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A mixed-integer linear programming model is developed for the problem, and an implicit enumeration and a tabu search heuristic are tested with a suite of problem examples.
In the first stage, all the feasible routes are generated by means of an implicit enumeration algorithm; afterwards, an integer programming model is designed to select in the second stage the optimum routes from the set of feasible routes.
Candler and Townsley (1982) presented an implicit enumeration scheme to solve the problem.
They present an implicit enumeration approach to the selection of an optimum subset of technological processes required to execute a process plan under a conventional tolerance control strategy.
An implicit enumeration method with an embedded least time path subproblem was developed.
An Implicit Enumeration Method for LTL Network Design, Transportation Research Record, 1120 1-11, May 1987.
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Finally, we embed the algorithms above into a unified implicit enumeration scheme which is run in parallel with an improved Dynamic Programming algorithm to effectively solve the problem to proven optimality.
The route allocation model is formulated as a 0-1 integer programming problem, and is solved by a heuristic implicit enumeration approach.
We also develop a link-based implicit enumeration with an embedded degree and time constrained spanning tree algorithm.
We formulate this problem as a mixed-integer program that is solved using implicit enumeration with an embedded pricing subproblem.
For this subproblem, which is modeled as an unbounded knapsack problem, we propose three algorithms: implicit enumeration, column generation which renders the overall methodology nested column generation, and a hybrid algorithm.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com