A talk given at CCWI 2016 presenting our work on using a sequence-based selection hyper-heuristic (MOSSHH) to optimise the multi-objective water distribution network design problem. The approach is demonstrated on the well-known New York Tunnels benchmark. The paper describing the work is available here: http://hdl.handle.net/10871/24217

1. Multi-objective Optimisation of a Water
Distribution Network with a Sequence-
based Selection Hyper-heuristic
David J. Walker, Ed Keedwell and Dragan Savić
Centre for Water Systems
College of Engineering, Mathematics and Physical Sciences
University of Exeter
D.J.Walker@exeter.ac.uk
November 2016

2. Introduction
• The water distribution network (WDN) design problem is well
understood – it can be solved using well understood
evolutionary algorithms
• Hyper-heuristics are nature-inspired algorithms that “optimise
the optimisers” – identify or generate a set of heuristics that
can be used to effectively optimise a problem
• They operate above the “domain barrier” – given a suitable
set of heuristics, a hyper-heuristic will identify which work
well for a specific instance of a problem without receiving
information about the problem beyond the fitness of a given
solution

3. Sequence-based Hyper-heuristic
• Sequence-based hyper-heuristic (SSHH) generates
“sequences” of low-level heuristics that applied to a candidate
solution should improve it
• Based on a hidden Markov model
– Transition probabilities: which low-level heuristic should be used next?
– Acceptance strategies: is the current sequence complete?
• Used in a variety of applications (including a single-objective
instance of the WDN design problem)
• Recently extended to the multi-objective domain

4. Multi-objective SSHH (MOSSHH)
• Uses Pareto dominance to
compare solutions
• Incorporates an elite archive
– the current approximation
of the Pareto front
• If the acceptance strategy is
met begin a new sequence
• If the solution was added to
the archive add the heuristic
to the sequence

5. WDN Design Problem
• New York Tunnels Problem
– Minimise cost
– Minimise the head deficit of
the network
– 16 pipe diameters for 21 pipes
– 20 nodes
• Optimise the two objectives
independently using
MOSSHH

6. Low-level Heuristics
• h1 change pipe – replace a single pipe with another diameter
• h2 swap – select two parameters and swap their diameters
• h3 change by one size – change the size of the pipe to the next
biggest or next smallest diameter
• h4 shuffle – select a group of 1-5 parameters and shuffle their
diameters
• h5 ruin and recreate – replace the entire chromosome with
one generated at random
• h6 archive parameter replacement – pick a pipe at random
and replace it with the corresponding parameter of a
randomly chosen member of the archive

7. Experimental Setup
• Runtime: 40,000 function evaluations
• Results compared using Hypervolume (dominated space
between the Pareto front approximation and a pre-determined
reference point)
• Compare to (1+1)—evolution strategies (each using one of the
low-level heuristics, except archive parameter replacement)
1. Generate a child from the current parent
2. Perturb the child using the given heuristic, evaluate the solution
according to the problem objectives and update the archive
3. If the parent does not dominate the child, replace the parent with the
child
4. Return to (1) and repeat

8. Summary Attainment Surfaces

9. Hypervolume results
• MOSSHH quickly takes the lead with a superior hypervolume –
superior to both recombination heuristics and perturbation
heuristics

10. Transition Probabilities and Acceptance Strategies
• Perturbation heuristics
preferred to ruin and recreate
• Change pipe by one size and
Archive parameter
replacement are the most
preferred heuristics

11. Conclusions & Future Work
Conclusions
• MOSSHH algorithm is able to effectively optimise the New York
Tunnels WDN design problem
• Online learning provides useful information about the
characteristics of the problem – which heuristics are most
useful?
Future Work
• More complicated Networks
• Investigate a wider range of heuristics and classes of heuristics
• Modifications to the algorithm’s reward mechanism