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Guided local search and its application to the traveling salesman problem
, 1998
"... The Traveling Salesman Problem (TSP) is one of the most famous problems in combinatorial optimization. In this paper, we are going to examine how the techniques of Guided Local Search (GLS) and Fast Local Search (FLS) can be applied to the problem. Guided Local Search sits on top of local search heu ..."
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Cited by 57 (16 self)
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The Traveling Salesman Problem (TSP) is one of the most famous problems in combinatorial optimization. In this paper, we are going to examine how the techniques of Guided Local Search (GLS) and Fast Local Search (FLS) can be applied to the problem. Guided Local Search sits on top of local search heuristics and has as a main aim to guide these procedures in exploring efficiently and effectively the vast search spaces of combinatorial optimization problems. Guided Local Search can be combined with the neighborhood reduction scheme of Fast Local Search which significantly speeds up the operations of the algorithm. The combination of GLS and FLS with TSP local search heuristics of different efficiency and effectiveness is studied in an effort to determine the dependence of GLS on the underlying local search heuristic used. Comparisons are made with some of the best TSP heuristic algorithms and general optimization techniques which demonstrate the advantages of GLS over alternative heuristic approaches suggested for the problem.
A Deductive and ObjectOriented Approach to a Complex Scheduling Problem
 Proc. of DOOD'93
, 1993
"... . This paper presents the application of combined deductive and objectoriented technologies to a complex scheduling (timetable) problem. This approach emphasizes local propagation of constraints, which we perform with deductive rules, and combines it with global pruning heuristics, which we represe ..."
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Cited by 29 (6 self)
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. This paper presents the application of combined deductive and objectoriented technologies to a complex scheduling (timetable) problem. This approach emphasizes local propagation of constraints, which we perform with deductive rules, and combines it with global pruning heuristics, which we represent with methods (in a procedural manner) attached to objects. Because both components are essential to ensure success, we see this scheduling application as an interesting demonstration of the synergy between objectoriented and deductive technology. We provide a precise description of the problem, discuss what makes it difficult, and present detailed techniques that we used for its resolution. 1. Introduction Timetable scheduling problems (e.g., course scheduling for universities [Car86]) are common problems that are usually solved by adhoc algorithms packaged as dedicated software. Such problems are not only difficult from a theoretical perspective (most of them are NPhard problems) but...
The Errand Scheduling Problem
, 1997
"... We consider the following natural errand scheduling problem (ESP). We must perform a set of errands at the nodes of an edgeweighted graph, and each errand can only be performed at a subset of the nodes. What is the shortest tour that allows us to complete all the errands? We also consider the close ..."
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Cited by 15 (0 self)
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We consider the following natural errand scheduling problem (ESP). We must perform a set of errands at the nodes of an edgeweighted graph, and each errand can only be performed at a subset of the nodes. What is the shortest tour that allows us to complete all the errands? We also consider the closely related tree cover problem (TCP), in which we seek a tree of minimum length that "covers" all errands. Both problems generalize a number of wellknown problems in combinatorial optimization and have a wide range of applications including job scheduling on multistate CNC machines and VLSI design. We focus on the case in which the graph is a weighted tree; this trivially generalizes the famous set cover problem. Under the assumption that no errand can be performed in "too many" nodes, we obtain an algorithm that asymptotically matches the best possible approximation ratio for set cover and approximates both errand scheduling and tree cover within O(log m), where m is the total number of e...
Teaching Integer Programming Formulations Using The Traveling Salesman Problem
 SIAM REV
, 2003
"... We designed a simple computational exercise to compare weak and strong integer programming formulations of the traveling salesman problem. Using commercial IP software, and a short (60 line long) Matlab code, students can optimally solve instances with up to 70 cities in a few minutes by adding cuts ..."
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Cited by 12 (0 self)
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We designed a simple computational exercise to compare weak and strong integer programming formulations of the traveling salesman problem. Using commercial IP software, and a short (60 line long) Matlab code, students can optimally solve instances with up to 70 cities in a few minutes by adding cuts from the stronger formulation to the weaker, but simpler one.
Fitness Landscapes And Performance Of MetaHeuristics
 MetaHeuristics: Advances and Trends in Local Search Paradigms for Optimization
, 1999
"... We perform a statistical analysis of the structure of the search space of some planar, euclidian instances of the traveling salesman problem. We want to depict this structure from the point of view of iterated local search algorithms. ..."
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Cited by 11 (0 self)
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We perform a statistical analysis of the structure of the search space of some planar, euclidian instances of the traveling salesman problem. We want to depict this structure from the point of view of iterated local search algorithms.
Transformations of generalized ATSP into ATSP
 Operations Research Letters
"... The Generalized Traveling Salesman Problem (GTSP) is stated as follows. Given a weighted complete digraph K ∗ n and a partition V1,..., Vk of its vertices, find a minimum weight cycle containing exactly one vertex from each set Vi, i = 1,..., k. We study transformations from GTSP to TSP. The ’exact ..."
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Cited by 10 (3 self)
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The Generalized Traveling Salesman Problem (GTSP) is stated as follows. Given a weighted complete digraph K ∗ n and a partition V1,..., Vk of its vertices, find a minimum weight cycle containing exactly one vertex from each set Vi, i = 1,..., k. We study transformations from GTSP to TSP. The ’exact ’ NoonBean transformation is investigated in computational experiments. We study the ’nonexact ’ FischettiSalazarToth (FST) transformation and its two modifications in computational experiments and theoretically using domination analysis. One of our conclusions is that one of the modifications of the FST transformation is better than the original FST transformation in the worst case in terms of domination analysis.
The traveling salesman problem with few inner points
 In Proc. 10th COCOON, volume 3106 of LNCS
, 2004
"... We propose two algorithms for the planar Euclidean traveling salesman problem. The first runs in O(k!kn) time and O(k) space, and the second runs in O(2 k k 2 n) time and O(2 k kn) space, where n denotes the number of input points and k denotes the number of points interior to the convex hull. ..."
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Cited by 10 (1 self)
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We propose two algorithms for the planar Euclidean traveling salesman problem. The first runs in O(k!kn) time and O(k) space, and the second runs in O(2 k k 2 n) time and O(2 k kn) space, where n denotes the number of input points and k denotes the number of points interior to the convex hull.
A CooperativeArchitecture Expert System for Solving Large Time/Travel Assignment Problems
, 1992
"... In this paper, we consider the problem of assigning tasks to operators according to a large set of constraints that include time sensitivity and travel optimization. Our practical instance of this problem combines computational complexity (scheduling the tasks for one technician is NPhard and littl ..."
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Cited by 9 (3 self)
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In this paper, we consider the problem of assigning tasks to operators according to a large set of constraints that include time sensitivity and travel optimization. Our practical instance of this problem combines computational complexity (scheduling the tasks for one technician is NPhard and little is known about getting a solution [CK92]) and size (around 20000 tasks stored in a database). We present a solution that has been successfully implemented and tested, which we describe as an expert system where expertise is applied to constraint satisfaction. By combining a constraint solver and a rulebased domain expert, we have obtained a satisfactory level of efficiency while keeping the flexibility and extensibility of a constraintbased approach.
Heuristics for planning with penalties and rewards formulated in logic and computed through circuits
, 2008
"... ..."
THE FAST INTERSECTION TRANSFORM WITH APPLICATIONS TO COUNTING PATHS
, 2008
"... We present an algorithm for evaluating a linear “intersection transform” of a function defined on the lattice of subsets of an nelement set. In particular, the algorithm constructs an arithmetic circuit for evaluating the transform in “downclosure time ” relative to the support of the function and ..."
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Cited by 6 (2 self)
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We present an algorithm for evaluating a linear “intersection transform” of a function defined on the lattice of subsets of an nelement set. In particular, the algorithm constructs an arithmetic circuit for evaluating the transform in “downclosure time ” relative to the support of the function and the evaluation domain. As an application, we develop an algorithm that, given as input a digraph with n vertices and bounded integer weights at the edges, counts paths by weight and given length 0 ≤ ℓ ≤ n − 1 in time O ∗ (exp(n · H(ℓ/(2n)))), where H(p) = −p log p − (1 − p) log(1 − p), and the notation O ∗ (·) suppresses a factor polynomial in n.