# The use of Heuristics in the Design of GPS Networks - PowerPoint PPT Presentation

1 / 22

The use of Heuristics in the Design of GPS Networks. Peter Dare and Hussain Saleh School of Surveying University of East London Longbridge Road Dagenham, Essex, England Email: Peter@uel.ac.uk. Topics. Aim GPS Sessions and Schedule Problem description

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

The use of Heuristics in the Design of GPS Networks

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

## The use of Heuristics in the Design of GPS Networks

Peter Dare and Hussain Saleh

School of Surveying

University of East London

Dagenham, Essex, England

Email: Peter@uel.ac.uk

### Topics

• Aim

• GPS Sessions and Schedule

• Problem description

• Formulation as a Travelling Salesman Problem

• Examples

• Simulated Annealing

• Recommendations and conclusions

### Aim

• To develop a method to determine the cheapest schedule given the sessions to be observed.

### GPS Session

• For a GPS session 2 or more receivers observe simultaneously.

• For a network we have a number of sessions.

• With 2 receivers, 6 sessions required for this network.

• List of sessions is a schedule.

### GPS Session

• Sessions Required

• A B

• C B

• C D

• A D

• A C

• B D

### Sessions and Schedule

Schedule: ab-ac-dc

### Problem Description

• Given the list of sessions required, what is the optimum order of the sessions?

• Need to define cost.

• Cost can be defined, for example, by time of travel or shortest distance.

• As optimum sought we aim to minimise the total cost incurred.

### One receiver problem

• Classic Travelling Salesman Problem (TSP) of Operational Research (OR).

• Solved using Branch-and-Bound algorithm in Turbo Pascal to make use of pointers.

• Limitations: Only one receiver; starts and ends at a point.

• Developments: 2 or more receivers; start and end at non-survey point; allow for more than one observing day.

### Example with one receiver

Cost to move

between B and C

Cost Matrix:

A B C D

A 0 5 6 3

B 5 0 4 1

C 6 4 0 3

D 3 1 3 0

Least-cost Solution: A-D-B-C-A

Cost: 14 units

### Two Receiver Problem

• For 2 receivers, cost is maximum of individual movements if time is criteria.

• For example, cost of changing from session AC to BD is:

• A to B: 5 units C to D: 3 units

• Total cost: 5 units.

• If distance is criteria, sum costs (e.g., total 8 units).

### Two Receiver Problem

• Need to allow reversal of sessions e.g., AC to DB. Cost is:

• A to D: 3 units C to B: 4 units Total cost: 4 units.

• However, now need to prevent receiver swaps.

• For example, AC to CA.

• Prevented by setting cost to infinity.

### Two receiver problem: example

• Four sessions: AB-BC-CD-DA

### Solution to Two Receiver Problem

• Modifications needed to standard TSP algorithm.

• Solution (costing 9 units) is:

• Rec. 1 A A D B A

• Rec. 2 B D C C B

• However, first and last sessions are duplicates!

• Concept of base station needed.

### Further Developments

• To incorporate base, introduce dummy point.

• To allow observations over more than one working day:

• Extra dummy points.

• Connect dummy points.

### Example Survey - 1

• Cost matrix: 20*20 400 elements not shown here!

• Observed schedule:

• Rec. 1 Day 1: 2 2 1 Day 2: 2 3 5 6 6

• Rec. 2 Day 1: 3 4 4 Day 2: 1 4 4 5 3

• Total time: 180 minutes.

### Example Survey - 2

• Optimal schedule:

• Rec. 1 Day 1: 1 1 2 2 Day 2: 3 4 6 6

• Rec. 2 Day 1: 2 4 4 3 Day 2: 4 5 5 3

• Total time: 173 minutes.

• But large cost matrix needed: 20*20.

• To work with larger networks, approximate solutions (heuristics) needed.

### Heuristics

• Heuristics belong to the field of OR.

• A Heuristic attempts to find near-optimal solutions in a reasonable amount of time.

• The solution may be optimal but no guarantee.

• Popular heuristics are:

• Simulated annealing

• Tabu search

### Simulated Annealing (SA)

• ‘Annealing’ - the cooling of material in a heat bath.

• Solid material

• Heated past melting point

• Cooled back to a solid

• Structure of new solid depends upon cooling rate

### Application to Schedule Design - 1

No SA:

• ‘Guess’ a schedule.

• Change schedule to reduce cost.

• Stop when no more improvements can be made.

• Problem - local optimum often found - need global optimum.

Cost

Start

Global optimum

Local optimum

Iterations

### Application to Schedule Design - 2

With SA:

• ‘Guess’ a schedule.

• Change schedule to reduce cost.

• Allow some ‘uphill’ moves climb out of local optimum.

• Stop when no more improvements can be made global optimum (hopefully!)

### Recommendations and conclusions

• Optimal solution obtainable for small networks. Heuristics for large networks.

• Further development of non-optimal solutions:

• simulated annealing; tabu search; genetic algorithms.

• Incorporate with other aspects of network design.