345 research outputs found
Equivalent instances of the simple plant location problem
In this paper we deal with a pseudo-Boolean representation of the simple plant location problem. We define instances of this problem that are equivalent, in the sense that each feasible solution has the same goal function value in all such instances. We further define a collection of polytopes whose union describes the set of instances equivalent to a given instance. We use the concept of equivalence to develop a method by which we can extend the set of instances that we can solve using our knowledge of polynomially solvable special cases. We also present a new preprocessing rule that allows us to determine sites in which facilities will not be located in an optimal solution and thereby reduce the size of a problem instance.
Equivalent instances of the simple plant location problem
AbstractIn this paper we deal with a pseudo-Boolean representation of the simple plant location problem. We define instances of this problem that are equivalent, in the sense that each feasible solution has the same goal function value in all such instances. We further define a collection of polytopes whose union describes the set of instances equivalent to a given instance. We use the concept of equivalence to develop a method by which we can extend the set of instances that we can solve using our knowledge of polynomially solvable special cases
On complexity of optimized crossover for binary representations
We consider the computational complexity of producing the best possible
offspring in a crossover, given two solutions of the parents. The crossover
operators are studied on the class of Boolean linear programming problems,
where the Boolean vector of variables is used as the solution representation.
By means of efficient reductions of the optimized gene transmitting crossover
problems (OGTC) we show the polynomial solvability of the OGTC for the maximum
weight set packing problem, the minimum weight set partition problem and for
one of the versions of the simple plant location problem. We study a connection
between the OGTC for linear Boolean programming problem and the maximum weight
independent set problem on 2-colorable hypergraph and prove the NP-hardness of
several special cases of the OGTC problem in Boolean linear programming.Comment: Dagstuhl Seminar 06061 "Theory of Evolutionary Algorithms", 200
Solving the simple plant location problem using a data correcting approach
The Data Correcting Algorithm is a branch and bound algorithm in which thedata of a given problem instance is ‘corrected’ at each branching in such a waythat the new instance will be as close as possible to a polynomially solvableinstance and the result satisfies an acceptable accuracy (the difference betweenoptimal and current solution). In this paper the data correcting algorithm isapplied to determining exact and approximate optimal solutions to the simpleplant location problem. Implementations of the algorithm are based on apseudo-Boolean representation of the goal function of the SPLP and a newreduction rule. We study the efficiency of the data correcting approach usingtwo different bounds, the combinatorial bound and the Erlenkotter bound. Wepresent computational results on several benchmark instances of the simpleplant location problem, which confirm the efficiency of the data-correcting approach.
Data Correcting Algorithms in Combinatorial Optimization
This paper describes data correcting algorithms. It provides the theory behind the algorithms and presents the implementation details and computational experience with these algorithms on the asymmetric traveling salesperson problem, the problem of maximizing submodular functions, and the simple plant location problem.
Optimal Recombination in Genetic Algorithms
This paper surveys results on complexity of the optimal recombination problem
(ORP), which consists in finding the best possible offspring as a result of a
recombination operator in a genetic algorithm, given two parent solutions. We
consider efficient reductions of the ORPs, allowing to establish polynomial
solvability or NP-hardness of the ORPs, as well as direct proofs of hardness
results
On a class of intersection graphs
Given a directed graph D = (V,A) we define its intersection graph I(D) =
(A,E) to be the graph having A as a node-set and two nodes of I(D) are adjacent
if their corresponding arcs share a common node that is the tail of at least
one of these arcs. We call these graphs facility location graphs since they
arise from the classical uncapacitated facility location problem. In this paper
we show that facility location graphs are hard to recognize and they are easy
to recognize when the graph is triangle-free. We also determine the complexity
of the vertex coloring, the stable set and the facility location problems on
that class
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