Discrete, Continuous, and Constrained Optimization Using Collectives

Aerospace systems continue to grow in complexity while demanding optimal performance. This requires the systems to be both designed and controlled optimally. Aerospace systems are also typically comprised of many interacting components, some of which may have competing requirements. The optimization approaches used for aerospace systems usually require centralized coordination and synchronous updates. In addition, while the approaches treat the large numbers of variables, they may not take advantage of the fact that the coupling may only be between a relatively small number of the variables. Distributed optimization algorithms, such as the approach based upon collectives presented in this paper, attempt to exploit this aspect. A collective is defined as a multi-agent system where each agent is self-interested and capable of learning. Furthermore, a collective has a specified system objective which rates the performance of the joint actions of the agents. Although collectives have been used for a number of distributed optimization problems in computer science, recent developments based upon Probability Collectives (PC) theory enhance their applicability to discrete, continuous, mixed, and constrained optimization problems. This paper will present the theoretical underpinnings of the approach for these various problem domains. Several example problems are used to illustrate the technique and to provide insight into its behavior. The examples include discrete, constrained, and continuous problems. In particular a constrained discrete structural optimization and a continuous trajectory optimization illustrate the breadth of the collectives approach.