Game-theoretic approaches for complex systems optimization.

Abstract

A complex system is an artificial system that cannot be modeled analytically or optimized in an effective manner, usually because it possesses the following properties: (1) the system can only be modeled as a simulation, (2) the size of the problem is untenable, so that even if the system could be modeled analytically, it would be impractical to solve it exactly, (3) necessary information required for problem solving is distributed in nature. This thesis presents methods for modeling and optimizing systems with the above challenging properties. We first discuss the important modeling decision of whether to include stochasticity. By employing a real-world case study, we show that a standard numerical procedure can indeed help us make this decision. Next, we use the challenging problem of finding coordinated signal timing plans to motivate the need of a new paradigm for simulation optimization. We employ the game-theoretic paradigm of sampled fictitious play (SFP) to iteratively converge to a locally optimal solution. The key to the empirical success of SFP is parallelization. Through parallelization, SFP is robustly scalable to realistic size networks modeled with high-fidelity simulations. Compared to other less adaptive approaches, significant savings are achieved. This procedure is standardized so that we can use it to solve many unconstrained discrete optimization problems. However, for constrained problems, additional effort is required in using SFP. We introduce the idea of feasible space mapping which, when combined with SFP, can be used in decomposing and approximating large-scale dynamic programming models. With a large scale decision making problem in automotive manufacturing, we demonstrate that high quality solutions can be obtained by this approach in several orders of magnitude faster time than the traditional global algorithm. Finally, for distributed problems, we address the decentralization issue with a market-based approach. The market-based approach involves: (1) agent strategy development, (2) empirical game-theoretic analysis, (3) assessing efficiency of the solution obtained by the market-based approach. We first introduce the market-based approach, with special attention on the strategy-pruning techniques. We then use task allocation for dynamic information processing environments as an example to illustrate the methodology and demonstrate its effectiveness.