode good decision policies in software. The reinforcement-learning methodology of "value function approximation" (VFA) offers an alternative: systems can learn effective decision policies autonomously, simply by simulating the task and keeping statistics on which decisions lead to good ultimate performance and which do not. This thesis advances the state of the art in VFA in two ways. First, it

. Ant Colony Optimization (ACO) is a new population oriented search metaphor that has been successfully applied to NP-hard combinatorial optimization problems. In this paper we discuss parallelization strategies for Ant Colony Optimization algorithms. We empirically test the most simple strategy, that of executing parallel independent runs of an algorithm. The empirical tests are performed applying MAX --MIN Ant System, one of the most efficient ACO algorithms, to the Traveling Salesman Problem and show that using parallel independent runs is very effective. 1 Introduction Ant Colony Optimization (ACO) is a new population based search metaphor inspired by the foraging behavior of real ants. Among the basic ideas underlying ACO is to use an algorithmic counterpart to the pheromone trail, used by real ants, as a medium for communication among a colony of artificial ants. The seminal work on ACO is Ant System [9, 11] which was first proposed for solving the Traveling Salesman Problem (TS...