B. Scheuermann a,∗, K. Sob, M. Guntsch a, M.
Middendorf c, O. Diessel b, H. ElGindy b, H. Schmecka
(2004)
A review by Jacob Gillson
Outline
P-ACO Introduction
 Algorithm
 Implementation on FPGA
 Experimental Results
 Contributions
 Critique
 Conclusion
 Q&A

Optimization
The goal is to find the best possible
solution to a hard problem
 Many problems take an impractical
amount of time to solve exactly. Can be
solved using heuristics
 Combinatorial optimization attempts to
find an optimal object (solution) from a
finite set of objects

 Travelling Salesman Problem
 Minimum Spanning Tree
P-ACO Overview
Population-based Ant Colony Optimization
 Based on the path-finding abilities of ant
workers
 Uses a heuristic
approach to solving
combinational
optimization problems
 The ants use pheromone
trails to guide other workers back to the
food source

Implementing P-ACO
Each FPGA maintains a colony of virtual
“ants” in the form of solution generators
 The generators choose their solutions
based on pheromones made from past
solutions
 Each solution from each generator is
compared to previous solutions
 The most successful x solutions are
added to a solution matrix

P-ACO Architecture
Finding Solutions
1.
2.
3.
4.
5.
6.
7.
The pheromone matrix is initialized with
random values
The ant chooses next path based on the
pheromone strength at current node
Adds choice to a solution register
Repeats until all nodes have been used
Solution is compared to other ants
Best x solutions are added to population
queue
New pheromone matrix is generated
Choosing The Solution

The process continues until a stopping
condition has been met
 Set # of iterations
 Best solution hasn’t changed after # iterations
The population module returns the elitist
solution to the top module
 This is hopefully a near optimal solution
to the problem given

Experimental Results
The colony was implemented on a Xilinx
Virtex-II Pro
 Compared to an AMD uni-processor
system clocked to 1540 MHz
 Runs a SMTTP (Single Machine Total
Tardiness Problem)
 Both the problem size n (number of
nodes) and the colony size m (number of
ants) are varied during experimentation

Resource Use
(a) Uses a fixed number of ants m = 8
(b) Uses a fixed problem size n = 64
Resource Use
Due to increasing complexity, as the
problem size and colony size increases,
so must the on board resource use
 With a fixed colony, the size complexity
of LUTs and REGs increases at
~O(nlog(n))
 With fixed problem
size, complexity is
~O(n)

Time Comparisons
Time Comparisons
The hardware implementation is at least
1.8x faster than software
 Fixed problem size shows a large
increase in speedup as all the ants run
in parallel

 Is limited by the number of BRAM cells on
the FPGA

Fixed colony size shows a more modest
speed-up
 But only reliant on LUTs and REGs
Contributions
Proves that P-ACO and other
optimization algorithms can be
implemented on commercially available
FPGAs
 Can be modified to obtain near-optimal
solutions for most combinational
optimization problems
 Provides a large advantage over
software-only implementations

Critiques





Very in-depth and technical paper. Explains
all decisions in detail and is entirely
reproducible
Concepts become to technical at points
and can be hard to follow
Many alternate designs and improvements
suggested but were not acted upon
Hardware implementation is realistically
limited to very small problem sets
The heuristic information was disregarded
in the hardware implementation
Conclusion
P-ACO algorithm successfully
implemented on Virtex-II Pro FPGA
 Showed that ant colony optimization
was possible on commercial boards
 Provided at least 1.8x speedup during
experimentation over software
 Limited to small problem sizes due to
lack of resources

References

Virtex-II datasheet http://www.xilinx.com/support/documentation/data_sheets/ds083.pdf

Virtex-VII datasheet http://www.xilinx.com/support/documentation/data_sheets/ds180_7Serie
s_Overview.pdf

Combinatorial Optimization https://en.wikipedia.org/wiki/Combinatorial_optimization
FPGA implementation of population-based
ant colony optimization - B. Scheuermann et al.
 Ant Colony Optimization - V. Maniezzo et al.
 Ant diagram - https://en.wikipedia.org/wiki/Ant_colony_optimization

Questions?
Extra Slides
Generator Block Architecture
Population Block Architecture
Comparator Block Architecture