Data networks
Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
Journal of Optimization Theory and Applications
A D. C. Optimization Algorithm for Solving the Trust-Region Subproblem
SIAM Journal on Optimization
Solving a Class of Linearly Constrained Indefinite QuadraticProblems by D.C. Algorithms
Journal of Global Optimization
The design of store-and-forward (s/f) networks for computer communications
The design of store-and-forward (s/f) networks for computer communications
Introduction to Global Optimization (Nonconvex Optimization and Its Applications)
Introduction to Global Optimization (Nonconvex Optimization and Its Applications)
Bounds for global optimization of capacity expansion and flow assignment problems
Operations Research Letters
A branch and reduce approach for solving a class of low rank d.c. programs
Journal of Computational and Applied Mathematics
Power-efficient radio configuration in fixed broadband wireless networks
Computer Communications
Adaptive memory in multistart heuristics for multicommodity network design
Journal of Heuristics
Hi-index | 0.00 |
We address a class of particularly hard-to-solve combinatorial optimization problems, namely that of multicommodity network optimization when the link cost functions are discontinuous step increasing. Unlike usual approaches consisting in the development of relaxations for such problems (in an equivalent form of a large scale mixed integer linear programming problem) in order to derive lower bounds, our d.c.(difference of convex functions) approach deals with the original continuous version and provides upper bounds. More precisely we approximate step increasing functions as closely as desired by differences of polyhedral convex functions and then apply DCA (difference of convex function algorithm) to the resulting approximate polyhedral d.c. programs. Preliminary computational experiments are presented on a series of test problems with structures similar to those encountered in telecommunication networks. They show that the d.c. approach and DCA provide feasible multicommodity flows x* such that the relative differences between upper bounds (computed by DCA) and simple lower bounds r:=(f(x*)-LB)/{f(x*)} lies in the range [4.2 %, 16.5 %] with an average of 11.5 %, where f is the cost function of the problem and LB is a lower bound obtained by solving the linearized program (that is built from the original problem by replacing step increasing cost functions with simple affine minorizations). It seems that for the first time so good upper bounds have been obtained.