On an iterative procedure for solving a routing problem with constraints

The generalized precedence constrained traveling salesman problem is considered in the case when travel costs depend explicitly on the list of tasks that have not been performed (by the time of the travel). The original routing problem with dependent variables is represented in terms of an equivalent extremal problem with independent variables. An iterative method based on this representation is proposed for solving the original problem. The algorithm based on this method is implemented as a computer program. © 2013 Pleiades Publishing, Ltd

On Control Problem with Constraints of Asymptotic Character

For the double integrator with a discontinuous coefficient at the control, we obtain an attraction set—an asymptotic variant of reachable sets corresponding to constraints of asymptotic character—and study the latter’s properties. These constraints correspond to a control mode in the class of short-time pulses. An additional requirement is to fully consume the available energy resources. To calculate the attraction set numerically, an algorithm was developed and implemented. The results of computational experiments are presented

On reachable sets for one-pulse controls under constraints of asymptotic character

We study asymptotic versions of reachable sets of linear systems for two intuitive formalizations of onepulse controls given constraints of asymptotic character. The results are presented for the simplest example of linear control systems, the double integrator, though they admit a straightforward extension to a generic linear system. We suppose that the coefficient at the control is a piecewise continuous function. To illustrate the developed theoretical framework for both formalizations, we demonstrate examples of linear control systems, the double integrator, though they admit a straightforward extension to a generic linear system. We suppose that the coefficient at the control is a piecewise continuous function. To illustrate the developed theoretical framework for both formalizations, we demonstrate examples of attraction sets, asymptotic versions of reachable sets

The routing problems with optimization of the starting point: Dynamic programming

The extreme routing problem focused on engineering applications in mechanical engineering is considered. We mean the well-known task of tool controlling in the CNC sheet cutting machines. A mathematical model is presented which includes a system of megalopolises (nonempty finite sets) and cost functions depending on the list of tasks. Megalopolises are constructed on the basis of discretization of equidistant curves of part contours. The dependence on the list of tasks is connected with reasons associated with the dynamic constraints that arise in the process of task completion. Among all restrictions, the conditions of precedence are distinguished (earlier cutting of the inner contours and more earlier cutting of large parts). Rational consideration of the precedence conditions allows one to reduce the complexity of calculations when widely understood dynamic programming (DP) is used in the implementation that develops R. Bellman’s scheme. This approach makes it possible to solve the problem of optimizing complexes, which include the initial state (starting point), the method of numbering megalopolises in the order of their visits, and the specific trajectory of the process. For a problem complicated by the dependence of the terminal function on the initial state, a decomposition algorithm is used, which allows, in a substantial part of the procedure, the application of a single (for all initial states) DP scheme. The optimal algorithm based on DP is implemented as a program for PC; a computational experiment is conducted. © 2019 A.G. Chentsov, P.A. Chentsov.Russian Foundation for Basic Research, RFBR: 17–08–01385Funding. This research was supported by the Russian Foundation for Basic Research (projects no. 17–08–01385)

Galactic Twins of the Ring Nebula Around SN1987A and a Possible LBV-like Phase for Sk-69 202

Some core-collapse supernovae show clear signs of interaction with dense circumstellar material that often appears to be non-spherical. Circumstellar nebulae around supernova progenitors provide clues to the origin of that asymmetry in immediate pre-supernova evolution. Here I discuss outstanding questions about the formation of the ring nebula around SN1987A and some implications of similar ring nebulae around Galactic B supergiants. Several clues hint that SN1987A's nebula may have been ejected in an LBV-like event, rather than through interacting winds in a transition from a red supergiant to a blue supergiant.Comment: 2 pages, to appear in procedings of "Massive stars: fundamental parameters and circumstellar interactions", conference in honor of Virpi Niemela's 70th birthda

ON ROUTING PROBLEM WITH STARTING POINT OPTIMIZATION

One problem focused on engineering applications is considered. It is assumed that sequential visits to megacities have been implemented. After all visits have been made, it is required to return to the starting point (a more complex dependence on the starting point is also considered). But the last requirement is not strict: some weakening of the return condition is acceptable. Under these assumptions, it is required to optimize the choice of starting point, route, and specific trajectory. The well-known dynamic programming (DP) is used for the solution. But when using DP, significant difficulties arise associated with the dependence of the terminal component of the criterion on the starting point. Starting point enumeration is required. We consider the possibility of reducing the enumeration associated with applied variants of universal (relative to the starting point) dynamic programming. Of course, this approach requires some transformation of the problem

In memory of Arkady Viktorovich Kryazhimskiy (1949-2014)

The article is devoted to the description of Academician Arkady Kryazhimskiy's life path. The facts of the scientific biography of Acad. Kryazhimskiy are presented with the emphasis on his outstanding contribution into the theory of dynamic inversion, the theory of differential games, and control theory. His personal talents in different spheres are also marked out

On the characterisation of paired monotone metrics

Hasegawa and Petz introduced the notion of dual statistically monotone metrics. They also gave a characterisation theorem showing that Wigner-Yanase-Dyson metrics are the only members of the dual family. In this paper we show that the characterisation theorem holds true under more general hypotheses.Comment: 12 pages, to appear on Ann. Inst. Stat. Math.; v2: changes made to conform to accepted version, title changed as wel