Journal of Applied and Industrial Mathematics最新文献

A new dynamic bin packing problem relevant to cloud computing is considered. Thecreation time, deletion time, and required resources are known for each item (virtual machine).The containers (servers) have a NUMA architecture and specific rules for placing the machines.The servers are grouped into racks, and some machines form groups. Each group is divided intopartitions. Machines from different partitions cannot be placed on the same rack to ensure systemfault tolerance. The objective is to pack all the machines into the minimum number of racks overa given planning horizon. A two-stage algorithm is developed to solve the problem: an initialsolution is constructed, where some constraints may be violated, followed by iterativeimprovement using local search aimed at eliminating the violations. Using the proposed approach,an average deviation of 3.8% from the lower bound was achieved on open test cases.

We consider a stadium antenna deployment problem. The stadium is divided into sectors.Several antennas are assigned to each sector. Users should receive a signal of a certain qualityfrom antennas assigned to their sector. The problem is to choose locations of antennas, theirtypes, angles, and assignments to sectors to maximize three quality criteria: the mean signal tointerference ratio (SIR), the number of clients with good signal quality, and the assignmentconsistency. We use a simulation to compute the signal quality. We present a three-stage heuristicapproach to the problem. It uses a constructive heuristic, a local improvement procedure, anda decomposition-based MIP heuristic. We carry out numerical experiments on test instances with94 antennas of 7 types, 19 sectors, and 4426 clients. It is possible to improve the provided baselinesolutions in 2 h and obtain solutions comparable to running a metaheuristic package for 24 h.

The paper considers the transverse vibrations of two strings connected to each other at acertain point. A mathematical model of this process, based on the law of conservation ofmomentum, expressed in the form of an integro-differential equation is constructed. This equationconnects the deviations of the strings during vibrations with their characteristics such as density,tension, and sources of external forces. This approach can be considered as a development of themethod proposed by A.N. Tikhonov for the equation of string vibrations with nonsmooth data.For the case where the densities of the strings are constants, we set a nonclassical problem for theintegro-differential equation. In addition to the Cauchy data, the problem includes necessarymatching conditions. A theorem on the existence and uniqueness of a solution to the problem isproved, and explicit formulas are obtained for its solution.

In this paper, we present a time domain extension of our strategy on manipulatingradiated scalar Helmholtz fields and discuss two important applied scenarios, namely (1) creatingpersonal sound zones inside a bounded domain and (2) shielded localized communication. Ourstrategy is based on the authors’ previous works establishing the possibility and stability ofcontrolling acoustic fields using an array of almost non-radiating coupling sources and presents adetailed Fourier synthesis approach towards a time-domain effect. We require that the array ofacoustic sources creates the desired fields on the control regions while maintaining a zero fieldbeyond a larger circumscribed sphere. This paper recalls the main theoretical results then presentsthe underlying Fourier synthesis paradigm and show, through relevant simulations, theperformance of our strategy.

A warehouse goods placement problem is considered, where the aim is to minimize thetotal time of fulfillment of orders from a given list. NP-hardness of this problem even inthe simplest special case is proved. An ILP model is suggested for this problem. Two heuristicalgorithms are developed for solving this problem; their effectiveness is analyzed using randomlygenerated instances.

A coalition in a graph( G ) is a pair of disjoint nondominating subsets of its vertices( V_1, V_2 subset V(G) ) such that( V_1cup V_2 ) is a dominating set. In the coalition partition( pi (G)={ V_1,V_2,dots ,V_k } ), every nondominating set( V_i ) is included in some coalition and if( V_i ) is dominating, then it is a single-vertex set. A coalition partition of verticesof a graph( G ) generates a coalition graph( text {CG}(G,pi ) ) whose vertices correspond to the partition sets, while two vertices areadjacent if the corresponding sets form a coalition. It is well known that all simple cycles of ordergreater than three generate in total 26 coalition graphs of order at most six. A universal cyclegenerates all such graphs. It is shown that only the cycles( C_{3k} ),( k ge 5 ), are universal.

Rounding errors inevitably occur when performing calculations on a computer. In thispaper, we study the impact of these errors on the accuracy of calculating the correction in theKrylov subspace. An estimate of the accuracy of the calculated correction, expressed viaperturbations of the original data, is obtained.

The two-dimensional inverse problem of determining the kernel of an elasticity equation ofmemory type is studied. It is assumed that the coefficients of the equations depend on only onespatial variable. Applying the linearization principle, the inverse problem is reduced to anequivalent linear system of integral equations. The generalized principle of compressed maps isapplied to the latter in the space of continuous functions. The theorem of unique solvability isproved and an estimate of the stability of the solution to the inverse problem is obtained.

We propose a model for the formation of a resource region development program usinga special mechanism of public-private partnership. It is based on the clustering of fields and thecreation of a system of consortia of private investors jointly implementing projects for theconstruction of the necessary production infrastructure. The mechanism for achievinga compromise between the interests of the government and private investors uses the Stackelbergmodel, in which the government is the leader. It determines quotas of compensation of consortia’scosts for the implementation of infrastructure projects. The role of the follower is assigned to thesystem of consortia, which forms the program of infrastructure construction. The solution of thecorresponding bilevel mathematical programming problem allows us to form a targeteddevelopment plan. Its components are lists of infrastructure projects to be implemented inconsortia, as well as schedules of costs for shared construction of infrastructure and theircompensation from the budget for private investors. It is shown that the government problem is( Sigma ^P_2 )-hard and belongs to the class( Sigma ^P_2text {O} ) if the variables defining the transfer schedule take only integer values. A newstochastic approximate hybrid algorithm is developed to solve the two-level problem based onmetaheuristics using the ideas of coordinate descent. The results of calculations on real data forthe Zabaikalsky Krai allow us to formulate a set of practical recommendations on the formation ofthe mechanism of shared construction and the policy of compensation payments.

The forward and inverse problems are investigated for the quasilinear wave equation( square u -q(x)u^{2}-Kast u=0 ) where the kernel( K(x,t) ) is represented in the form( K(x,t)=p(x) K_0(t) ) with( p(x) ) being a continuous function. The inverse problem is devoted to thedetermination of the compact functions( q(x) ) and( p(x) ). Traces of the derivative with respect to( x ) of two solutions to the forward initial–boundary value problem related to twoarbitrary boundary data are given for( x=0 ) on the finite segment( [0,T] ) as an additional information for the solution to the inverse problem. Theconditions for the unique solvability of the forward problem are found. A local existence anduniqueness theorem is proved for the inverse problem.