### Book

## Proceedings of DOOR 2016 Conference, special issue of CEUR Workshop Proceedings

A graph is König for a q-path if every its induced subgraph has the following property. The maximum number of pairwise vertex-disjoint induced paths each on q vertices is equal to the minimum number of vertices, such that removing all the vertices produces a graph having no an induced path on q vertices. In this paper, for every q>4, we describe all Konig graphs for a q-path obtained from forests and simple sycles by replacing some vertices into graphs not containing induced paths on q vertices.

In this paper, we consider a large class of hierarchical congestion population games. One can show that the equilibrium in a game of such type can be described as a minimum point in a properly constructed multi-level convex optimization problem. We propose a fast primal-dual composite gradient method and apply it to the problem, which is dual to the problem describing the equilibrium in the considered class of games. We prove that this method allows to find an approximate solution of the initial problem without increasing the complexity.

The volume is dedicated to Boris Mirkin on the occasion of his 70th birthday. In addition to his startling PhD results in abstract automata theory, Mirkin’s ground breaking contributions in various fields of decision making and data analysis have marked the fourth quarter of the 20th century and beyond. Mirkin has done pioneering work in group choice, clustering, data mining and knowledge discovery aimed at finding and describing non-trivial or hidden structures—first of all, clusters, orderings, and hierarchies—in multivariate and/or network data.

This volume contains a collection of papers reflecting recent developments rooted in Mirkin's fundamental contribution to the state-of-the-art in group choice, ordering, clustering, data mining, and knowledge discovery. Researchers, students, and software engineers will benefit from new knowledge discovery techniques and application directions.

Financial Decision Making Using Computational Intelligence covers all the recent developments in complex financial decision making through computational intelligence approaches. Computational intelligence has evolved rapidly in recent years and it is now one of the most active fields in operations research and computer science. The increasing complexity of financial problems and the enormous volume of financial data often make it difficult to apply traditional modeling and algorithmic procedures. In this context, the field of computational intelligence provides a wide range of useful techniques, including new modeling tools for decision making under risk and uncertainty, data mining techniques for analyzing complex data bases, and powerful algorithms for complex optimization problems.

This book constitutes the proceedings of the 9th International Conference on Discrete Optimization and Operations Research, DOOR 2016, held in Vladivostok, Russia, in September 2016.

The 39 full papers presented in this volume were carefully reviewed and selected from 181 submissions. They were organized in topical sections named: discrete optimization; scheduling problems; facility location; mathematical programming; mathematical economics and games; applications of operational research; and short communications.

This paper represents our solution for the problem of movement organization based on timetable optimization on the problematic part of railway system, i.e. single-track line. The approximate solution of this problem was founded on the heuristic method. The method gives the exact results in the case of limited amount of parameters and also can be used in the case with huge number of parameters due to reasonable computational time.

In this paper, we consider some scheduling problems on a single machine, where weighted or unweighted total tardiness has to be maximized in contrast to usual minimization problems. These problems are theoretically important and have also practical interpretations. For the weighted tardiness maximization problem, we present an NP-hardness proof and a pseudo-polynomial solution algorithm. For the unweighted total tardiness maximization problem with release dates, NP-hardness is proven. Complexity results for some other classical objective functions (e.g., the number of tardy jobs, total completion time) and various additional constraints (e.g., deadlines, weights and/or release dates of jobs may be given) are presented as well.

In this note, we consider a single machine scheduling problem with generalized total tardiness objective function. A pseudo-polynomial time solution algorithm is proposed for a special case of this problem. Moreover, we present a new graphical algorithm for another special case, which corresponds to the classical problem of minimizing the weighted number of tardy jobs on a single machine. The latter algorithm improves the complexity of an existing pseudo-polynomial algorithm by Lawler. Computational results are presented for both special cases considered.

Global Equilibrium Search (GES) is a meta-heuristic framework that shares similar ideas with the simulated annealing method. GES accumulates a compact set of information about the search space to generate promising initial solutions for the techniques that require a starting solution, such as the simple local search method. GES has been successful for many classic discrete optimization problems: the unconstrained quadratic programming problem, the maximum satisfiability problem, the max-cut problem, the multidimensional knapsack problem and the job-shop scheduling problem. GES provides state-of-the-art performance on all of these domains when compared to the current best known algorithms from the literature. GES algorithm can be naturally extended for parallel computing as it performs search simultaneously in distinct areas of the solution space. In this talk, we provide an overview of Global Equilibrium Search and discuss some successful applications.

A railway connection of two stations by a single railway track is usually found on branch lines of railway network and is very common in various manufacturing supply chains. Our paper isДля книг на иностранных языках concerned with a scheduling problem for two stations with a single railway track with one siding. On single-track railway sidings or passing loops are used to increase the capacity of the line. In our paper we developed exact optimization algorithm by analysing the structure of optimal schedule for the proposed model. The algorithm produces a schedule that completes all transportations between two stations at minimal time. We present algorithm to construct an optimal schedule in O(1) operations. Optimal schedule analyse allows the development of exact optimization algorithms with other models and objective functions, i.e. results can be generalized and used in future work for a number of regular objective functions, commonly used in scheduling.

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.

The problem of minimizing the root mean square deviation of a uniform string with clamped ends from an equilibrium position is investigated. It is assumed that the initial conditions are specified and the ends of the string are clamped. The Fourier method is used, which enables the control problem with a partial differential equation to be reduced to a control problem with a denumerable system of ordinary differential equations. For the optimal control problem in the l2 space obtained, it is proved that the optimal synthesis contains singular trajectories and chattering trajectories. For the initial problem of the optimal control of the vibrations of a string it is also proved that there is a unique solution for which the optimal control has a denumerable number of switchings in a finite time interval.

For a class of optimal control problems and Hamiltonian systems generated by these problems in the space *l *2, we prove the existence of extremals with a countable number of switchings on a finite time interval. The optimal synthesis that we construct in the space *l *2 forms a fiber bundle with piecewise smooth two-dimensional fibers consisting of extremals with a countable number of switchings over an infinite-dimensional basis of singular extremals.

This proceedings publication is a compilation of selected contributions from the “Third International Conference on the Dynamics of Information Systems” which took place at the University of Florida, Gainesville, February 16–18, 2011. The purpose of this conference was to bring together scientists and engineers from industry, government, and academia in order to exchange new discoveries and results in a broad range of topics relevant to the theory and practice of dynamics of information systems. Dynamics of Information Systems: Mathematical Foundation presents state-of-the art research and is intended for graduate students and researchers interested in some of the most recent discoveries in information theory and dynamical systems. Scientists in other disciplines may also benefit from the applications of new developments to their own area of study.

In this paper, we construct a new distribution corresponding to a real noble gas as well as the equation of state for it.