A hybrid algorithm for large-scale non-separable nonlinear multicommodity flow problems

We propose an approach for large-scale non-separable nonlinear multicommodity flow problems by solving a sequence of subproblems which can be addressed by commercial solvers. Using a combination of solution methods such as modified gradient projection, shortest path algorithm and golden section search, the approach can handle general problem instances, including those with (i) non-separable cost, (ii) objective function not available analytically as polynomial but are evaluated using black-boxes, and (iii) additional side constraints not of network flow types. Implemented as a toolbox in commercial solvers, it allows researchers and practitioners, currently conversant with linear instances, to easily manage large-scale convex instances as well. In this article, we compared the proposed algorithm with alternative approaches in the literature, covering both theory and large test cases. New test cases with non-separable convex costs and non-network flow side constraints are also presented and evaluated. The toolbox is available free for academic use upon request.