Decentralized Optimization Systems and Their Application to a Class of Transportation Problem

Abstract

We are concerned with a class of organizations composed of a coordinating central system and plural semi-autonomous subsystems, such that each of them has a decision-making unit. Such a problem is regarded as that of a decentralized two-level optimization. The basic principle of planning for this organization is that the central system allocates resources so as to optimize its own objective, while the subsystems optimize their own objectives using the given resources.
Within this framework of decision making, we consider a transportation problem in which N transport agents transport their own commodity. Each transport agent n, n=1, …, N, finds optimal flow patterns of the associated commodity n so that the transportation cost is minimized based on its own objective function under the arc capacity restriction imposed by the central agent. The coordinating central agent governs the transport agents through the way of allocating the arc capacity so that the optimality of whole network system is achieved. Here, the lower level problem is composed of a set of single commodity minimum cost flow problems of the transport agents, each of which can be easily solved separately by the subsystem.
The decentralized optimization problem is solved in principle by a parametric approach. A feasible direction algorithm using directional derivative and application of a constraint simplex method are proposed to solve the formulated network flow problem.