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### Ant Colony Optimization called

### Advantages and Disadvantages called

### Questions? called

ISE 410 Heuristics in OptimizationParticle Swarm Optimizationhttp://www.particleswarm.info/http://www.swarmintelligence.org/

Swarm Intelligence

- Origins in Artificial Life (Alife) Research
- ALife studies how computational techniques can help when studying biological phenomena
- ALife studies how biological techniques can help out with computational problems

- Two main Swarm Intelligence based methods
- Particle Swarm Optimization (PSO)
- Ant Colony Optimization(ACO)

Swarm Intelligence

- Swarm Intelligence (SI) is the property of a system whereby
the collective behaviors of (unsophisticated) agents

interacting locally with their environment

cause coherent functional global patterns to emerge.

- SI provides a basis with which it is possible to explore collective (or distributed) problem solving without centralized control or the provision of a global model.
- Leverage the power of complex adaptive systems to solve difficult non-linear stochastic problems

Swarm Intelligence

- Characteristics of a swarm:
- Distributed, no central control or data source;
- Limited communication
- No (explicit) model of the environment;
- Perception of environment (sensing)
- Ability to react to environment changes.

Swarm Intelligence

- Social interactions (locally shared knowledge) provides the basis for unguided problem solving
- The efficiency of the effort is related to but not dependent upon the degree or connectedness of the network and the number of interacting agents

Swarm Intelligence

- Robust exemplars of problem-solving in Nature
- Survival in stochastic hostile environment
- Social interaction creates complex behaviors
- Behaviors modified by dynamic environment.

- Emergent behavior observed in:
- Bacteria, immune system, ants, birds
- And other social animals

Particle Swarm Optimization(PSO)

- History
- Main idea and Algorithm
- Comparisons with GA
- Advantages and Disadvantages
- Implementation and Applications

Particle Swarm Optimization(PSO)

- History
- Main idea and Algorithm
- Comparisons with GA
- Advantages and Disadvantages
- Implementation and Applications

Origins and Inspiration of PSO

- Population based stochastic optimization technique inspired by social behaviour of bird flocking or fish schooling.
- Developed by Jim Kennedy, Bureau of Labor Statistics, U.S. Department of Labor and Russ Eberhart, Purdue University
- A concept for optimizing nonlinear functions using particle swarm methodology

- Inspired by simulation social behavior
- Related to bird flocking, fish schooling and swarming theory
- steer toward the center

- match neighbors’ velocity

- avoid collisions

- Suppose
- a group of birds are randomly searching food in an area.
- There is only one piece of food in the area being searched.
- All the birds do not know where the food is. But they know how far the food is in each iteration.
- So what's the best strategy to find the food? The effective one is to follow the bird which is nearest to the food.

What is PSO?

- In PSO, each single solution is a "bird" in the search space.
- Call it "particle".
- All of particles have fitness values
- which are evaluated by the fitness function to be optimized, and

- have velocities
- which direct the flying of the particles.

- The particles fly through the problem space by following the current optimum particles.

PSO Algorithm

- Initialize with randomly generated particles.
- Update through generations in search for optima
- Each particle has a velocity and position
- Update for each particle uses two “best” values.
- Pbest: best solution (fitness) it has achieved so far. (The fitness value is also stored.)
- Gbest: best value, obtained so far by any particle in the population.

- PSO algorithm is not only a tool for optimization, but also a tool for representing sociocognition of human and artificial agents, based on principles of social psychology.
- A PSO system combines local search methods with global search methods, attempting to balance exploration and exploitation.

- Population-based search procedure in which individuals called particles change their position (state) with time.
individual has position

& individual changes velocity

- Particles called fly around in a multidimensional search space. During flight, each particle adjusts its position according to its own experience, and according to the experience of a neighboring particle, making use of the best position encountered by itself and its neighbor.

Particle Swarm Optimization (PSO) Process called

- Initialize population in hyperspace
- Evaluate fitness of individual particles
- Modify velocities based on previous best and global (or neighborhood) best positions
- Terminate on some condition
- Go to step 2

PSO Algorithm called

- Update each particle, each generation
v[i]= v[i] + c1 * rand() * (pbest[i] - present[i]) + c2 * rand() * (gbest[i] - present[i])and

present[i] = persent[i] + v[i]

where c1 and c2 are learning factors (weights)

a

b

inertia called

Personal influence

Social (global) influence

PSO Algorithm- Update each particle, each generation
v[i] = v[i] + c1 * rand() * (pbest[i] - present[]) + c2 * rand() * (gbest[i] - present[i])and

present[i] = present[i] + v[i]

where c1 and c2 are learning factors (weights)

a

b

PSO Algorithm called

- Inertia Weight
d is the dimension, c1 and c2 are positive constants, rand1and rand2 are random numbers, and w is the inertia weight

Velocity can be limited to Vmax

Particle Swarm Optimization called (PSO)

- History
- Main idea and Algorithm
- Comparisons with GA
- Advantages and Disadvantages
- Implementation and Applications

PSO and GA Comparison called

- Commonalities
- PSO and GA are both population based stochastic optimization
- both algorithms start with a group of a randomly generated population,
- both have fitness values to evaluate the population.
- Both update the population and search for the optimium with random techniques.
- Both systems do not guarantee success.

PSO and GA Comparison called

- Differences
- PSO does not have genetic operators like crossover and mutation. Particles update themselves with the internal velocity.
- They also have memory, which is important to the algorithm.
- Particles do not die
- the information sharing mechanism in PSO is significantly different
- Info from best to others, GA population moves together

- PSO has a memory called
not “what” that best solution was, but “where” that best solution was

- Quality: population responds to quality factors pbest and gbest
- Diverse response: responses allocated between pbest and gbest
- Stability: population changes state only when gbest changes
- Adaptability: population does change state when gbest changes

- There is no selection in PSO called
all particles survive for the length of the run

PSO is the only EA that does not remove candidate population members

- In PSO, topology is constant; a neighbor is a neighbor
- Population size: Jim 10-20, Russ 30-40

PSO Velocity Update Equations called

- Global version vs Neighborhood version
change pgd to pld .

where pgd is the global best position

and pld is the neighboring best position

Inertia Weight called

- Large inertia weight facilitates global exploration, small on facilitates local exploration
- w must be selected carefully and/or decreased over the run
- Inertia weight seems to have attributes of temperature in simulated annealing

V called max

- An important parameter in PSO; typically the only one adjusted
- Clamps particles velocities on each dimension
- Determines “fineness” with which regions are searched
if too high, can fly past optimal solutions

if too low, can get stuck in local minima

PSO – Pros and Cons called

- Simple in concept
- Easy to implement
- Computationally efficient
- Application to combinatorial problems?
Binary PSO

Books and Website called

- Swarm Intelligence by Kennedy, Eberhart, and Shi, Morgan Kaufmann division of Academic Press, 2001.
http://www.engr.iupui.edu/~eberhart/web/PSObook.html

- http://www.particleswarm.net/
- http://web.ics.purdue.edu/~hux/PSO.shtml
- http://www.cis.syr.edu/~mohan/pso/
- http://clerc.maurice.free.fr/PSO/index.htm
- http://users.erols.com/cathyk/jimk.html

ACO Concept called

- Ants (blind) navigate from nest to food source
- Shortest path is discovered via pheromone trails
- each ant moves at random
- pheromone is deposited on path
- ants detect lead ant’s path, inclined to follow
- more pheromone on path increases probability of path being followed

ACO System called

- Virtual “trail” accumulated on path segments
- Starting node selected at random
- Path selected at random
- based on amount of “trail” present on possible paths from starting node
- higher probability for paths with more “trail”

- Ant reaches next node, selects next path
- Continues until reaches starting node
- Finished “tour” is a solution

ACO System, cont. called

- A completed tour is analyzed for optimality
- “Trail” amount adjusted to favor better solutions
- better solutions receive more trail
- worse solutions receive less trail
- higher probability of ant selecting path that is part of a better-performing tour

- New cycle is performed
- Repeated until most ants select the same tour on every cycle (convergence to solution)

ACO System, cont. called

- Often applied to TSP (Travelling Salesman Problem): shortest path between n nodes
- Algorithm in Pseudocode:
- Initialize Trail
- Do While (Stopping Criteria Not Satisfied) – Cycle Loop
- Do Until (Each Ant Completes a Tour) – Tour Loop
- Local Trail Update
- End Do
- Analyze Tours
- Global Trail Update

- End Do

ACO Background called

- Discrete optimization problems difficult to solve
- “Soft computing techniques” developed in past ten years:
- Genetic algorithms (GAs)
- based on natural selection and genetics

- Ant Colony Optimization (ACO)
- modeling ant colony behavior

- Genetic algorithms (GAs)

ACO Background, cont. called

- Developed by Marco Dorigo (Milan, Italy), and others in early 1990s
- Some common applications:
- Quadratic assignment problems
- Scheduling problems
- Dynamic routing problems in networks

- Theoretical analysis difficult
- algorithm is based on a series of random decisions (by artificial ants)
- probability of decisions changes on each iteration

What is ACO as Optimization Tech called

- Probabilistictechnique for solvingcomputational problems which can be reduced to finding good paths through graphs
- They are inspired by the behavior of ants in finding paths from the colonyto food.

Implementation called

- Can be used for both Static and Dynamic Combinatorial optimization problems
- Convergence is guaranteed, although the speed is unknown
- Value
- Solution

The Algorithm called

- Ant Colony Algorithms are typically use to solve minimum cost problems.
- We may usually have N nodes and A undirected arcs
- There are two working modes for the ants: either forwards or backwards.
- Pheromones are only deposited in backward mode. (so that we know how good the path was to update its trail)

The Algorithm called

- The ants memory allows them to retrace the path it has followed while searching for the destination node
- Before moving backward on their memorized path, they eliminate any loops from it. While moving backwards, the ants leave pheromones on the arcs they traversed.

The Algorithm called

- The ants evaluate the cost of the paths they have traversed.
- The shorter paths will receive a greater deposit of pheromones. An evaporation rule will be tied with the pheromones, which will reduce the chance for poor quality solutions.

The ACO Algorithm called

- At the beginning of the search process, a constant amount of pheromone is assigned to all arcs. When located at a node i an ant k uses the pheromone trail to compute the probability of choosing j as the next node:
- where is the neighborhood of ant k when in node i.

The Algorithm called

- When the arc (i,j) is traversed , the pheromone value changes as follows:
- By using this rule, the probability increases that forthcoming ants will use this arc.

The Algorithm called

- After each ant k has moved to the next node, the pheromones evaporate by the following equation to all the arcs:
- where is a parameter. An iteration is a complete cycle involving ants’ movement, pheromone evaporation, and pheromone deposit.

Steps for Solving a Problem by ACO called

- Represent the problem in the form of sets of components and transitions, or by a set of weighted graphs, on which ants can build solutions
- Define the meaning of the pheromone trails
- Define the heuristic preference for the ant while constructing a solution
- If possible implement a efficient local search algorithm for the problem to be solved.
- Choose a specific ACO algorithm and apply to problem being solved
- Tune the parameter of the ACO algorithm.

1 called

5

2

4

3

ApplicationsEfficiently Solves NP hard Problems

- Routing
- TSP (Traveling Salesman Problem)
- Vehicle Routing
- Sequential Ordering

- Assignment
- QAP (Quadratic Assignment Problem)
- Graph Coloring
- Generalized Assignment
- Frequency Assignment
- University Course Time Scheduling

Applications called

- Scheduling
- Job Shop
- Open Shop
- Flow Shop
- Total tardiness (weighted/non-weighted)
- Project Scheduling
- Group Shop

- Subset
- Multi-Knapsack
- Max Independent Set
- Redundancy Allocation
- Set Covering
- Weight Constrained Graph Tree partition
- Arc-weighted L cardinality tree
- Maximum Clique

Applications called

- Other
- Shortest Common Sequence
- Constraint Satisfaction
- 2D-HP protein folding
- Bin Packing

- Machine Learning
- Classification Rules
- Bayesian networks
- Fuzzy systems

- Network Routing
- Connection oriented network routing
- Connection network routing
- Optical network routing

Ant Colony Algorithms called

- Let um and lm be the number of ants that have used the upper and lower branches.
- The probability Pu(m) with which the (m+1)th ant chooses the upper branch is:

Traveling Salesperson Problem called

- Famous NP-Hard Optimization Problem
- Given a fully connected, symmetric G(V,E) with known edge costs, find the minimum cost tour.
- Artificial ants move from vertex to vertex to order to find the minimum cost tour using only pheromone mediated trails.

Traveling Salesperson Problem called

- The three main ideas that this ant colony algorithm has adopted from real ant colonies are:
- The ants have a probabilistic preference for paths with high pheromone value
- Shorter paths tend to have a higher rate of growth in pheromone value
- It uses an indirect communication system through pheromone in edges

Traveling Salesperson Problem called

- Ants select the next vertex based on a weighted probability function based on two factors:
- The number of edges and the associated cost
- The trail (pheromone) left behind by other ant agents.

- Each agent modifies the environment in two different ways :
- Local trail updating: As the ant moves between cities it updates the amount of pheromone on the edge
- Global trail updating: When all ants have completed a tour the ant that found the shortest route updates the edges in its path

Traveling Salesperson Problem called

- Local Updating is used to avoid very strong pheromone edges and hence increase exploration (and hopefully avoid locally optimal solutions).
- The Global Updating function gives the shortest path higher reinforcement by increasing the amount of pheromone on the edges of the shortest path.

Empirical Results called

- Compared Ant Colony Algorithm to standard algorithms and meta-heuristic algorithms on Oliver 30 – a 30 city TSP
- Standard: 2-Opt, Lin-Kernighan,
- Meta-Heuristics: Tabu Search and Simulated Annealing
- Conducted 10 replications of each algorithm and provided averaged results

Comparison to Standard Algorithms called

- Examined Solution Quality – not speed; in general, standard algorithms were significantly faster.
- Best ACO solution - 420

Comparison to Meta-Heuristic Algorithms called

- Meta-Heuristics are algorithms that can be applied to a variety of problems with a minimum of customization.
- Comparing ACO to other Meta-heuristics provides a “fair market” comparison (vice TSP specific algorithms).

Other Application Areas called

- Scheduling : Scheduling is a widespread problem of practical importance.
- Paul Forsyth & Anthony Wren, University of Leeds Computer Science department developed a bus driver scheduling application using ant colony concepts.

Advantages and Disadvantages called

- For TSPs (Traveling Salesman Problem), relatively efficient
- for a small number of nodes, TSPs can be solved by exhaustive search
- for a large number of nodes, TSPs are very computationally difficult to solve (NP-hard) – exponential time to convergence

- Performs better against other global optimization techniques for TSP (neural net, genetic algorithms, simulated annealing)
- Compared to GAs (Genetic Algorithms):
- retains memory of entire colony instead of previous generation only
- less affected by poor initial solutions (due to combination of random path selection and colony memory)

Advantages and Disadvantages, cont. called

- Can be used in dynamic applications (adapts to changes such as new distances, etc.)
- Has been applied to a wide variety of applications
- As with GAs, good choice for constrained discrete problems (not a gradient-based algorithm)

Advantages and Disadvantages, cont. called

- Theoretical analysis is difficult:
- Due to sequences of random decisions (not independent)
- Probability distribution changes by iteration
- Research is experimental rather than theoretical

- Convergence is guaranteed, but time to convergence uncertain

Advantages and Disadvantages, cont. called

- Tradeoffs in evaluating convergence:
- In NP-hard problems, need high-quality solutions quickly – focus is on quality of solutions
- In dynamic network routing problems, need solutions for changing conditions – focus is on effective evaluation of alternative paths

- Coding is somewhat complicated, not straightforward
- Pheromone “trail” additions/deletions, global updates and local updates
- Large number of different ACO algorithms to exploit different problem characteristics

Sources called

- Dorigo, Marco and Stützle, Thomas. (2004) Ant Colony Optimization, Cambridge, MA: The MIT Press.
- Dorigo, Marco, Gambardella, Luca M., Middendorf, Martin. (2002) “Guest Editorial,” IEEE Transactions on Evolutionary Computation, 6(4): 317-320.
- Thompson, Jonathan, “Ant Colony Optimization.” http://www.orsoc.org.uk/region/regional/swords/swords.ppt, accessed April 24, 2005.
- Camp, Charles V., Bichon, Barron, J. and Stovall, Scott P. (2005) “Design of Steel Frames Using Ant Colony Optimization,” Journal of Structural Engineeering, 131 (3):369-379.
- Fjalldal, Johann Bragi, “An Introduction to Ant Colony Algorithms.” http://www.informatics.sussex.ac.uk/research/nlp/gazdar/teach/atc/1999/web/johannf/ants.html, accessed April 24, 2005.

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