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20
Combining Simulated Annealing with Local Search Heuristics
, 1993
"... We introduce a metaheuristic 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 tech ..."
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Cited by 81 (7 self)
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We introduce a metaheuristic 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 metaheuristic 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 3opt by 1.6%, and on LinKernighan local search by 1.3%. For the partitioni...
Solving Steiner tree problems in graphs to optimality
 Networks
, 1998
"... Abstract: In this paper, we present the implementation of a branchandcut algorithm for solving Steiner tree problems in graphs. Our algorithm is based on an integer programming formulation for directed graphs and comprises preprocessing, separation algorithms, and primal heuristics. We are able to ..."
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Cited by 46 (1 self)
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Abstract: In this paper, we present the implementation of a branchandcut algorithm for solving Steiner tree problems in graphs. Our algorithm is based on an integer programming formulation for directed graphs and comprises preprocessing, separation algorithms, and primal heuristics. We are able to solve nearly all problem instances discussed in the literature to optimality, including one problem that—to our knowledge—has not yet been solved. We also report on our computational experiences with some very large Steiner tree problems arising from the design of electronic circuits. All test problems are gathered in a newly introduced library called SteinLib that is accessible via the World Wide Web. � 1998 John
Maximum Planar Subgraphs and Nice Embeddings: Practical Layout Tools
 ALGORITHMICA
, 1996
"... ..."
Packing Steiner Trees: A Cutting Plane Algorithm and Computational Results
 Mathematical Programming
, 1992
"... In this paper we describe a cutting plane algorithm for the Steiner tree packing problem. We use our algorithm to solve some switchbox routing problems of VLSIdesign and report on our computational experience. This includes a brief discussion of separation algorithms, a new LPbased primal heuristi ..."
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Cited by 31 (12 self)
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In this paper we describe a cutting plane algorithm for the Steiner tree packing problem. We use our algorithm to solve some switchbox routing problems of VLSIdesign and report on our computational experience. This includes a brief discussion of separation algorithms, a new LPbased primal heuristic and implementation details. The paper is based on the polyhedral theory for the Steiner tree packing polyhedron developed in our companion paper [GMW92] and meant to turn this theory into an algoritmic tool for the solution of practical problems.
The Node Capacitated Graph Partitioning Problem: A Computational Study
, 1996
"... In this paper we consider the problem of kpartitioning the nodes of a graph with capacity restrictions on the sum of the node weights in each subset of the partition, and the objective of minimizing the sum of the costs of the edges between the subsets of the partition. Based on a study of valid in ..."
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Cited by 25 (2 self)
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In this paper we consider the problem of kpartitioning the nodes of a graph with capacity restrictions on the sum of the node weights in each subset of the partition, and the objective of minimizing the sum of the costs of the edges between the subsets of the partition. Based on a study of valid inequalities, we present a variety of separation heuristics for cycle, cycle with ears, knapsack tree and pathblockcycle inequalities among others. The separation heuristics, plus primal heuristics, have been implemented in a branchandcut routine using a formulation including variables for the edges with nonzero costs and node partition variables. Results are presented for three classes of problems: equipartitioning problems arising in finite element methods and partitioning problems associated with electronic circuit layout and compiler design.
Practical Problem Solving with Cutting Plane Algorithms in Combinatorial Optimization
, 1994
"... Cutting plane algorithms have turned out to be practically successful computational tools in combinatorial optimization, in particular, when they are embedded in a branch and bound framework. Implementations of such "branch and cut" algorithms are rather complicated in comparison to many p ..."
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Cited by 20 (5 self)
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Cutting plane algorithms have turned out to be practically successful computational tools in combinatorial optimization, in particular, when they are embedded in a branch and bound framework. Implementations of such "branch and cut" algorithms are rather complicated in comparison to many purely combinatorial algorithms. The purpose of this article is to give an introduction to cutting plane algorithms from an implementor's point of view. Special emphasis is given to control and data structures used in practically successful implementations of branch and cut algorithms. We also address the issue of parallelization. Finally, we point out that in important applications branch and cut algorithms are not only able to produce optimal solutions but also approximations to the optimum with certified good quality in moderate computation times. We close with an overview of successful practical applications in the literature.
Routing Through Virtual Paths in Layered Telecommunication Networks
, 1995
"... We study a network configuration problem in telecommunications where one wants to set up paths in a capacitated network to accommodate given pointtopoint traffic demand. The problem is formulated as an integer linear programming model where 01 variables represent different paths. An associated in ..."
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Cited by 15 (1 self)
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We study a network configuration problem in telecommunications where one wants to set up paths in a capacitated network to accommodate given pointtopoint traffic demand. The problem is formulated as an integer linear programming model where 01 variables represent different paths. An associated integral polytope is studied and different classes of facets are described. These results are used in a cutting plane algorithm. Computational results for some realistic problems are reported.
Solving the Maximum Weight Planar Subgraph Problem by Branch and Cut
 PROCEEDINGS OF THE THIRD CONFERENCE ON INTEGER PROGRAMMING AND COMBINATORIAL OPTIMIZATION
, 1993
"... In this paper we investigate the problem of identifying a planar subgraph of maximum weight of a given edge weighted graph. In the theoretical part of the paper, the polytope of all planar subgraphs of a graph G is defined and studied. All subgraphs of a graph G, which are subdivisions of K 5 or K 3 ..."
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Cited by 8 (1 self)
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In this paper we investigate the problem of identifying a planar subgraph of maximum weight of a given edge weighted graph. In the theoretical part of the paper, the polytope of all planar subgraphs of a graph G is defined and studied. All subgraphs of a graph G, which are subdivisions of K 5 or K 3;3 , turn out to define facets of this polytope. We also present computational experience with a branch and cut algorithm for the above problem. Our approach is based on an algorithm which searches for forbidden substructures in a graph that contains a subdivision of K 5 or K 3;3 . These structures give us inequalities which are used as cutting planes.
FLEXMAP  A Neural Network For The Traveling Salesman Problem With Linear Time And Space Complexity
, 1991
"... We present a selforganizing "neural" network for the traveling salesman problem. It is partly based on the model of Kohonen. Our approach differs from former work in this direction as no ring structure with a fixed number of elements is used. Instead a small initial structure is enlarged ..."
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Cited by 4 (0 self)
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We present a selforganizing "neural" network for the traveling salesman problem. It is partly based on the model of Kohonen. Our approach differs from former work in this direction as no ring structure with a fixed number of elements is used. Instead a small initial structure is enlarged during a distribution process. This allows us to replace the central search step, which normally needs time O(n), by a local procedure that needs time O(1). Since the total number of search steps we have to perform is O(n) the runtime of our model scales linear with problem size. This is better than every known neural or conventional algorithm. The path lengths of the generated solutions are less than 9 percent longer than the optimum solutions of solved problems from the literature.