Optimization Algorithms for Multiple Objective Programs and Decentralized Hierarchical Systems

We study optimization methods for systems with plural objective functions. First, several algorithms for the unique solution to multiple objective programs are proposed by introducing concept of satisfaction conditions and preference ordering among objective functions. The resulting solutions satisfy Pareto optimality. Second, an optimization problem for a decentralized hierarchical system is formulated such that local systems have their own, independent objectives within some restrictions imposed by a central system. The central system governs local ones by means of resource allocation and optimizes its own objective by suitably allocating resources to them, and each local system optimized its own objective consuming the given resources. Finally, relation between Pareto optimality and decentralized hierarchical optimization is discussed.