Artificial intelligence in transport

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2020: FEFU and MIPT develop mathematical algorithms for solving transport problems and working with data

On April 28, 2020, it became known that scientists from the Far Eastern Federal University (FEFU), together with colleagues from the Moscow Institute of Physics and Technology (MIPT), are developing mathematical methods of convex optimization to accelerate the solution of the widest range of problems in economics, science, and many applied areas of human activity. Scientists reported their results in the book "Numerical Methods of Convex Optimization" by Springer.

According to the company, algorithms they are adaptive, that is, in the process of work distinguish , all the necessary parameters themselves are economical, and their work requires a relatively small amount of memory. It is advisable to use these algorithms, for example, to simulate transport flows, combat traffic jams and optimize freight routes, transport calculate fares, rank web pages, solve reverse problems when it is necessary to understand the reasons that gave rise to some consequences.

Non-smooth or convex optimization is based on the decomposition principle. This means that a large task can often be divided into many small ones, which are then linked to each other using a special coordinating task. For April 2020, this is relevant for working with big data. In the modern world, there is often a need to process, transmit data measured by gigabytes or more, as well as solve very complex problems on their basis. A naive direct approach, even using the fastest supercomputers, will take hundreds and thousands of years to solve such problems. Mathematics accelerates these processes so much that they acquire practical meaning. told Evgeny Nurminsky, Professor of the School of Natural Sciences of FEFU

The scientist said that for the classical problem of solving a system of linear equations, modern algorithms are many times more efficient than traditional methods, the labor intensity of which is approximately equal to the cube of the number of variables.

If there are 5 variables in the task, then you spend 125 operations and, say, 1 second of time to solve it. If there are 50 variables, then you will need 125 thousand operations and about 15 minutes. Imagine that the variables are 5000. It will take about 30 years to solve the problem in the traditional way. These methods will reduce this time to 40 seconds. Of course, you can spend tens of billions of rubles. or dollars, build a supercomputer the size of the Cheops pyramid and the power consumption of an icebreaker, which will still solve your problem in a day. But is it not better to allocate a thousandth of this amount for talented students who will do much more? Of course, the supercomputer will not hurt! supplemented by Evgeny Nurminsky, professor at the School of Natural Sciences of FEFU

Based on algorithms, you can create a way to process a "heavy" image so that at the output it requires 10 times less space than at the input, but retains 95 percent of the original properties. At the same time, such a picture cannot be distinguished by eye from the original one.

Speaking very mundane, optimization helps to dig less both literally and figuratively. For example, you need to decide how to dig an underpass connecting four points at an intersection so that you can get into any exit on the other side of the road from any entrance. It would seem that you need to draw a square and dig tunnels along its two diagonals. Mathematics tells us that for less labor, digging will have to be different. By designing very large mechanical structures, convex optimization methods can calculate how to obtain the smallest mass of these structures without losing strength. Another example is that convex optimization helps determine the optimal way to collect tolls on toll roads, leading to minimization of the total losses of network users on the road. explained Alexander Gasnikov, Associate Professor, Department of Mathematical Foundations of Management, Moscow Institute of Physics and Technology

The scientist noted that optimization problems are directly related to life, that is, nature itself often speaks the language of mathematics, and in order to understand its structure, it is necessary to solve the optimization problem.

In complex (non-convex) problems, however, in most cases we cannot get an ideal solution, but often this is not required. In practice, suboptimal results obtained with some error, but in a reasonable time, are often quite satisfied. This applies, for example, to many deep learning tasks. added Alexander Gasnikov, Associate Professor, Department of Mathematical Foundations of MIPT Management

The book "Numerical Methods of Convex Optimization" reveals traditional and more modern methods of convex optimization. The work is intended for students, faculty, academics and practitioners whose field of activity involves convex optimization. Scientists of FEFU and MIPT spoke about their methods of convex optimization in a separate chapter "Subgradient methods for solving the problem of convex optimization with low memory costs."

Publishers have assembled under one cover leading scientists who are developing the field of convex optimization. The book can be useful for anyone who wishes to obtain up-to-date information about the state of affairs and the tools that this field of mathematics contains.

Convex optimization algorithms can be applied to the correct construction of real world models, and in areas such as data collection, processing and transmission machine learning , and, artificial intelligence engineering, sciences economics and business, computer chemistry, physics and. medicine