25 May 2005 Exploiting phase transitions for fusion optimization problems
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Abstract
Many optimization problems that arise in multi-target tracking and fusion applications are known to be NP-complete, ie, believed to have worst-case complexities that are exponential in problem size. Recently, many such NP-complete problems have been shown to display threshold phenomena: it is possible to define a parameter such that the probability of a random problem instance having a solution jumps from 1 to 0 at a specific value of the parameter. It is also found that the amount of resources needed to solve the problem instance peaks at the transition point. Among the problems found to display this behavior are graph coloring (aka clustering, relevant for multi-target tracking), satisfiability (which occurs in resource allocation and planning problem), and the travelling salesperson problem. Physicists studying these problems have found intriguing similarities to phase transitions in spin models of statistical mechanics. Many methods previously used to analyze spin glasses have been used to explain some of the properties of the behavior at the transition point. It turns out that the transition happens because the fitness landscape of the problem changes as the parameter is varied. Some algorithms have been introduced that exploit this knowledge of the structure of the fitness landscape. In this paper, we review some of the experimental and theoretical work on threshold phenomena in optimization problems and indicate how optimization problems from tracking and sensor resource allocation could be analyzed using these results.
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Pontus Svenson, "Exploiting phase transitions for fusion optimization problems", Proc. SPIE 5809, Signal Processing, Sensor Fusion, and Target Recognition XIV, (25 May 2005); doi: 10.1117/12.602741; https://doi.org/10.1117/12.602741
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