We propose the first algorithmic. approach which reoptimizes the shortest paths when any subset of arcs of the input graph is affected by a change of the costs;which can be either lower or higher than the old ones. Th...
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We propose the first algorithmic. approach which reoptimizes the shortest paths when any subset of arcs of the input graph is affected by a change of the costs;which can be either lower or higher than the old ones. This situation is more general than the ones addressed in the literature so far. We analyze the worst case time. complexity of the algorithm as. a function of both the input size and the overall cost perturbation, and discuss cases for which the proposed reoptimization method theoretically outperforms the approach of,applying a standard shortest path algorithm-after the change of the arc costs. (C) 2002 Elsevier Science B.V. All rights reserved.
The source-to-all maximum cost-to-time ratio problem is the problem of finding the maximum cost-to-time ratio path from a source node to every other node. The motivation comes from an application in large-scale linear...
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The source-to-all maximum cost-to-time ratio problem is the problem of finding the maximum cost-to-time ratio path from a source node to every other node. The motivation comes from an application in large-scale linear programming. We present three algorithms for solving the problem. We give proofs of correctness and we analyze the running times. One of the algorithms is polynomial and the remaining two are pseudopolynomial. We present extensive computational results on several networks. (C) 2003 Wiley Periodicals, Inc.
We develop a tabu search approach for the fixed charge transportation (FCT) problem using recency based and frequency based memories, together with two strategies for each of the intermediate and long term memory proc...
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We develop a tabu search approach for the fixed charge transportation (FCT) problem using recency based and frequency based memories, together with two strategies for each of the intermediate and long term memory processes, making use of a network based implementation of the simplex method as the local search method. Our approach is evaluated computationally on randomly generated problems of different sizes and of different ranges of magnitude of fixed costs relative to variable costs. Comparisons are made with two leading methods previously proposed, one in the category of exact methods and one in the category of heuristic methods. Our tabu search procedure obtains optimal or near-optimal solutions more than a thousand times faster than the exact solution algorithm for simple problems and thoroughly dominates the exact algorithm on all dimensions for more complex problems. Compared to the heuristic approach, on very small and easy test problems the tabu search procedure required about the same amount of solution time and found solutions at least as good. However, for larger problems and for problems with higher fixed to variable costs, the tabu search procedure was 3-4 times faster than the competing heuristic, and found significantly better solutions in all cases. (C) 1998 Elsevier Science B.V. All rights reserved.
The proportional equity dow problem extends a class of problems referred to as equity flow problems whose objective is to equitably distribute dow among the arcs in a how circulation network. The proportionally bounde...
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The proportional equity dow problem extends a class of problems referred to as equity flow problems whose objective is to equitably distribute dow among the arcs in a how circulation network. The proportionally bounded dow circulation problem places lower and upper bounds on each are flow that are nondecreasing continuous functions of the flow through one special are, and the objective is to maximize the flow through the special arc. The proportional equity dow problem for terminal arcs (Problem TA) is then defined as a special case where all the proportional arcs enter a sink vertex. Applications of both the general problem and Problem TA are given. Two optimality conditions for Problem TA are developed, as well as an algorithm that is polynomially bounded for many types of nondecreasing, continuous, proportional bounding functions. Specifically, the algorithm is shown to be polynomially bounded if the largest root of an equation can be found in polynomial time.
The network synthesis problem is to design an undirected network with a minimum total construction cost which non-simultaneously satisfies given flow requirements between pairs of nodes. This well-known problem was in...
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The network synthesis problem is to design an undirected network with a minimum total construction cost which non-simultaneously satisfies given flow requirements between pairs of nodes. This well-known problem was introduced by Gomory and Hu (1961) who formulated it as a very large linear program and solved it by a method similar to column generation. We provide an efficient algorithm for this problem when the underlying graph is a cycle.
We consider a scheduling problem that involves two types of processors, but three types of jobs. Each job has a fixed start time and a fixed completion time, and falls into one of three types. Jobs of type 1 can be do...
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We consider a scheduling problem that involves two types of processors, but three types of jobs. Each job has a fixed start time and a fixed completion time, and falls into one of three types. Jobs of type 1 can be done only by type-1 processors, type-2 jobs only by type-2 processors, and type-0 jobs by either type of processors. We present a polynomial algorithm for finding the minimal cost combination of the two types of processors required to complete all jobs. The steps of the algorithm consist of constructing a job schedule network, transforming it into a single-commodity flow problem and finding the maximal flow through it.
We consider a family of problems defined on a common solution space. A problem is characterized by a subset of the solution space whose elements are defined to be feasible for that problem. Each solution is associated...
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We consider a family of problems defined on a common solution space. A problem is characterized by a subset of the solution space whose elements are defined to be feasible for that problem. Each solution is associated with a cost. Solving a problem means finding a feasible solution of minimum cost. It is assumed that an algorithm for solving any single problem is available. We show how to solve all of the problems in the family by selecting and solving a small subset of them.
As known in literature a flow-type approach to the Euclidean Traveling Salesman Problem gives better assignment lower bounds, using cities on the convex hull as sources and sinks, By selecting them carefully this appr...
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A simple transformation of the distance matrix for the Euclidean traveling salesman problem is presented that produces a tighter lower bound on the length of the optimal tour than has previously been attainable using ...
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A simple transformation of the distance matrix for the Euclidean traveling salesman problem is presented that produces a tighter lower bound on the length of the optimal tour than has previously been attainable using the assignment relaxation. The improved lower bound is obtained by exploiting geometric properties of the problem to produce fewer and larger subtours on the first solution of the assignment problem. This research should improve the performance of assignment based exact procedures and may lead to improved heuristics for the traveling salesman problem.
An algorithm for finding the K best cuts in a network is presented. Using a branch technique introduced by Lawler [4] we reduce the problem to K computations of 2nd best cuts. The latter problem can be solved by an O(...
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