David Walker (University of Exeter) and Matthew Craven (University of Plymouth) Presented at EvoStar 2018 in Parma, Italy (05/04/2018) Paper: https://link.springer.com/chapter/10.1007/978-3-319-77538-8_38 Abstract: A visualisation method is presented that is intended to assist evolutionary algorithm users with the parametrisation of their algorithms. The visualisation method presents the convergence and diversity properties such that different parametrisations can be easily compared, and poor performing parameter sets can be easily identified and discarded. The efficacy of the visualisation is presented using a set of benchmark optimisation problems from the literature, as well as a benchmark water distribution network design problem. Results show that it is possible to observe the different performance caused by different parametrisations. Future work discusses the potential of this visualisation within an online tool that will enable a user to discard poor parametrisations as they execute to free up resources for better ones.

1. Toward the Online Visualisation of Algorithm
Performance for Parameter Selection
David J. Walker (University of Exeter)
Matthew J. Craven (University of Plymouth)
D.J.Walker@exeter.ac.uk
April 2018 – EvoAPPS
D. J. Walker & M. J. Craven Visualising Algorithm Performance April 2018 1 / 15

2. Introduction
Nature-inspired methods provide industry with a range of
optimisation tools that can be used for a plethora of tasks, however:
I Methods are often “black boxes” and unintuitive to non-experts
I Most nature-inspired methods are sensitive to their parameter settings
– finding the right settings is therefore vital
Visualisation
I “Lifts the lid” on the black box
I Visualisation task: to present the data generated by a nature-inspired
technique to a non-expert in an intuitive way
I Eventual goal: incorporate an online visualisation into a
nature-inspired framework so that non-experts can identify poor
parametrisations and release their resources to better
parametrisations
D. J. Walker & M. J. Craven Visualising Algorithm Performance April 2018 2 / 15

3. Introduction
I Optimise multi-objective problems (2 and 3 objectives)
I Problems are continuous and discrete
I “Parameter” refers to algorithm parameters (rather than decision
variables comprising a solution)
I Optimise using population-based methods and keep an archive of
solutions
D. J. Walker & M. J. Craven Visualising Algorithm Performance April 2018 3 / 15

4. Our Proposed Visualisation
I A dot represents a single solution
generated by an EA
I Each dot has a radius, an angle
and a colour:
I Radius: algorithm
parametrisation (describes the
type of mutation used herein)
I Angle: illustrates the distance
from the starting point
(hypervolume)
I Colour: indicates the crowding
distance of the solution
✓
r
O
D. J. Walker & M. J. Craven Visualising Algorithm Performance April 2018 4 / 15

5. Example: DTLZ2 (three objectives – GA)
GA using Pareto sorting (solutions are generated using crossover between
two randomly generated parents followed by an additive Gaussian mutation
(standard deviation 2 (0, 1))
I Solutions are initially scattered across the extent of the visualisation
I As they converge the solutions move toward the origin line
I Search population diversity reduces as the PF is located (archive
diversity is maintained)
D. J. Walker & M. J. Craven Visualising Algorithm Performance April 2018 5 / 15

6. Example: DTLZ2 (three objectives – GA)
I Blue solutions have a small
standard deviation (⇠ 0.1) and
have converged
I Red solutions have larger
standard deviations and have
not converged
D. J. Walker & M. J. Craven Visualising Algorithm Performance April 2018 6 / 15

7. Example: DTLZ2 (three objectives – random search)
At each generation the population is replaced by one generated at random
(uniformly)
I To begin with the solutions are scattered across the extent of the
visualisation
I As they converge the solutions move toward the origin line
I Solutions retain a reasonably high crowding distance
D. J. Walker & M. J. Craven Visualising Algorithm Performance April 2018 7 / 15

8. Example: DTLZ2 (three objectives – GA (average rank))
Algorithm operates as per the first GA but uses average rank to rank the
population for selection instead of nondominated sorting
I Very good convergence
I Population diversity collapses
much earlier
D. J. Walker & M. J. Craven Visualising Algorithm Performance April 2018 8 / 15

9. Example: DTLZ1 (two objectives)
I DTLZ1 comprises “deceptive fronts” –
local optima
I Two regions of parametrisations can be
seen
I Those populations optimised with a large
mutation are progressing faster than those
with small mutations
I Eventually all populations converge (after
50,000 function evaluations)
D. J. Walker & M. J. Craven Visualising Algorithm Performance April 2018 9 / 15

10. Water Distribution Network Design
I Design a water distribution
network by selecting pipe
diameters to simultaneously
minimise
I Network cost:
f1 =
PK
k=1 1.1d1.24
k ⇥ lk
I Head deficit: f2 =
PN
n=1
⇣
max
⇣
ˆhn hn
⌘
, 0
⌘
for K pipes connecting N nodes
I For the New York Tunnels
benchmark network K=20 and
N=21 with 16 pipe diameters
available
I Hydraulic properties modelled
with EPANET
D. J. Walker & M. J. Craven Visualising Algorithm Performance April 2018 10 / 15

11. Optimiser
The GA used for earlier examples is used
I Single-point crossover between two randomly chosen parents
I Mutation
I Pareto sorting selection
Creep mutation – a randomly chosen pipe’s diameter is replaced with
the next largest or smallest available diameter.
Shu✏e – a randomly selected block of diameters is randomly
reordered.
Ruin & recreate – the solution is replaced with an entirely new
chromosome.
Change pipe – a randomly chosen pipe’s diameter is replaced with a
randomly chosen available pipe.
Swap – two randomly chosen pipe diameters are swapped.
D. J. Walker & M. J. Craven Visualising Algorithm Performance April 2018 11 / 15

12. Results
D. J. Walker & M. J. Craven Visualising Algorithm Performance April 2018 12 / 15

13. Enhancing the visualisation – summary statistics
DTLZ2
New York Tunnels
Walker, DJ and Craven, MJ.
“Visualising the Operation of
Evoluationary Algorithms Optimising
Water Distribution Network Design
Problems”, Hydroinformatics
Conference (HIC 2018), accepted.
D. J. Walker & M. J. Craven Visualising Algorithm Performance April 2018 13 / 15

14. Future Work
1 Expand the range of nature-inspired techniques and problems
for demonstration to better characterise visualisations
I Demonstrate continuous and discrete problems with other
algorithms (e.g., PSO, DE. . . )
I Expand the range of problem features that can be identified
using the visualisation (e.g., non-dominated solutions. . . )
I Many-objective optimisation
2 Expand the range of indicators
I Incorporate decision space
I Better approaches for online evaluation – both for convergence
and diversity
3 “Towards” online visualisation
I Port the code to run on GPUs and incorporate it into a MOEA
framework
D. J. Walker & M. J. Craven Visualising Algorithm Performance April 2018 14 / 15

15. Summary
I Visualising algorithm performance provides non-expert
nature-inspired method users with valuable insight into algorithm
operation
I This method illustrates both convergence and diversity properties
of a range of GAs optimising continuous and discrete problems
I Known algorithmic characteristics have been identified but a
greater range of benchmark problems must be tested to expand
those characteristics the visualisation can show
I Further work is required to move the method towards online
visualisation
D. J. Walker & M. J. Craven Visualising Algorithm Performance April 2018 15 / 15