Highly Optimized Tolerance Theory

Excerpt from: Doctoral Dissertation of the Graduate University of the Chinese Academy of Sciences "Theoretical Exploration of Sustainable Development and Its Application in Inner Mongolia Grasslands" Author: Xu Guanghua There are a large number of complex systems operating in uncertain environments in nature and engineering. These systems have been highly optimized through natural selection or engineering design, thereby exhibiting a certain degree of robustness to disturbances. However, like self-organized criticality, these systems also exhibit power-law characteristics, which are the result of a trade-off among three factors: system benefits, resource consumption, and tolerance to risk. To this end, Jean Carlson from the University of California, Santa Barbara, and John Doyle from the California Institute of Technology proposed the HOT (Highly Optimized Tolerance) theory to generalize this behavior different from self-organized critical systems (Carlson and Doyle, 1999, 2000, 2002). Tolerance emphasizes that the robustness of complex systems is conditional and limited, requiring management and protection. Highly Optimized emphasizes that complex systems are not random combinations, but highly structured, arising from intentional design or evolution, thus distinguishing them from self-organized criticality. Systems in the HOT state are highly robust to disturbances within the design, but exhibit fragility to factors not considered during the design. That is, HOT systems are both robust and fragile. The HOT theory posits that the power-law distribution patterns in complex systems and other characteristics such as robustness to disturbances and sensitivity to structural defects are due to optimization behaviors in system design or evolution (Newman, 2000). For complex systems composed of many interconnected subsystems, whether naturally evolved or artificially designed, when the system can effectively tolerate certain uncertainties (possessing robustness), it becomes more sensitive to other unconsidered uncertainties. The systems of interest in HOT theory are those that have been optimized, whether through natural selection or engineering design, to provide reliable functions in uncertain environments. It is believed that the power laws in these systems result from trade-offs between output, resource consumption, and tolerance to risk. The characteristics of HOT are (Carlson and Doyle, 1999): 1) High efficiency, high performance, and high reliability against uncertainties targeted by the design. 2) High sensitivity to design errors and unconsidered disturbances. 3) Possession of specific structures. 4) Power laws. Examples of HOT include: biology, epidemics, aviation and automotive design, forest and environmental studies, Internet traffic, and power systems (Carlson and Doyle, 1999). Carlson and Doyle (2002) also compared HOT and SOC, arguing that self-organized criticality is not the sole source of power laws. Moreover, in engineering and biology, complex systems are almost inherently complex, and evolution tends toward deterministic behavior in variable environments. SOC and HOT are two of many mechanisms that generate power laws (Table 3-1). If SOC is the intrinsic mechanism generating complexity, then power laws arise from the criticality of its internal structure, where event size is independent of its cause, and large events occur because connectivity reaches the system scale at the critical state. In contrast, for HOT, the power-law statistical characteristics are a manifestation of "robust, yet fragile." The author considers this to be the key aspect of complexity. The long tail reflects a trade-off in systems with high density and productivity, where internal variables are tuned to incur only small losses in the face of frequently occurring disturbances, but suffer large losses for rare events, even if such disturbances are small (Carlson and Doyle, 2002).