On a New Type of Information Processing for Efficient Management of Complex Systems

It is a challenge to manage complex systems efficiently without confronting NP-hard problems. To address the situation we suggest to use self-organization processes of prime integer relations for information processing. Self-organization processes of prime integer relations define correlation structures of a complex system and can be equivalently represented by transformations of two-dimensional geometrical patterns determining the dynamics of the system and revealing its structural complexity. Computational experiments raise the possibility of an optimality condition of complex systems presenting the structural complexity of a system as a key to its optimization. From this perspective the optimization of a system could be all about the control of the structural complexity of the system to make it consistent with the structural complexity of the problem. The experiments also indicate that the performance of a complex system may behave as a concave function of the structural complexity. Therefore, once the structural complexity could be controlled as a single entity, the optimization of a complex system would be potentially reduced to a one-dimensional concave optimization irrespective of the number of variables involved its description. This might open a way to a new type of information processing for efficient management of complex systems.Comment: 5 pages, 2 figures, to be presented at the International Conference on Complex Systems, Boston, October 28 - November 2, 200

On Beyond LP: Optimization of Complex Systems

Many engineers designing a complex system would like to optimize its performance, and perform trade-off studies to better understand the impact of decisions. The complex systems are often modeled with functions that are non-linear, non-convex, multimodal, discontinuous and available only through computer programs. They may involve continuous and integer variables. In this talk, I will summarize some theoretical results regarding performance of random search algorithms, and discuss a new meta-control methodology that adaptively guides an interacting-particle algorithm with a filtering technique. Numerical results will be presented demonstrating how the meta-control methodology dynamically heats and cools a temperature parameter based on observed behavior of the algorithm to achieve desired performance characteristics (e.g., quality of the final outcome, algorithm running time, etc.). An application in engineering design of composites structures for aircraft fuselage, such as the new 787 Boeing composite aircraft, will be mentioned

Efficient design optimization of complex electromagnetic systems using parametric macromodeling techniques

We propose a new parametric macromodeling technique for complex electromagnetic systems described by scattering parameters, which are parameterized by multiple design variables such as layout or substrate feature. The proposed technique is based on an efficient and reliable combination of rational identification, a procedure to find scaling and frequency shifting system coefficients, and positive interpolation schemes. Parametric macromodels can be used for efficient and accurate design space exploration and optimization. A design optimization example for a complex electromagnetic system is used to validate the proposed parametric macromodeling technique in a practical design process flow

Extremal Optimization of Graph Partitioning at the Percolation Threshold

The benefits of a recently proposed method to approximate hard optimization problems are demonstrated on the graph partitioning problem. The performance of this new method, called Extremal Optimization, is compared to Simulated Annealing in extensive numerical simulations. While generally a complex (NP-hard) problem, the optimization of the graph partitions is particularly difficult for sparse graphs with average connectivities near the percolation threshold. At this threshold, the relative error of Simulated Annealing for large graphs is found to diverge relative to Extremal Optimization at equalized runtime. On the other hand, Extremal Optimization, based on the extremal dynamics of self-organized critical systems, reproduces known results about optimal partitions at this critical point quite well.Comment: 7 pages, RevTex, 9 ps-figures included, as to appear in Journal of Physics

Complex System Optimization using Biogeography-Based Optimization

Complex systems are frequently found in modern industry. But with their multisubsystems, multiobjectives, and multiconstraints, the optimization of complex systems is extremely hard. In this paper, a new algorithm adapted from biogeography-based optimization (BBO) is introduced for complex system optimization. BBO/Complex is the combination of BBO with a multiobjective ranking system, an innovative migration approach, and effective diversity control. Based on comparisons with three complex system optimization algorithms (multidisciplinary feasible (MDF), individual discipline feasible (IDF), and collaborative optimization (CO)) on four real-world benchmark problems, BBO/Complex demonstrates competitive performance. BBO/Complex provides the best performance in three of the benchmark problems and the second best in the fourth problem