Design algorithms mechanisms

Noam Nisan and Amir Ronen. Algorithmic mechanism design. Games and Economic Behavior, 35 166-196, 2001. 

AI methods may be used in various ways. The models may be used as a standalone application, e.g., in recent work on the design of microwave absorbers using particle swarm optimization (PSO).6 Alternatively, a computational tool, such as a finite element analysis or a quantum mechanical calculation, may be combined with an AI technique, such as an evolutionary algorithm. 

Fig. 8. Reconstruction of Young s modulus map in a simulated object. A 3D breast phantom was first designed in silico from MR anatomical images. Then a given 3D Young s modulus distribution was supposed with a 1 cm diameter stiff inclusion of 200 kPa (A). The forward problem was the computing of the 3D-displacement field using the partial differential equation [Eq. (5)]. The efficiency of the 3D reconstruction (inverse problem) of the mechanical properties from the 3D strain data corrupted with 15% added noise can be assessed in (B). The stiff inclusion is detected by the reconstruction algorithm, but its calculated Young s modulus is about 130 kPa instead of 200 kPa. From Ref. 44, reprinted by permission of Wiley-Liss, Inc., a subsidiary of John Wiley Sons, Inc.

The methods of simulated annealing (26), genetic algorithms (27), and taboo search (29) are three of the most popular stochastic optimization techniques, inspired by ideas from statistical mechanics, theory of evolutionary biology, and operations research, respectively. They are applicable to our current problem and have been used by researchers for computational library design. Because SA is employed in this chapter, a more-detailed description of the (generalized) SA is given below. 

We will delay a more detailed discussion of ensemble thermodynamics until Chapter 10 indeed, in this chapter we will make use of ensembles designed to render the operative equations as transparent as possible without much discussion of extensions to other ensembles. The point to be re-emphasized here is that the vast majority of experimental techniques measure molecular properties as averages - either time averages or ensemble averages or, most typically, both. Thus, we seek computational techniques capable of accurately reproducing these aspects of molecular behavior. In this chapter, we will consider Monte Carlo (MC) and molecular dynamics (MD) techniques for the simulation of real systems. Prior to discussing the details of computational algorithms, however, we need to briefly review some basic concepts from statistical mechanics. 

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