3 research outputs found
Column Generation Algorithms for Nonlinear Optimization II: Numerical Investigations
García et al. present a class of column generation (CG) algorithms for nonlinear programs. Its main
motivation from a theoretical viewpoint is that under some circumstances, finite convergence can be
achieved, in much the same way as for the classic simplicial decomposition method; the main practical
motivation is that within the class there are certain nonlinear column generation problems that can
accelerate the convergence of a solution approach which generates a sequence of feasible points. This
algorithm can, for example, accelerate simplicial decomposition schemes by making the subproblems
nonlinear. This paper complements the theoretical study on the asymptotic and finite convergence of
these methods given in
[1]
with an experimental study focused on their computational efficiency.
Three types of numerical experiments are conducted. The first group of test problems has been
designed to study the parameters involved in these methods. The second group has been designed to
investigate the role and the computation of the prolongation of the generated columns to the relative
boundary. The last one has been designed to carry out a more complete investigation of the difference
in computational efficiency between linear and nonlinear column generation approaches.
In order to carry out this investigation, we consider two types of test problems: the first one is the
nonlinear, capacitated single-commodity network flow problem of which several large-scale instances
with varied degrees of nonlinearity and total capacity are constructed and investigated, and the second
one is a combined traffic assignment mode
Using ACCPM in a simplicial decomposition algorithm for the traffic assignment problem
Traffic assignment problem, Variational inequalities, Simplicial decomposition, Analytic center cutting plane method,
Using ACCPM in a simplicial decomposition algorithm for the traffic assignment problem
The purpose of the traffic assignment problem is to obtain a traffic flow
pattern given a set of origin-destination travel demands and flow dependent link performance functions of a road network. In the general case, the traffic assignment
problem can be formulated as a variational inequality, and several algorithms have
been devised for its efficient solution. In this work we propose a new approach that
combines two existing procedures: the master problem of a simplicial decomposition
algorithm is solved through the analytic center cutting plane method. Four variants
are considered for solving the master problem. The third and fourth ones, which
heuristically compute an appropriate initial point, provided the best results. The computational experience reported in the solution of real large-scale diagonal and difficult asymmetric problems—including a subset of the transportation networks of Madrid and Barcelona—show the effectiveness of the approach.Peer Reviewe