̽��ֱ�� of Cambridge - Amanda Prorok

Improved approach to the ‘Travelling Salesperson Problem’ could improve logistics and transport sectors

sc604 — Tue, 26 Apr 2022 09:02:31 +0000

A notorious theoretical question that has puzzled researchers for 90 years, the Travelling Salesperson Problem also has real relevance to industry today. Essentially a question about how best to combine a set of tasks so that they can be performed in the fastest and most efficient way, finding good solutions to the problem can greatly help improve sectors such as transport and logistics.

Researchers from the ̽��ֱ�� of Cambridge have developed a hybrid, data-driven approach to the problem that not only produces high-quality solutions, but at a faster rate than other state-of-the-art approaches. Their results are presented this week at the International Conference on Learning Representations.

“ ̽��ֱ��importance of global logistics system was brought home to us during the pandemic,” said Dr Amanda Prorok from Cambridge’s Department of Computer Science and Technology, who led the research. “We’re highly reliant on this kind of infrastructure to be more efficient – and our solution could help with that as it targets both in-warehouse logistics, such as the routing of robots around a warehouse to collect goods for delivery, and those outside it, such as the routing of goods to people.”

̽��ֱ��Travelling Salesperson Problem involves a notional delivery driver who must call at a set number of cities – say, 20, 50 or 100 – that are connected by highways all in one journey. ̽��ֱ��challenge is to find the shortest possible route that calls at each destination once and to find it quickly.

“There are two key components to the problem. We want to order the stops, and we also want to know the cost, in time or distance, of going from one stop to another in that order,” said Prorok.

Twenty years ago the route from the warehouse to the destinations might have been fixed in advance. But with today’s availability of real-time traffic information, and the ability to send messages to the driver to add or remove delivery locations on the fly, the route may now change during the journey. But minimising its length or duration still remains key.

There’s often a cost attributed to waiting for an optimal solution or hard deadlines at which decisions must be taken. For example, the driver cannot wait for a new solution to be computed – they may miss their deliveries, or the traffic conditions may change again.

And that is why there is a need for general, anytime combinatorial optimisation algorithms that produce high-quality solutions under restricted computation time.

̽��ֱ��Cambridge-developed hybrid approach does this by combining a machine learning model that provides information about what the previous best routes have been, and a ‘metaheuristic’ tool that uses this information to assemble the new route.

“We want to find the good solutions faster,” said Ben Hudson, the paper’s first author. “If I’m a driver for a courier firm I have to decide what my next destination is going to be as I’m driving. I can’t afford to wait for a better solution. So that’s why in our research we focused on the trade-off between the computational time needed and the quality of the solution we got.”

To do this, Hudson came up with a Guided Local Search algorithm that could differentiate routes from one city to another that would be costly – in time or distance – from routes that would be less costly to include in the journey. This enabled the researchers to identify high-quality, rather than optimal, solutions quickly.

They did this by using a measure of what they call the ‘global regret’ – the cost of enforcing one decision relative to the cost of an optimal solution – of each city-to-city route in the Guided Local Search algorithm. They used machine learning to come up with an approximation of this ‘regret’.

“We already know the correct solution to a set of these problems,” said Hudson. “So we used some machine learning techniques to try and learn from those solutions. Based on that, we try to learn for a new problem – for a new set of cities in different locations – which paths between the cities are promising.

“When we have this information, it then feeds into the next part of the algorithm – the part that actually draws the routes. It uses that extra information about what the good paths may be to build a good solution much more quickly than it could have done otherwise.”

̽��ֱ��results they came up with were impressive. Their experiments demonstrated that the hybrid, data-driven approach converges to optimal solutions at a faster rate than three recent learning-based approaches for the Travelling Salesperson Problem.

In particular, when trying to solve the problem when it had a 100-city route, the Cambridge method reduced the mean optimality gap from 1.534% to 0.705%, a two-fold improvement. When generalising from the 20-city problem route to the 100-city problem route, the method reduced the optimality gap from 18.845% to 2.622%, a seven-fold improvement.

“A lot of logistics companies are using routing methods in real life,” said Hudson. “Our goal with this research is to improve such methods so that they produce better solutions – solutions that result in lower distances being travelled and therefore lower carbon emissions and reduced impact on the environment.”

Amanda Prorok is a Fellow of Pembroke College, Cambridge.

Reference:
Benjamin Hudson et al. ‘Graph Neural Network Guided Local Search for the Traveling Salesperson Problem.’ Paper presented at the International Conference on Learning Representations: https://iclr.cc/virtual/2022/calendar.

A new approach to solving the Travelling Salesperson Problem – one of the most difficult questions in computer science – significantly outperforms current approaches.

We’re highly reliant on this kind of infrastructure to be more efficient – and our solution could help with that

Amanda Prorok

Luis Alvarez

Courier checking parcel for delivery

̽��ֱ��text in this work is licensed under a Creative Commons Attribution 4.0 International License. Images, including our videos, are Copyright © ̽��ֱ�� of Cambridge and licensors/contributors as identified. All rights reserved. We make our image and video content available in a number of ways – as here, on our main website under its Terms and conditions, and on a range of channels including social media that permit your use and sharing of our content under their respective Terms.

Yes

Major European starting grants awarded

ta385 — Mon, 14 Sep 2020 11:30:00 +0000

Six Cambridge researchers are among the latest recipients of European Union awards given to early-career researchers.

Driverless cars working together can speed up traffic by 35 percent

sc604 — Sun, 19 May 2019 23:00:45 +0000

̽��ֱ��researchers, from the ̽��ֱ�� of Cambridge, programmed a small fleet of miniature robotic cars to drive on a multi-lane track and observed how the traffic flow changed when one of the cars stopped.

When the cars were not driving cooperatively, any cars behind the stopped car had to stop or slow down and wait for a gap in the traffic, as would typically happen on a real road. A queue quickly formed behind the stopped car and overall traffic flow was slowed.

However, when the cars were communicating with each other and driving cooperatively, as soon as one car stopped in the inner lane, it sent a signal to all the other cars. Cars in the outer lane that were in immediate proximity of the stopped car slowed down slightly so that cars in the inner lane were able to quickly pass the stopped car without having to stop or slow down significantly.

Additionally, when a human-controlled driver was put on the ‘road’ with the autonomous cars and moved around the track in an aggressive manner, the other cars were able to give way to avoid the aggressive driver, improving safety.

̽��ֱ��results, to be presented today at the International Conference on Robotics and Automation (ICRA) in Montréal, will be useful for studying how autonomous cars can communicate with each other, and with cars controlled by human drivers, on real roads in the future.

“Autonomous cars could fix a lot of different problems associated with driving in cities, but there needs to be a way for them to work together,” said co-author Michael He, an undergraduate student at St John’s College, who designed the algorithms for the experiment.

“If different automotive manufacturers are all developing their own autonomous cars with their own software, those cars all need to communicate with each other effectively,” said co-author Nicholas Hyldmar, an undergraduate student at Downing College, who designed much of the hardware for the experiment.

̽��ֱ��two students completed the work as part of an undergraduate research project in summer 2018, in the lab of Dr Amanda Prorok from Cambridge’s Department of Computer Science and Technology.

Many existing tests for multiple autonomous driverless cars are done digitally, or with scale models that are either too large or too expensive to carry out indoor experiments with fleets of cars.

Starting with inexpensive scale models of commercially-available vehicles with realistic steering systems, the Cambridge researchers adapted the cars with motion capture sensors and a Raspberry Pi, so that the cars could communicate via wifi.

They then adapted a lane-changing algorithm for autonomous cars to work with a fleet of cars. ̽��ֱ��original algorithm decides when a car should change lanes, based on whether it is safe to do so and whether changing lanes would help the car move through traffic more quickly. ̽��ֱ��adapted algorithm allows for cars to be packed more closely when changing lanes and adds a safety constraint to prevent crashes when speeds are low. A second algorithm allowed the cars to detect a projected car in front of it and make space.

They then tested the fleet in ‘egocentric’ and ‘cooperative’ driving modes, using both normal and aggressive driving behaviours, and observed how the fleet reacted to a stopped car. In the normal mode, cooperative driving improved traffic flow by 35% over egocentric driving, while for aggressive driving, the improvement was 45%. ̽��ֱ��researchers then tested how the fleet reacted to a single car controlled by a human via a joystick.

“Our design allows for a wide range of practical, low-cost experiments to be carried out on autonomous cars,” said Prorok. “For autonomous cars to be safely used on real roads, we need to know how they will interact with each other to improve safety and traffic flow.”

In future work, the researchers plan to use the fleet to test multi-car systems in more complex scenarios including roads with more lanes, intersections and a wider range of vehicle types.

Reference:
Nicholas Hyldmar, Yijun He, Amanda Prorok. ‘A Fleet of Miniature Cars for Experiments in Cooperative Driving.’ Paper presented at the International Conference on Robotics and Automation (ICRA 2019). Montréal, Canada.

A fleet of driverless cars working together to keep traffic moving smoothly can improve overall traffic flow by at least 35 percent, researchers have shown.

For autonomous cars to be safely used on real roads, we need to know how they will interact with each other

Amanda Prorok

Can cars talk to each other?

Yes