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

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 “optimisethe 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

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

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

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

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

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

Summary Attainment Surfaces

Hypervolume results

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

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

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