91,296 research outputs found
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
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Design, implementation and testing of an integrated branch and bound algorithm for piecewise linear and discrete programming problems within an LP framework
A number of discrete variable representations are well accepted and find regular use within LP systems. These are Binary variables, General Integer variables, Variable Upper Bounds or Semi Continuous variables, Special Ordered Sets of type One and type Two. The FortLP system has been extended to include these representations. A Branch and Bound algorithm is designed in which the choice of sub-problems and branching variables are kept general. This provides considerable scope of experimentation with tree development heuristics and the tree search can then be guided by search parameters specified by user subroutines. The data structures for representing the variables and the definition of the branch and bound tree are described. The results of experimental investigation for a few test problems are reported
Projection methods in conic optimization
There exist efficient algorithms to project a point onto the intersection of
a convex cone and an affine subspace. Those conic projections are in turn the
work-horse of a range of algorithms in conic optimization, having a variety of
applications in science, finance and engineering. This chapter reviews some of
these algorithms, emphasizing the so-called regularization algorithms for
linear conic optimization, and applications in polynomial optimization. This is
a presentation of the material of several recent research articles; we aim here
at clarifying the ideas, presenting them in a general framework, and pointing
out important techniques
A sequential semidefinite programming method and an application in passive reduced-order modeling
We consider the solution of nonlinear programs with nonlinear
semidefiniteness constraints. The need for an efficient exploitation of the
cone of positive semidefinite matrices makes the solution of such nonlinear
semidefinite programs more complicated than the solution of standard nonlinear
programs. In particular, a suitable symmetrization procedure needs to be chosen
for the linearization of the complementarity condition. The choice of the
symmetrization procedure can be shifted in a very natural way to certain linear
semidefinite subproblems, and can thus be reduced to a well-studied problem.
The resulting sequential semidefinite programming (SSP) method is a
generalization of the well-known SQP method for standard nonlinear programs. We
present a sensitivity result for nonlinear semidefinite programs, and then
based on this result, we give a self-contained proof of local quadratic
convergence of the SSP method. We also describe a class of nonlinear
semidefinite programs that arise in passive reduced-order modeling, and we
report results of some numerical experiments with the SSP method applied to
problems in that class
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