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## Distributed Optimization on the Base of AMPL Modeling Language and Everest Platform

Optimization modeling in science and industry requires the use of state-of-the-art software and high-performance computing resources. A common problem faced by researchers is how to integrate related software and leverage available computing resources in a distributed environment. The paper presents an approach for solving this problem based on unifying remote access to optimization software via RESTful web services and using AMPL (A Mathematical Programming Language) to describe scenarios of computing with optimization models. This approach is implemented in AMPLX toolkit that enables modifying any AMPL script to solve problems by a pool of distributed solvers. The toolkit is based on Everest platform that is used to expose optimization tools as web services and run these tools across distributed resources. The proposed approach and AMPLX toolkit have been verified by a number of decomposition algorithms including branch-and-bound algorithm for a special nonlinear optimization problem.

In this paper, we consider the minimizing total weighted completion time in preemptive equal-length job with release dates scheduling problem on a single machine. This problem is known to be open. Here, we give some properties of optimal schedules for the problem and its special cases.

Consideration was given to a graphic realization of the method of dynamic programming. Its concept was demonstrated by the examples of the partition and knapsack problems. The proposed method was compared with the existing algorithms to solve these problems.

This chapter describes an economic model for independent job flow management in distributed computing environments with non-dedicated resources. The model is based on the concept of fair resource distribution between users and owners of computational nodes by means of economic mechanisms in a virtual organization. Scheduling is performed in cycles in accordance with dynamically updated schedules on local processor nodes. Schedule optimization is performed using dynamic programming methods using the set of criteria in accordance with the economic policy of the virtual organization.

This work presents slot selection algorithms in economic models for independent job batch scheduling in distributed computing with non-dedicated resources. Existing approaches towards resource co-allocation and multiprocessor job scheduling in economic models of distributed computing are based on search of time-slots in resource occupancy schedules. The sought time-slots must match requirements of necessary span, computational resource properties, and cost. Usually such scheduling methods consider only suited variant of time-slot set. This work discloses a scheduling scheme that features multi-variant search. Two algorithms of linear complexity for search of alternative variants are proposed and compared. Having several optional resource configurations for each job makes an opportunity to perform an optimization of execution of the whole batch of jobs and to increase overall efficiency of scheduling.

In this article we describe a system allowing companies to organize an efficient inventory management with 40 suppliers of different products. The system consists of four modules, each of which can be improved: demand planning, inventory management, procurement planning and KPI reporting. Described system was implemented in a real company, specializing on perishable products totaling over 600 SKUs. The system helped the company to increase its turnover by 7% while keeping the same level of services.

In this paper the authors analyze the optimization of public service delivery in Russia. The role of the optimization of administrative processes in the modernization of public administration is also considered; major activities aimed at the optimization of the public services delivery in 2010-2011 are described; some background information for decision making process is revealed; major methods of improving quality and accessibility of public services are analyzed; the key methodological approaches for the reengineering of public services and spheres of government regulations are presented. Basing on the researches conducted, the authors propose the ways of making the activities aimed at the optimization of public services effi cient.

A model for organizing cargo transportation between two node stations connected by a railway line which contains a certain number of intermediate stations is considered. The movement of cargo is in one direction. Such a situation may occur, for example, if one of the node stations is located in a region which produce raw material for manufacturing industry located in another region, and there is another node station. The organization of freight traﬃc is performed by means of a number of technologies. These technologies determine the rules for taking on cargo at the initial node station, the rules of interaction between neighboring stations, as well as the rule of distribution of cargo to the ﬁnal node stations. The process of cargo transportation is followed by the set rule of control. For such a model, one must determine possible modes of cargo transportation and describe their properties. This model is described by a ﬁnite-dimensional system of diﬀerential equations with nonlocal linear restrictions. The class of the solution satisfying nonlocal linear restrictions is extremely narrow. It results in the need for the “correct” extension of solutions of a system of diﬀerential equations to a class of quasi-solutions having the distinctive feature of gaps in a countable number of points. It was possible numerically using the Runge–Kutta method of the fourth order to build these quasi-solutions and determine their rate of growth. Let us note that in the technical plan the main complexity consisted in obtaining quasi-solutions satisfying the nonlocal linear restrictions. Furthermore, we investigated the dependence of quasi-solutions and, in particular, sizes of gaps (jumps) of solutions on a number of parameters of the model characterizing a rule of control, technologies for transportation of cargo and intensity of giving of cargo on a node station.

Event logs collected by modern information and technical systems usually contain enough data for automated process models discovery. A variety of algorithms was developed for process models discovery, conformance checking, log to model alignment, comparison of process models, etc., nevertheless a quick analysis of ad-hoc selected parts of a journal still have not get a full-fledged implementation. This paper describes an ROLAP-based method of multidimensional event logs storage for process mining. The result of the analysis of the journal is visualized as directed graph representing the union of all possible event sequences, ranked by their occurrence probability. Our implementation allows the analyst to discover process models for sublogs defined by ad-hoc selection of criteria and value of occurrence probability

The geographic information system (GIS) is based on the first and only Russian Imperial Census of 1897 and the First All-Union Census of the Soviet Union of 1926. The GIS features vector data (shapefiles) of allprovinces of the two states. For the 1897 census, there is information about linguistic, religious, and social estate groups. The part based on the 1926 census features nationality. Both shapefiles include information on gender, rural and urban population. The GIS allows for producing any necessary maps for individual studies of the period which require the administrative boundaries and demographic information.

It is well-known that the class of sets that can be computed by polynomial size circuits is equal to the class of sets that are polynomial time reducible to a sparse set. It is widely believed, but unfortunately up to now unproven, that there are sets in EXPNP, or even in EXP that are not computable by polynomial size circuits and hence are not reducible to a sparse set. In this paper we study this question in a more restricted setting: what is the computational complexity of sparse sets that are *selfreducible*? It follows from earlier work of Lozano and Torán (in: Mathematical systems theory, 1991) that EXPNP does not have sparse selfreducible hard sets. We define a natural version of selfreduction, tree-selfreducibility, and show that NEXP does not have sparse tree-selfreducible hard sets. We also construct an oracle relative to which all of EXP is reducible to a sparse tree-selfreducible set. These lower bounds are corollaries of more general results about the computational complexity of sparse sets that are selfreducible, and can be interpreted as super-polynomial circuit lower bounds for NEXP.