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Physical Optimization and Physical Computation -- CPS713 update from November 1992 Talk at Houston Keck Symposium

Given by Geoffrey C. Fox at CPSP713 Case studies in Computational Science on Spring Semester 1996. Foils prepared 15 March 1996

Physical Optimization applies a set of Optimization (minimization) methods motivated by physical processes to general optimization problems
These include simulated annealing, neural networks, deterministic annealing, simulated tempering and genetic algorithms
We look at general TSP, clustering in physical spaces, track finding, navigation, school class scheduling, Random field Ising Models and data decomposition and other computing optimization problems
We discuss when methods such as neural networks are effective

Table of Contents for Physical Optimization and Physical Computation -- CPS713 update from November 1992 Talk at Houston Keck Symposium

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1 Physical Optimization and Computation
2 Abstract of Physical Computation/Optimization Presentation
3 Physical Optimization and Computation Approaches and their Field of Origin
4 Optimization as used by Mother Nature and Physics
5 Some Overall Questions Relevant In Classisfying Optimization Problems and Methods
6 Two Types of Global Mininum and their relation to Local Minima
7 Characteristics of Some Basic Optimization Methods
8 Basic Philosophy of Physical Computation
9 Typical Formalism for Physical Optimization
10 Global and Local Minima in Temperature Dependent Free Energy
11 Comparison of Physical Optimization Methods
12 Sample Problem Illustrating Deterministic Annealing (Gurewitz and Rose)
13 A deterministic annealing approach to clustering (Gurewitz and Rose)
14 Details of Clustering Algorithm
15 Comparison of Isodata and Deterministic Annealing
16 Temperature Dependence of Deterministic Annealing
17 Temperature Lowered "below" cluster size
18 Phase Transitions in Physical Optimization Approach
19 TSP or Travelling Salesperson Problem
Classic NP-complete discrete optimization problem
20 Neural Net Compared to Elastic Net
21 Generalized Elastic Network
(Simic's derivation of Durbin and Willshaw's Elastic Net for TSP)
22 Terms in Neural and Elastic Net Energy Functions
23 General Structure of Physical Optimization
24 Comparison of Strategy in Elastic and Strategy
25 Physical Model Underlying Elastic Net
26 Typical TSP Solution with Elastic Net
27 Deterministic Annealing versus Multistate Neurons
28 Elastic Net for Navigation
29 Physical Optimization Formulation of Navigation Problems
30 Results of a Simple Two Vehicle Navigation Problem
31 Results of a Simple Four Vehicle Navigation Problem
32 Deterministic Annealing for Navigation
33 General Comments on Physical Optimization for Navigation
34 Physical Optimization in Computational Chemistry
35 Some Applications of Deterministic Annealing
36 Simulated Tempering -- a New Approach to Monte Carlo Optimization/Simulated Annealing
37 The Conventional Simulated Annealing and its Problems for Random Field Ising Models
38 Key Idea in The Tempering Approach
39 RFIM with Simulated Tempering
40 RFIM with Simulated Tempering
41 Some Scheduling Problems in NASA
42 Physical Computation Formulation of University Class Scheduling Problems
43 Hard Constraints in University Class Scheduling
44 Soft(er) Constraints
45 Soft(er) Constraints -- Continued
46 Approaches to Complexity
47 Computing as a set of Maps
48 Computing is "just" an optimization problem but what should we optimize?
49 General Issues for Physical Optimization in Computing
50 Physical Optimization in the Execution of Programs
51 Use of Physical Optimization in High Performance Fortran
52 Typical Example of Data Mapping Problem
53 Next slide is also page 26 of aus talk a
Features of Data to Processor Space Mapping:
54 Data Allocation Approaches
55 Computing as a Physics Problem
56 Mapping Problem: Criteria
57 Decomposition of an Arch onto 16 Processors in a Hypercube
58 Comparison of Parallel Data Decomposition Algorithms
59 Comparison of Parallel Data Decomposition Algorithms
60 MultiScale Methods in Parallel Data Decomposition
61 Mapping Times for Multiscale Algorithms
62 One can get Different Answers from Heuristics depending on Initial Labelling
63 Note: Lesson from 1990 CRPC workshop on TSP at Rice
64 An Irregular Decomposition for Fluid Flow
65 Comparison of Neural Networks for TSP and Data Decomposition
66 NP Completeness and Neural Networks In Summary
67 Optimization in Program Preparation / Code Generation
68 Track Finding Posed as a Problem
69 Track Finding when there are a lot of tracks
70 Neural Networks for Track Finding
71 Track Finding in Intermediate Cases
72 Original Data Set Used by Gurewitz and Rose
73 Results of Deterministic Annealing applied to Dirty Dataset
74 Conclusions on Physical Optimization for Track Finding
75 Conclusions in Physical Optimization
76 Goodbye! Many Choices - Which is best When?
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