Multiobjective Optimization for Complex Systems

Complex systems are becoming more and more apparent in a variety of disciplines, making solution methods for these systems valuable tools. The solution of complex systems requires two significant skills. The first challenge of developing mathematical models for these systems is followed by the difficulty of solving these models to produce preferred solutions for the overall systems. Both issues are addressed by this research. This study of complex systems focuses on two distinct aspects. First, models of complex systems with multiobjective formulations and a variety of structures are proposed. Using multiobjective optimization theory, relationships between the efficient solutions of the overall system and the efficient solutions of its subproblems are derived. A system with a particular structure is then selected and further analysis is performed regarding the connection between the original system and its decomposable counterpart. The analysis is based on Kuhn-Tucker efficiency conditions. The other aspect of this thesis pertains to the study of a class of complex systems with a structure that is amenable for use with analytic target cascading (ATC), a decomposition and coordination approach of special interest to engineering design. Two types of algorithms are investigated. Modifications to a subgradient optimization algorithm are proposed and shown to improve the speed of the algorithm. A new family of biobjective algorithms showing considerable promise for ATC-decomposable problems is introduced for two-level systems, and convergence results for a specified algorithm are given. Numerical examples showing the effectiveness of all algorithms are included

Decomposition and Coordination for Multiobjective Complex Systems

Complex systems are modeled as collections of multiobjective programs each representing a subsystem (or component) of the overall system. The subsystems interact with each other in various ways adding to the complexity of the overall problem. Since the calculation of efficient sets of these complex systems presents a challenging problem, it is desirable to decompose the overall system into component multiobjective programs that are more easily solvable and then construct the efficient set of the overall system. Selected cases of complex system are presented and relationships between their efficient sets the efficient sets of their subsystems are given