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A major factor affecting the clarity of graphical displays that include text labels is the degree to which labels obscure display features (including other labels) as a result of spatial overlap. Point-feature label placement (PFLP) is the problem of placing text labels adjacent to point features on a map or diagram so as to maximize legibility. This problem occurs frequently in the production of many types of informational graphics, though it arises most often in automated cartography. In this paper we present a comprehensive treatment of the PFLP problem, viewed as a type of combinatorial optimization problem. Complexity analysis reveals that the basic PFLP problem and most interesting variants of it are NP-hard. These negative results help inform a survey of previously reported algorithms for PFLP; not surprisingly, all such algorithms either have exponential time complexity or are incomplete. To solve the PFLP problem in practice, then, we must rely on good heuristic methods. We pr...

. The satisfiability (SAT) problem is a core problem in mathematical logic and computing theory. In practice, SAT is fundamental in solving many problems in automated reasoning, computer-aided design, computeraided manufacturing, machine vision, database, robotics, integrated circuit design, computer architecture design, and computer network design. Traditional methods treat SAT as a discrete, constrained decision problem. In recent years, many optimization methods, parallel algorithms, and practical techniques have been developed for solving SAT. In this survey, we present a general framework (an algorithm space) that integrates existing SAT algorithms into a unified perspective. We describe sequential and parallel SAT algorithms including variable splitting, resolution, local search, global optimization, mathematical programming, and practical SAT algorithms. We give performance evaluation of some existing SAT algorithms. Finally, we provide a set of practical applications of the sat...

This report describes an implementation of the Lin-Kernighan heuristic, one of the most successful methods for generating optimal or nearoptimal solutions for the symmetric traveling salesman problem. Computational tests show that the implementation is highly effective. It has found optimal solutions for all solved problem instances we have been able to obtain, including a 7397-city problem (the largest nontrivial problem instance solved to optimality today). Furthermore, the algorithm has improved the best known solutions for a series of large-scale problems with unknown optima, among these an 85900-city problem. 1.

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

We introduce a meta-heuristic to combine simulated annealing with local search methods for CO problems. This new class of Markov chains leads to significantly more powerful optimization methods than either simulated annealing or local search. The main idea is to embed deterministic local search techniques into simulated annealing so that the chain explores only local optima. It makes large, global changes, even at low temperatures, thus overcoming large barriers in configuration space. We have tested this meta-heuristic for the traveling salesman and graph partitioning problems. Tests on instances from public libraries and random ensembles quantify the power of the method. Our algorithm is able to solve large instances to optimality, improving upon state of the art local search methods very significantly. For the traveling salesman problem with randomly distributed cities in a square, the procedure improves on 3-opt by 1.6%, and on Lin-Kernighan local search by 1.3%. For the partitioni...

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Ant System is a general purpose algorithm inspired by the study of the behavior of Ant Colonies. It is based on a cooperative search paradigm that is applicable to the solution of combinatorial optimization problems. In this paper we introduce MAX --MIN Ant System, an improved version of basic Ant System, and report our results for its application to symmetric and asymmetric instances of the well known Traveling Salesman Problem. We show how MAX --MIN Ant System can be significantly improved extending it with local search heuristics. Our results clearly show that MAX --MIN Ant System has the property of effectively guiding the local search heuristics towards promising regions of the search space by generating good initial tours. I. Introduction The Ant System algorithm, originally introduced in [3], [4], is a new cooperative search algorithm inspired by the behavior of real ants. Ants are able to find good solutions to shortest path problems between a food source and their home colony...

The combination of local search heuristics and genetic algorithms has been shown to be an effective approach for finding near-optimum solutions to the traveling salesman problem. In this paper, previously proposed genetic local search algorithms for the symmetric and asymmetric traveling salesman problem are revisited and potential improvements are identified. Since local search is the central component in which most of the computation time is spent, improving the efficiency of the local search operators is crucial for improving the overall performance of the algorithms. The modifications of the algorithms are described and the new results obtained are presented. The results indicate that the improved algorithms are able to arrive at better solutions in significantly less time. I. Introduction Consider a salesman who wants to start from his home city, visit each of a set of n cities exactly once, and then return home. Since the salesman is interested in finding the shortest possible r...

The combination of local search heuristics and genetic algorithms is a promising approach for finding nearoptimum solutions to the traveling salesman problem (TSP). In this paper, an approach is presented in which local search techniques are used to find local optima in a given TSP search space, and genetic algorithms are used to search the space of local optima in order to find the global optimum. New genetic operators for realizing the proposed approach are described, and the quality and efficiency of the solutions obtained for a set of symmetric and asymmetric TSP instances are discussed. The results indicate that it is possible to arrive at high quality solutions in reasonable time. I. Introduction In the Traveling Salesman Problem (TSP) [18], [27], a number of cities with distances between them is given and the task is to find the minimum--length closed tour that visits each city once and returns to its starting point. A symmetric TSP (STSP) is one where the distance between any...