A Nonlinear Network Flow Algorithm for Maximization of Benefits in a Hydroelectric Power System

TLDR

The Tennessee Valley Authority framed the problem as an optimization model with a nonseparable nonlinear objective and linear network flow constraints. The authors present a nonlinear network flow algorithm to maximize benefits in a multireservoir hydroelectric power system. The algorithm combines a modified reduced‑gradient method with primal linear network flows, uses an integer‑programming subproblem to determine the superbasic set and search directions, and is implemented via an efficient basis‑tree labeling system based on a single node‑length array tailored to the system’s physical structure. On a 6‑reservoir TVA subsystem, the algorithm solved test problems with computational costs well within an affordable range.

Abstract

A nonlinear network flow algorithm for maximization of benefits in a multireservoir hydroelectric power system is presented. The problem was posed by Tennessee Valley Authority (TVA) as an optimization model with a nonseparable nonlinear objective function and with linear network flow constraints. The proposed algorithm is based on reduced gradient methodology (with somewhat nonstandard modifications) and on primal linear network flows (with simplifications resulting from the special structure of the problem network). An unusual feature of the algorithm is an integer programming subproblem whose exact solution determines the superbasic set and the search directions. The algorithm is coded by means of an efficient basis-tree labeling system which consists of a single node-length array and which is specifically designed for the physical context of the problem. Test problems on a 6-reservoir TVA subsystem were solved with computer costs well within the “affordable” range.