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Existing concepts of complexity provide useful classifications, but have not resulted in laws of complex systems as much as the concept of energy. At the same time, it is still believed that understanding of complexity may provide the ability to optimize a complex system efficiently. As complex systems play an increasingly important role in human activities, the solution of the problem becomes a critical issue.§The book suggests a new perspective to the problem by recognizing the possibility of a general optimality condition that determines the optimal performance of a complex system. According to the condition a complex system demonstrates the optimal performance, if its complexity is in a certain relationship with the complexity of the environment. In this context the complexity would become the key to the optimization of the system. Existing concepts of complexity provide useful classifications, but have not resulted in laws of complex systems such as a concept of energy. At the same time, it is still believed that a better understanding of complexity may allow more efficient optimization in complex systems. As complex systems play an increasingly important role in human activities, the solution of these problem becomes a critical issue.§This book suggests a new perspective on understanding complexity by recognizing the possibility of a general optimality condition that determines the optimal performance of a complex system. According to the condition, a complex system demonstrates optimal performance if its complexity is in a certain relationship with the complexity of the environment. In this context, characterizing a system's complexity would become the key to the optimization of the system.§This book can serve as resource to garaduate students and researchers whose work involves the optimization or modeling of complex systems.
