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BBC – The Future – The problem with mathematics that could stop the world

It's not easy to predict exactly what people want and when they want it. We looked for creatures, expecting the world to make quick decisions for our complex and varied contemporary problems.

Over the past few decades, researchers have developed a number of pretty effective mathematical solutions that can separate resources in various industries and scenarios so they can try to keep up with the everyday demands of our lives place. But when the allocation made at one time influences the subsequent allocations, the problem becomes dynamic, and the passing time must be considered as part of the equation. This casts a mathematical key in the works, asking these solutions to take into account the change and uncertainty of the real world.

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Such problems are collectively known as problems in the dynamic allocation of resources. They appear wherever you find a limited resource that needs to be assigned in real time.

Whether you are waiting for a taxi or delivery the next day, the list of dynamic resource allocation resources and their everyday applications is "almost infinite," according to Warren Powell, an engineer at Princeton University, who examines these problems from the 1980s.

But the dynamic resources for allocating resources are not concerned only with giving people what they want, when they want it. They will also be essential to tackle some of the most fundamental and complex issues in the world, including climate change, because they help us distribute the most scarce and impoverished resources on our planet in the most effective ways.

But first, let's look at a simpler example to see the problem of the dynamic resource allocation resource and making it so difficult to solve.

Imagine that you are preparing a cooked dinner for your four-member family. You decide on beef with all the remains, safe in the knowledge that it is a family of a family. But just as you want to serve, your daughter announces it is vegetarian, your affiliate texts say they are late, and your son tells you that a few "friends" are invited during dinner. Then, your dog runs away from the beef joints while you are desperately trying to discover how you will meet the needs of all these (quite honest) very hard and disobedient individuals.

They will be essential to tackle some of the most fundamental and complex issues in the world, including climate change

This is a trivial example of a dynamic resource allocation resource, but it shows some of the key challenges that researchers face when dealing with these problems. For starters, the parameters that affect demand are unexpectedly changing both in the short and long term. There is no way that you could accurately anticipate your daughter's new dietary requirements, the pleasant arrival of your partner or additional guests to your son while preparing this meal.

In the long run, the demand for meals in your house is also changing day by day. You may need to feed two or twenty people at each sitting. From meal to meal, you have no idea who you want to feed, whatever they want or when they want it. You can take educated assumptions based on previous experience, but this is not a robust method, because human nature and many other parameters that affect demand are unpredictable.

The activities of individuals in this scenario also affect the future state of the system. Every time you give a specific meal to a person, it changes the system. Removes both hungry persons and food from your kitchen.

"All [dynamic resource allocation] the examples need to deal with changing inputs and environments that are very dynamic and difficult to assess and predict, since the future burden is not statistically dependent on the current burden, "said Eiko Joneki, senior researcher who led the group of centric data systems at the Computer Lab at the University of Cambridge. "One change causes another change, and if you want to control the system with correct decisions, the future status of the system must be considered."

What's more, as more people or meal options come to your kitchen, things are complicated further. Now you have more ways to separate different meals from different people. This number of combinations extensively scales while adding more people or meals to the system.

This is exactly what might be faced by a large hospital, for example, when trying to feed all patients coming through his doors. The same goes for when you try to treat these patients. The drugs they need, which themselves have a limited shelf life and the equipment needed for diagnosis and treatment, will constantly change when different patients arrive. Scarce resources such as MRI scanners, doctors and nurses should also be allocated. In order to respond to this and prevent costs from getting out of control, hospital management can deploy mathematical models to help coordinate all of these things.

The problem is that most existing methods rely on historical data to make predictions. This method is not very good for such systems and can not handle even the smallest changes. If a change occurs, they return to the first place and start working on the solution again. Such problems quickly become calculated unbearable, even for quite a small number of people and resources – whether it is a meal or a MFA scanner.

Dynamic resource allocation resources also arise from a number of different scenarios and each has its own specific problems. For example, Yoneki examines the implications of these problems to help our computer systems and applications work faster and more efficiently.

"Modern computer systems are complex, and many configuration parameters need to be adjusted, including resource allocation, such as memory, capacity to compute, communication capability and any entry for the systems," she says. "Computer systems are dynamic and deal with ever-changing environments, which requires a dynamic control methodology."

Mobile phone networks and cloud computing rely on resolving these problems too

So, the computer on which you are reading this article almost certainly fights with some dynamic resources for resource allocation at this time. Mobile phone networks and cloud computing rely on resolving these problems too.

Extension firms also deal with dynamic resources to allocate resources to speed up deliveries. For example, the UPS developed its integrated system for optimization and navigation (Orion) on the way to optimize its routes using advanced algorithms. The company claims the solution saved 100 million miles a year – but other reports reveal that the system is struggling in complex urban environments.

Procurement chains are another "problem that will never disappear," Powell says, due to the complex nature of today's products. For example, if you want to build a standard smartphone, you need to coordinate hundreds of components around the world, all of which are collected for a specific purpose on the factory floor. "Supply chain disruptions are a major problem when we try to meet the needs of society," he adds.

Our energy supply is also more complex, relying on unpredictable renewable sources such as wind and solar energy. The results of these sources can fluctuate fluctuations, as it may require energy at a given time. Energy prices can also vary – electricity prices can lead to up to 50 times their average within five minutes.

In truth, you will struggle to find an industry that does not face the challenges of managing a dynamic resource for allocating resources in one form or another. "Electricity prices, the supply of parts in the supply chain, the time of travel, the failure of equipment and people's behavior are issues that I had to deal with," says Powell. "This problem is so rich that there are at least 15 different research communities working on this problem from different perspectives."

This is an important point. The diversity of dynamic resource allocation resources means that there should be standardization of the various computer techniques and methods used to deal with it. Powell is one of those trying to gather different communities working on dynamic resources for resource allocation. "Our approach does not replace the previous work," he says. "Instead, it brings all this together and helps to identify cross-fertilization opportunities."

The progress in machine learning offers new hopes to deal with the dynamic allocation of resources

A rich set of operational management tools have been very effective over the past few decades to cope with the rapid resource allocation resources, helping airlines in the world, logistics firms and road networks to increase their performance in different ways. However, "high dimensionality" – where many different parameters need to be taken into account – and uncertainty "remains a challenge," according to Powell.

The progress in machine learning offers new hopes to deal with the dynamic allocation of resources. Technical artificial intelligence called deep amplification learning allows an algorithm to learn what to do with interaction with the environment. The algorithm is designed to learn without human intervention by being rewarded for proper execution and punishment for improper execution. In an attempt to maximize rewards and minimize penalties, it can quickly reach an optimum state.

Deep reinforcement learning has recently enabled AlphaGo program from Google DeepMind to defeat the world champion in Go. The system began to know nothing about the Go game, and then played against it to train and optimize its performance. While games are an important proof of the concept of deepening learning techniques, learning how to play games is not the ultimate goal for such methods.

Yoneki and her team are working to provide a viable alternative to human-generated heuristics for performance tuning in computer systems using deep amplification learning. The computer system they develop can solve the problems of making decisions that were previously incredibly disobedient. It addresses the issue of computational complexity and can respond to changing parameters in real time.

Systems using this approach have already been used to optimize system performance in the areas, including resource management, optimization of device payments, and cooling of the data center. "Such applications are at the beginning and open up a new world of opportunity," Yoneki says.

A team of researchers at the launch of artificial intelligence called, based in Cambridge, UK, also uses its own machine learning approach to deal with dynamic resource problems. His algorithms provide an incentive to induce specific behavior in the system. In a context in the real world, this can be equivalent to introducing smart tolls to stimulate drivers to use certain roads and minimize traffic congestion and pollution.

Given that our populations continue to grow and our hunger for demand-driven services is increasing, the complexity of the dynamic resource allocation resources will only be intensified

But there is still a lot of work to be done in the area of ​​machine learning, says Yoneki.

"The use of learning enhancement will drive dynamic resource allocation problems forward, but requires a lot of data to build a strengthened learning model, and is still in an experimental phase, especially computer systems where more complex parameters need to be addressed than simple game cases, "she says. "Research on this subject is rapidly progressing".

We are still somehow flushing this unique set of problems, because today's techniques and computer resources are rapidly leaking out of steam when we are trying to cope with the complexity and accidental nature of the real world. But as our populations continue to grow and our hunger for demand-driven services grows, the complexity of the dynamic resource allocation resources and their impact on our daily lives will only intensify.

And if we do not begin to solve the dynamic resources for resource allocation now, we will not only struggle to eat a table at a table – the whole world can stand still.

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