1. Some issues of design philosophy…
Basic Concepts
Some issues of design philosophy…

2. Memory-Processor Link and the von Neumann Bottleneck
Processor = CPU
Memory = hierarchy of caches, main memory, and bulk storage
Connection = address, control, data busses
Source of contention = bus traffic during the FETCH/EXECUTE cycle
8/23/2019
Copyright G.A. Tagliarini, PhD

3. Memory-Processor Link
Biological systems
Memory unit = processor
Large numbers of independent but interacting processors (circa 1010 neurons)
Small computational complexity
Massive connectivity (circa 1012 synapses)
Connections and state represent solutions
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Copyright G.A. Tagliarini, PhD

4. Common Characteristics of BIP
Parallel distributed processing
Rummelhart, McClelland and Hinton
Stigmergy
Feedback
Negative
Positive
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5. Copyright G.A. Tagliarini, PhD
Emergent Behavior
Adaptation
Learning
Supervised – a teacher instructs using a set of examples and the student generalizes to produce a representation
Unsupervised – examples are presented and a rule for forming group representations may be given
Evolution
Fitness/selective pressure
Crossover/recombination
Mutation
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6. Emergent Behavior (continued)
Self-organization
Cooperation
Coordination
Order arises without external intervention
Contrast with
Templates
Supervisors
Instructions/blueprints
Key question: How to formulate behaviors that give rise to self-organization?
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7. Example: How to Get Ants to Cooperate when Foraging
Suppose ants have been endowed with search behaviors and individual carrying capacity?
Allow the reward structure to be changeable
What behaviors or conditions would elicit cooperation?
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Copyright G.A. Tagliarini, PhD

8. A Search Problem: Satisfiability
Given
A set of m logic variables {p1, p2, …, pm}
A collection of n disjunctive clauses, e.g., ci = (p1 + p2’ + p5)
Place the clauses in conjunctive normal form (CNF) to create c = c1 c2 …ci …cn
Question
Is there an assignment of truth values that satisfies c?
“…satisfies c…” means “…for which c is true…”
See further:
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Copyright G.A. Tagliarini, PhD

9. An Optimization Problem: Maximum Satisfiability
Given
A set of m logic variables {p1, p2, …, pm}
A collection of n disjunctive clauses, e.g., ci = (p1 + p2’ + p5)
Place the clauses in conjunctive normal form (CNF) to create c = c1 c2 …ci …cn
Question
What is the assignment of truth values that maximizes the number of clauses satisfied?
8/23/2019
Copyright G.A. Tagliarini, PhD

10. An Optimization Problem: Weighted Maximum Satisfiability
Given
A set of m logic variables {p1, p2, …, pm}
A collection of n disjunctive clauses, e.g., ci = (p1 + p2’ + p5)
Each clause ci has a corresponding nonnegative weight wi
Question
What assignment of truth values maximizes the sum of the weights of the satisfied of clauses?
See further:
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Copyright G.A. Tagliarini, PhD

11. General Problem Solving Concerns
Goal
Representation
Constraints (How do I know I have a solution?)
“No free lunch theorem” (Wolpert and Macready, 1997)
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12. Copyright G.A. Tagliarini, PhD
Goal
Search
Find any solution; time to verify a solution bounded by some polynomial
E.g., queen placement, knight’s tour, map coloring, SAT
Leads to a Boolean assessment function
Optimize
Find solutions of a given “quality” (Maximize/Minimize)
E.g., TSP, weighted MAX-SAT, WTA, QAP, network flow
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13. Copyright G.A. Tagliarini, PhD
Representation
Choosing a feature space
Telling time: rectangular versus polar coordinates
Speech recognition: time domain versus frequency domain
Face recognition: templates, eigenfaces
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14. Copyright G.A. Tagliarini, PhD
Constraints
How do I know I have a solution?
Linear
Nonlinear
Inequality
Integer
Zero/One
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Copyright G.A. Tagliarini, PhD

15. Why Can’t I Just Learn One Problem Solving Method?
“No free lunch theorem” (Wolpert and Macready, 1997)
No single optimization method will perform best on all instances of all problems.
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Copyright G.A. Tagliarini, PhD

16. Two Conventional Benchmark Techniques
Hill Climbing
Simulated Annealing
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17. Hill Climbing (Minimization)
Assume:
Candidate solutions → s0 and s1 in a space S
Goal → g
Fitness function f such that f:S →R+
Repetition limit → L
Algorithm
Initialize s0 = s1, f0 = f(s0), f1 = f(s1), Counter
While (counter<L, f0>g)
s1 = mutate(s0), f1 = f(s1)
If f1 < f0 (Note: Improvements are always kept)
s0 = s1
f0 = f(s0)
Increment counter
8/23/2019
Copyright G.A. Tagliarini, PhD

18. Stochastic Hill Climbing (Minimization)
Assume:
Candidate solutions, goal, fitness function, solution space, and iteration limit as in basic hill climbing
A scaling parameter T
Algorithm
Initialize
While (counter<L, f0>g)
s1 = mutate(s0), f1 = f(s1)
Df = (f0 – f1)
If rand >1/ (1+exp(Df/T) (Note: Improvements are often kept)
s0 = s1
f0 = f(s0)
Increment counter
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19. Copyright G.A. Tagliarini, PhD
Simulated Annealing
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20. Evolutionary Algorithms
Based on analogy to evolution in biological systems
Key process elements
Fitness function
“Artificial selection”
Crossover and recombination
Mutation
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Copyright G.A. Tagliarini, PhD