Object Oriented Programming

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Object Oriented Programming

• Assignment Introduction

Dr. Mike Spann m.spann_at_bham.ac.uk
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Assignment Introduction

• Aims/Objectives
• To produce a C implementation of the ANT colony
  optimisation algorithm (ACO) and derivatives
• To apply to the Travelling Salesman Problem

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ANT algorithms
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ANT algorithms

• Ants are practically blind but they still manage
  to find their way to and from food. How do they
  do it?
• These observations inspired a new type of
  algorithm called ant algorithms (or ant systems)
• These algorithms are very new (Dorigo, 1996) and
  is still very much a research area where they are
  applied to the solution of hard discrete
  optimization problems

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ANT algorithms

• Ant systems are a population based approach. In
  this respect they is similar to genetic
  algorithms
• There is a population of ants, with each ant
  finding a solution and then communicating with
  the other ants
• Communication is not peer to peer but indirect
  with the use of pheromone

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ANT algorithms

• Real ants can find the shortest path to a food
  source by laying a pheromone trail
• The ants which take the shortest path, lay the
  largest amount of pheromone per unit time
• Positive feedback reinforces this behaviour and
  more ants take the shortest path resulting in
  more pheromone being laid

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Travelling Salesman Problem

• Classic discrete optimisation problem
• Salesman needs to visit all cities just once and
  return back home
• Find the best route (minimum route length)

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Travelling Salesman Problem

• The TSP is a NP-hard problem
• Essentially it means there is no polynomial time
  solution (complexity O(Nk) ) nor can a solution
  be verified in polynomial time
• We would need to check the solution over all
  possible routes to verify it
• One of many NP hard problems

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Travelling Salesman Problem

• N cities -gt (N-1)!/2 routes
• Small problem involving 29 cities in Western
  Sahara has 2x1028 routes!
• Currently TSPs involving 1000s cities are being
  studied
• You should restrict your algorithm to problems
  with lt1000 cities!
• The ACO algorithm has proved to be an effective
  approach with performances close to optimal

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Applying the ACO algorithm to the TSP

• ACO is an iterative algorithm
• During each iteration a number of ants are
  released to search the solution space
• Typically the number of ants number of cities
• Each ant makes a probabilistic choice about its
  route
• The higher the pheromone on an edge in the TSP
  graph, the higher the chance of selecting that
  edge

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Applying the ACO algorithm to the TSP

• dij distance between cities i and j
• tij the amount of pheremone between cities i and
  j
• ß determines influence of arc length over
  accumulated pheromone

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Applying the ACO algorithm to the TSP

• After each ant has completed its route, the
  route length for each ant is computed
• Assumes each ant has a local memory of where its
  been unlike biological ants!
• The pheromone on the edges of each route are
  updated according to the route length
• Also, it is assumed that a certain amount of
  pheromone evaporation takes place so that old
  routes are forgotten

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Applying the ACO algorithm to the TSP
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Improvements to the basic ACO algorithm

• The performance of the basic ACO is not great
• But definitely better than the Greedy algorithm!
• A number of improvements are possible which
  produce closer to optimal solutions
• These include
• Min-Max algorithm
• Rank order algorithm
• Elitist algorithm
• Non-probabilistic transition
• Also local search algorithms can refine the
  solution

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Improvements to the basic ACO algorithm

• Elitist algorithm
• Only update the pheromone on the currently
  optimum route
• The pheromone on all edges still undergoes
  evaporation
• Makes a big difference in performance over the
  basic ACO

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Improvements to the basic ACO algorithm

• Non probablistic transition
• Choose a non-probabilistic transition rule
  according to some annealing schedule
• Choose a random number 0ltqlt1 and some threshold
  parameter q0(t)
• qlt q0(t) probabilistic transition rule applied as
  before
• Otherwise, a deterministic transition rule is
  applied

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Improvements to the basic ACO algorithm

• q0(t) defines an annealing schedule
• q0(t) small for small t, the normal probabilistic
  transition rule is favoured
• Exploration
• q0(t) approaches 1 for increasing t, the
  deterministic transition rule is favoured
• Exploitation

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Improvements to the basic ACO algorithm

• Local search
• Exchanges edges to reduce the edge length
• k-opt algorithms
• Can impose a huge computational burden for kgt3
• I implemented a simple approach which requires a
  single comparison at each node

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Improvements to the basic ACO algorithm
a
e
c
d
b
f
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Assessment

• Programming report (deadlines are on the handout)
• Follow closely the marking pro-forma
• The report should contain discussions about
  object orientation, code re-useability, object
  interaction, algorithm performance and
  comparisons (close to optimal?)
• A formal design discussion is not expected but
  informal class/object diagrams and pseudo-code
  should be used

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Demo